Abstract

We propose a quantum critical detector (QCD) to amplify weak input signals. Our detector exploits a first-order discontinuous quantum-phase-transition and exhibits giant sensitivity (χN2) when biased at the critical point. We propose a model consisting of spins with long-range interactions coupled to a bosonic mode to describe the time-dynamics in the QCD. We numerically demonstrate dynamical features of the first order (discontinuous) quantum phase transition such as time-dependent quantum gain in a system with 80 interacting spins. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio during the time evolution of the device. Our work shows that engineering first order discontinuous quantum phase transitions can lead to a device application for metrology, weak signal amplification, and single photon detection.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
    [Crossref] [PubMed]
  2. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
    [Crossref] [PubMed]
  3. L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum semiclassical optics 4, S176 (2002).
    [Crossref]
  4. A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
    [Crossref]
  5. M. A. Nielsen and I. Chuang, “Quantum computation and quantum information,” (2002).
  6. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
    [Crossref]
  7. W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
    [Crossref]
  8. B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. i,” Phys. Rev. 160, 1076–1096 (1967).
    [Crossref]
  9. U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
    [Crossref]
  10. A. Roy and M. Devoret, “Introduction to parametric amplification of quantum signals with josephson circuits,” Comptes Rendus Physique 17, 740–755 (2016).
    [Crossref]
  11. M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039 (2000).
    [Crossref] [PubMed]
  12. M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
    [Crossref]
  13. G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
    [Crossref]
  14. D. A. Glaser, “Some effects of ionizing radiation on the formation of bubbles in liquids,” Phys. Rev. 87, 665 (1952).
    [Crossref]
  15. J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
    [Crossref] [PubMed]
  16. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
    [Crossref] [PubMed]
  17. R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
    [Crossref] [PubMed]
  18. S. Sachdev, Quantum phase transitions (Wiley Online Library, 2007).
  19. H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
    [Crossref] [PubMed]
  20. E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16, 407–466 (1961).
    [Crossref]
  21. H. J. Lipkin, N. Meshkov, and A. Glick, “Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory,” Nucl. Phys. 62, 188–198 (1965).
    [Crossref]
  22. N. Meshkov, A. Glick, and H. Lipkin, “Validity of many-body approximation methods for a solvable model:(ii). linearization procedures,” Nucl. Phys. 62, 199–210 (1965).
    [Crossref]
  23. A. Glick, H. Lipkin, and N. Meshkov, “Validity of many-body approximation methods for a solvable model:(iii). diagram summations,” Nucl. Phys. 62, 211–224 (1965).
    [Crossref]
  24. K. Hepp and E. H. Lieb, “On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model,” Annals Phys. 76, 360–404 (1973).
    [Crossref]
  25. Y. K. Wang and F. Hioe, “Phase transition in the dicke model of superradiance,” Phys. Rev. A 7, 831 (1973).
    [Crossref]
  26. C. F. Lee and N. F. Johnson, “First-order superradiant phase transitions in a multiqubit cavity system,” Phys. review letters 93, 083001 (2004).
    [Crossref]
  27. A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
    [Crossref]
  28. J. Vidal, R. Mosseri, and J. Dukelsky, “Entanglement in a first-order quantum phase transition,” Phys. Rev. A 69, 054101 (2004).
    [Crossref]
  29. L. Del Re, M. Fabrizio, and E. Tosatti, “Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition,” Phys. Rev. B 93, 125131 (2016).
    [Crossref]
  30. S. Gammelmark and K. Mølmer, “Phase transitions and heisenberg limited metrology in an ising chain interacting with a single-mode cavity field,” New J. Phys. 13, 053035 (2011).
    [Crossref]
  31. M. Raghunandan, J. Wrachtrup, and H. Weimer, “High-density quantum sensing with dissipative first order transitions,” Phys. Rev. Lett. 120, 150501 (2018).
    [Crossref] [PubMed]
  32. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
    [Crossref]
  33. V. S. Zapasskii, “Spin-noise spectroscopy: from proof of principle to applications,” Adv. Opt. Photonics 5, 131–168 (2013).
    [Crossref]
  34. P. Pfeuty, “The one-dimensional ising model with a transverse field,” ANNALS Phys. 57, 79–90 (1970).
    [Crossref]
  35. L.-P. Yang and Z. Jacob, Engineering Quantum Phase Transitions for Weak Signal Detection (2018). Under preparation.
  36. Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
    [Crossref]
  37. Y. Imry, “Finite-size rounding of a first-order phase transition,” Phys. Rev. B 21, 2042 (1980).
    [Crossref]
  38. M. Skotiniotis, P. Sekatski, and W. Dür, “Quantum metrology for the ising hamiltonian with transverse magnetic field,” New J. Phys. 17, 073032 (2015).
    [Crossref]
  39. J. Dziarmaga, “Dynamics of a quantum phase transition and relaxation to a steady state,” Adv. Phys. 59, 1063–1189 (2010).
    [Crossref]
  40. L.-P. Yang, H. X. Tang, and Z. Jacob, “Concept of quantum timing jitter and non-markovian limits in single-photon detection,” Phys. Rev. A 97, 013833 (2018).
    [Crossref]
  41. H. Yuen, “States that give the maximum signal-to-quantum noise ratio for a fixed energy,” Phys. Lett. A 56, 105–106 (1976).
    [Crossref]
  42. K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
    [Crossref] [PubMed]
  43. L.-P. Yang, Y. Li, and C. Sun, “Franck-condon effect in central spin system,” The Eur. Phys. J. D 66, 300 (2012).
    [Crossref]
  44. K. Husimi, “Some formal properties of the density matrix,” Proc. Physico-Mathematical Soc. Jpn. 3rd Ser. 22, 264–314 (1940).
  45. C. T. Lee, “q representation of the atomic coherent states and the origin of fluctuations in superfluorescence,” Phys. Rev. A 30, 3308–3310 (1984).
    [Crossref]
  46. J. Radcliffe, “Some properties of coherent spin states,” J. Phys. A: Gen. Phys. 4, 313 (1971).
    [Crossref]
  47. F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
    [Crossref]
  48. A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).
    [Crossref] [PubMed]
  49. B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).
  50. C. Schuck, W. H. Pernice, and H. X. Tang, “Waveguide integrated low noise nbtin nanowire single-photon detectors with milli-hz dark count rate,” Sci. Reports 3, 1893 (2013).
    [Crossref]
  51. B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
    [Crossref]

2018 (3)

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

M. Raghunandan, J. Wrachtrup, and H. Weimer, “High-density quantum sensing with dissipative first order transitions,” Phys. Rev. Lett. 120, 150501 (2018).
[Crossref] [PubMed]

L.-P. Yang, H. X. Tang, and Z. Jacob, “Concept of quantum timing jitter and non-markovian limits in single-photon detection,” Phys. Rev. A 97, 013833 (2018).
[Crossref]

2017 (2)

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

2016 (3)

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

A. Roy and M. Devoret, “Introduction to parametric amplification of quantum signals with josephson circuits,” Comptes Rendus Physique 17, 740–755 (2016).
[Crossref]

L. Del Re, M. Fabrizio, and E. Tosatti, “Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition,” Phys. Rev. B 93, 125131 (2016).
[Crossref]

2015 (1)

M. Skotiniotis, P. Sekatski, and W. Dür, “Quantum metrology for the ising hamiltonian with transverse magnetic field,” New J. Phys. 17, 073032 (2015).
[Crossref]

2014 (1)

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

2013 (2)

V. S. Zapasskii, “Spin-noise spectroscopy: from proof of principle to applications,” Adv. Opt. Photonics 5, 131–168 (2013).
[Crossref]

C. Schuck, W. H. Pernice, and H. X. Tang, “Waveguide integrated low noise nbtin nanowire single-photon detectors with milli-hz dark count rate,” Sci. Reports 3, 1893 (2013).
[Crossref]

2012 (2)

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

L.-P. Yang, Y. Li, and C. Sun, “Franck-condon effect in central spin system,” The Eur. Phys. J. D 66, 300 (2012).
[Crossref]

2011 (2)

S. Gammelmark and K. Mølmer, “Phase transitions and heisenberg limited metrology in an ising chain interacting with a single-mode cavity field,” New J. Phys. 13, 053035 (2011).
[Crossref]

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
[Crossref]

2010 (2)

J. Dziarmaga, “Dynamics of a quantum phase transition and relaxation to a steady state,” Adv. Phys. 59, 1063–1189 (2010).
[Crossref]

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
[Crossref] [PubMed]

2008 (1)

2006 (2)

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

2004 (4)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

J. Vidal, R. Mosseri, and J. Dukelsky, “Entanglement in a first-order quantum phase transition,” Phys. Rev. A 69, 054101 (2004).
[Crossref]

C. F. Lee and N. F. Johnson, “First-order superradiant phase transitions in a multiqubit cavity system,” Phys. review letters 93, 083001 (2004).
[Crossref]

2003 (1)

A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
[Crossref]

2002 (1)

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum semiclassical optics 4, S176 (2002).
[Crossref]

2001 (1)

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

2000 (1)

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039 (2000).
[Crossref] [PubMed]

1984 (1)

C. T. Lee, “q representation of the atomic coherent states and the origin of fluctuations in superfluorescence,” Phys. Rev. A 30, 3308–3310 (1984).
[Crossref]

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
[Crossref]

1980 (1)

Y. Imry, “Finite-size rounding of a first-order phase transition,” Phys. Rev. B 21, 2042 (1980).
[Crossref]

1976 (1)

H. Yuen, “States that give the maximum signal-to-quantum noise ratio for a fixed energy,” Phys. Lett. A 56, 105–106 (1976).
[Crossref]

1973 (2)

K. Hepp and E. H. Lieb, “On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model,” Annals Phys. 76, 360–404 (1973).
[Crossref]

Y. K. Wang and F. Hioe, “Phase transition in the dicke model of superradiance,” Phys. Rev. A 7, 831 (1973).
[Crossref]

1972 (1)

F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
[Crossref]

1971 (1)

J. Radcliffe, “Some properties of coherent spin states,” J. Phys. A: Gen. Phys. 4, 313 (1971).
[Crossref]

1970 (1)

P. Pfeuty, “The one-dimensional ising model with a transverse field,” ANNALS Phys. 57, 79–90 (1970).
[Crossref]

1967 (1)

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. i,” Phys. Rev. 160, 1076–1096 (1967).
[Crossref]

1965 (3)

H. J. Lipkin, N. Meshkov, and A. Glick, “Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory,” Nucl. Phys. 62, 188–198 (1965).
[Crossref]

N. Meshkov, A. Glick, and H. Lipkin, “Validity of many-body approximation methods for a solvable model:(ii). linearization procedures,” Nucl. Phys. 62, 199–210 (1965).
[Crossref]

A. Glick, H. Lipkin, and N. Meshkov, “Validity of many-body approximation methods for a solvable model:(iii). diagram summations,” Nucl. Phys. 62, 211–224 (1965).
[Crossref]

1961 (2)

E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16, 407–466 (1961).
[Crossref]

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
[Crossref]

1952 (1)

D. A. Glaser, “Some effects of ionizing radiation on the formation of bubbles in liquids,” Phys. Rev. 87, 665 (1952).
[Crossref]

1940 (1)

K. Husimi, “Some formal properties of the density matrix,” Proc. Physico-Mathematical Soc. Jpn. 3rd Ser. 22, 264–314 (1940).

Allmaras, J.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Altomare, F.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Amin, M. H.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Arecchi, F.

F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
[Crossref]

Autry, T.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Baragiola, B. Q.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Barrett, T.

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

Baumann, K.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
[Crossref] [PubMed]

Becker, P.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Berkley, A. J.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Bernien, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Bersin, E.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Boothby, K.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Brambilla, E.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum semiclassical optics 4, S176 (2002).
[Crossref]

Branczyk, A. M.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Brennecke, F.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
[Crossref] [PubMed]

Bunyk, P.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
[Crossref]

Chen, G.

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

Cheranovskii, V. O.

A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
[Crossref]

Choi, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Chuang, I.

M. A. Nielsen and I. Chuang, “Quantum computation and quantum information,” (2002).

Chulkova, G.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Colangelo, M.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Combes, J.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Cook, R. L.

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Courtens, E.

F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
[Crossref]

Crouch, G.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Dane, A.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

DeCola, P.

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

Del Re, L.

L. Del Re, M. Fabrizio, and E. Tosatti, “Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition,” Phys. Rev. B 93, 125131 (2016).
[Crossref]

Deng, C.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Devoret, M.

A. Roy and M. Devoret, “Introduction to parametric amplification of quantum signals with josephson circuits,” Comptes Rendus Physique 17, 740–755 (2016).
[Crossref]

Devoret, M. H.

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039 (2000).
[Crossref] [PubMed]

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
[Crossref]

Dmitriev, D. V.

A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
[Crossref]

Dubayah, R.

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

Dukelsky, J.

J. Vidal, R. Mosseri, and J. Dukelsky, “Entanglement in a first-order quantum phase transition,” Phys. Rev. A 69, 054101 (2004).
[Crossref]

Dür, W.

M. Skotiniotis, P. Sekatski, and W. Dür, “Quantum metrology for the ising hamiltonian with transverse magnetic field,” New J. Phys. 17, 073032 (2015).
[Crossref]

Dzardanov, A.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Dziarmaga, J.

J. Dziarmaga, “Dynamics of a quantum phase transition and relaxation to a steady state,” Adv. Phys. 59, 1063–1189 (2010).
[Crossref]

Eisaman, M.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
[Crossref]

Enderud, C.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Endres, M.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Esslinger, T.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
[Crossref] [PubMed]

Fabrizio, M.

L. Del Re, M. Fabrizio, and E. Tosatti, “Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition,” Phys. Rev. B 93, 125131 (2016).
[Crossref]

Fan, J.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
[Crossref]

Frasca, S.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Gammelmark, S.

S. Gammelmark and K. Mølmer, “Phase transitions and heisenberg limited metrology in an ising chain interacting with a single-mode cavity field,” New J. Phys. 13, 053035 (2011).
[Crossref]

Gatti, A.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum semiclassical optics 4, S176 (2002).
[Crossref]

Gavish, U.

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

Gerrits, T.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Gilmore, R.

F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Glaser, D. A.

D. A. Glaser, “Some effects of ionizing radiation on the formation of bubbles in liquids,” Phys. Rev. 87, 665 (1952).
[Crossref]

Glauber, R. J.

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. i,” Phys. Rev. 160, 1076–1096 (1967).
[Crossref]

Glick, A.

A. Glick, H. Lipkin, and N. Meshkov, “Validity of many-body approximation methods for a solvable model:(iii). diagram summations,” Nucl. Phys. 62, 211–224 (1965).
[Crossref]

H. J. Lipkin, N. Meshkov, and A. Glick, “Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory,” Nucl. Phys. 62, 188–198 (1965).
[Crossref]

N. Meshkov, A. Glick, and H. Lipkin, “Validity of many-body approximation methods for a solvable model:(ii). linearization procedures,” Nucl. Phys. 62, 199–210 (1965).
[Crossref]

Gol’Tsman, G.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Gong, Z.-X.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Gorshkov, A. V.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Greiner, M.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Guerlin, C.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
[Crossref] [PubMed]

Harris, R.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Hepp, K.

K. Hepp and E. H. Lieb, “On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model,” Annals Phys. 76, 360–404 (1973).
[Crossref]

Hess, P. W.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Hioe, F.

Y. K. Wang and F. Hioe, “Phase transition in the dicke model of superradiance,” Phys. Rev. A 7, 831 (1973).
[Crossref]

Hoskinson, E.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Huang, S.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Husimi, K.

K. Husimi, “Some formal properties of the density matrix,” Proc. Physico-Mathematical Soc. Jpn. 3rd Ser. 22, 264–314 (1940).

Imry, Y.

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

Y. Imry, “Finite-size rounding of a first-order phase transition,” Phys. Rev. B 21, 2042 (1980).
[Crossref]

Jacob, Z.

L.-P. Yang, H. X. Tang, and Z. Jacob, “Concept of quantum timing jitter and non-markovian limits in single-photon detection,” Phys. Rev. A 97, 013833 (2018).
[Crossref]

L.-P. Yang and Z. Jacob, Engineering Quantum Phase Transitions for Weak Signal Detection (2018). Under preparation.

Jia, S.

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

Johnson, M. W.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Johnson, N. F.

C. F. Lee and N. F. Johnson, “First-order superradiant phase transitions in a multiqubit cavity system,” Phys. review letters 93, 083001 (2004).
[Crossref]

Kaplan, H.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Keesling, A.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Korzh, B.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Krivnov, V. Y.

A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
[Crossref]

Kyprianidis, A.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Ladizinsky, E.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Ladizinsky, N.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Lanting, T.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Lee, C. F.

C. F. Lee and N. F. Johnson, “First-order superradiant phase transitions in a multiqubit cavity system,” Phys. review letters 93, 083001 (2004).
[Crossref]

Lee, C. T.

C. T. Lee, “q representation of the atomic coherent states and the origin of fluctuations in superfluorescence,” Phys. Rev. A 30, 3308–3310 (1984).
[Crossref]

Levine, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Li, R.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Li, Y.

L.-P. Yang, Y. Li, and C. Sun, “Franck-condon effect in central spin system,” The Eur. Phys. J. D 66, 300 (2012).
[Crossref]

Liang, J.-Q.

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

Lieb, E.

E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16, 407–466 (1961).
[Crossref]

Lieb, E. H.

K. Hepp and E. H. Lieb, “On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model,” Annals Phys. 76, 360–404 (1973).
[Crossref]

Lipatov, A.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Lipkin, H.

A. Glick, H. Lipkin, and N. Meshkov, “Validity of many-body approximation methods for a solvable model:(iii). diagram summations,” Nucl. Phys. 62, 211–224 (1965).
[Crossref]

N. Meshkov, A. Glick, and H. Lipkin, “Validity of many-body approximation methods for a solvable model:(ii). linearization procedures,” Nucl. Phys. 62, 199–210 (1965).
[Crossref]

Lipkin, H. J.

H. J. Lipkin, N. Meshkov, and A. Glick, “Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory,” Nucl. Phys. 62, 188–198 (1965).
[Crossref]

Lita, A. E.

Liu, X. F.

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Louisell, W. H.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Lugiato, L.

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum semiclassical optics 4, S176 (2002).
[Crossref]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Mattis, D.

E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16, 407–466 (1961).
[Crossref]

Medina, T.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Meshkov, N.

H. J. Lipkin, N. Meshkov, and A. Glick, “Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory,” Nucl. Phys. 62, 188–198 (1965).
[Crossref]

N. Meshkov, A. Glick, and H. Lipkin, “Validity of many-body approximation methods for a solvable model:(ii). linearization procedures,” Nucl. Phys. 62, 199–210 (1965).
[Crossref]

A. Glick, H. Lipkin, and N. Meshkov, “Validity of many-body approximation methods for a solvable model:(iii). diagram summations,” Nucl. Phys. 62, 211–224 (1965).
[Crossref]

Migdall, A.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
[Crossref]

Miller, A. J.

Molavi, R.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Mollow, B. R.

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. i,” Phys. Rev. 160, 1076–1096 (1967).
[Crossref]

Mølmer, K.

S. Gammelmark and K. Mølmer, “Phase transitions and heisenberg limited metrology in an ising chain interacting with a single-mode cavity field,” New J. Phys. 13, 053035 (2011).
[Crossref]

Monroe, C.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Mosseri, R.

J. Vidal, R. Mosseri, and J. Dukelsky, “Entanglement in a first-order quantum phase transition,” Phys. Rev. A 69, 054101 (2004).
[Crossref]

Nam, S. W.

Neufeld, R.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Nielsen, M. A.

M. A. Nielsen and I. Chuang, “Quantum computation and quantum information,” (2002).

Nori, F.

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

Oh, T.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Okunev, O.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Omran, A.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Ovchinnikov, A. A.

A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
[Crossref]

Pagano, G.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Pavlov, I.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Perminov, I.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Pernice, W. H.

C. Schuck, W. H. Pernice, and H. X. Tang, “Waveguide integrated low noise nbtin nanowire single-photon detectors with milli-hz dark count rate,” Sci. Reports 3, 1893 (2013).
[Crossref]

Pfeuty, P.

P. Pfeuty, “The one-dimensional ising model with a transverse field,” ANNALS Phys. 57, 79–90 (1970).
[Crossref]

Pichler, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Polyakov, S. V.

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
[Crossref]

Poulin-Lamarre, G.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Quan, H. T.

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

Radcliffe, J.

J. Radcliffe, “Some properties of coherent spin states,” J. Phys. A: Gen. Phys. 4, 313 (1971).
[Crossref]

Raghunandan, M.

M. Raghunandan, J. Wrachtrup, and H. Weimer, “High-density quantum sensing with dissipative first order transitions,” Phys. Rev. Lett. 120, 150501 (2018).
[Crossref] [PubMed]

Reis, M.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Rich, C.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Roy, A.

A. Roy and M. Devoret, “Introduction to parametric amplification of quantum signals with josephson circuits,” Comptes Rendus Physique 17, 740–755 (2016).
[Crossref]

Sachdev, S.

S. Sachdev, Quantum phase transitions (Wiley Online Library, 2007).

Sato, Y.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Schoelkopf, R. J.

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039 (2000).
[Crossref] [PubMed]

Schuck, C.

C. Schuck, W. H. Pernice, and H. X. Tang, “Waveguide integrated low noise nbtin nanowire single-photon detectors with milli-hz dark count rate,” Sci. Reports 3, 1893 (2013).
[Crossref]

Schultz, T.

E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16, 407–466 (1961).
[Crossref]

Schwartz, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Sekatski, P.

M. Skotiniotis, P. Sekatski, and W. Dür, “Quantum metrology for the ising hamiltonian with transverse magnetic field,” New J. Phys. 17, 073032 (2015).
[Crossref]

Semenov, A.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Skotiniotis, M.

M. Skotiniotis, P. Sekatski, and W. Dür, “Quantum metrology for the ising hamiltonian with transverse magnetic field,” New J. Phys. 17, 073032 (2015).
[Crossref]

Smirnov, A.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Smirnov, K.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Sobolewski, R.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Song, Z.

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

Sun, C.

L.-P. Yang, Y. Li, and C. Sun, “Franck-condon effect in central spin system,” The Eur. Phys. J. D 66, 300 (2012).
[Crossref]

Sun, C. P.

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

Swatantran, A.

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

Swenson, L.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Tang, H.

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

Tang, H. X.

L.-P. Yang, H. X. Tang, and Z. Jacob, “Concept of quantum timing jitter and non-markovian limits in single-photon detection,” Phys. Rev. A 97, 013833 (2018).
[Crossref]

C. Schuck, W. H. Pernice, and H. X. Tang, “Waveguide integrated low noise nbtin nanowire single-photon detectors with milli-hz dark count rate,” Sci. Reports 3, 1893 (2013).
[Crossref]

Thomas, H.

F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
[Crossref]

Tosatti, E.

L. Del Re, M. Fabrizio, and E. Tosatti, “Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition,” Phys. Rev. B 93, 125131 (2016).
[Crossref]

Tsai, N.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Vidal, J.

J. Vidal, R. Mosseri, and J. Dukelsky, “Entanglement in a first-order quantum phase transition,” Phys. Rev. A 69, 054101 (2004).
[Crossref]

Volkmann, M.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Voronov, B.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Wang, Y. K.

Y. K. Wang and F. Hioe, “Phase transition in the dicke model of superradiance,” Phys. Rev. A 7, 831 (1973).
[Crossref]

Weimer, H.

M. Raghunandan, J. Wrachtrup, and H. Weimer, “High-density quantum sensing with dissipative first order transitions,” Phys. Rev. Lett. 120, 150501 (2018).
[Crossref] [PubMed]

Whittaker, J.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Williams, C.

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Wrachtrup, J.

M. Raghunandan, J. Wrachtrup, and H. Weimer, “High-density quantum sensing with dissipative first order transitions,” Phys. Rev. Lett. 120, 150501 (2018).
[Crossref] [PubMed]

Yang, L.-P.

L.-P. Yang, H. X. Tang, and Z. Jacob, “Concept of quantum timing jitter and non-markovian limits in single-photon detection,” Phys. Rev. A 97, 013833 (2018).
[Crossref]

L.-P. Yang, Y. Li, and C. Sun, “Franck-condon effect in central spin system,” The Eur. Phys. J. D 66, 300 (2012).
[Crossref]

L.-P. Yang and Z. Jacob, Engineering Quantum Phase Transitions for Weak Signal Detection (2018). Under preparation.

Yao, J.

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Yu, L.

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

Yuen, H.

H. Yuen, “States that give the maximum signal-to-quantum noise ratio for a fixed energy,” Phys. Lett. A 56, 105–106 (1976).
[Crossref]

Yurke, B.

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

Zanardi, P.

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

Zapasskii, V. S.

V. S. Zapasskii, “Spin-noise spectroscopy: from proof of principle to applications,” Adv. Opt. Photonics 5, 131–168 (2013).
[Crossref]

Zhang, J.

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

Zhao, Q.

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

Zibrov, A. S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

V. S. Zapasskii, “Spin-noise spectroscopy: from proof of principle to applications,” Adv. Opt. Photonics 5, 131–168 (2013).
[Crossref]

Adv. Phys. (1)

J. Dziarmaga, “Dynamics of a quantum phase transition and relaxation to a steady state,” Adv. Phys. 59, 1063–1189 (2010).
[Crossref]

ANNALS Phys. (1)

P. Pfeuty, “The one-dimensional ising model with a transverse field,” ANNALS Phys. 57, 79–90 (1970).
[Crossref]

E. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys. 16, 407–466 (1961).
[Crossref]

K. Hepp and E. H. Lieb, “On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model,” Annals Phys. 76, 360–404 (1973).
[Crossref]

Appl. Phys. Lett. (1)

G. Gol’Tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, “Picosecond superconducting single-photon optical detector,” Appl. Phys. Lett. 79, 705–707 (2001).
[Crossref]

Comptes Rendus Physique (1)

A. Roy and M. Devoret, “Introduction to parametric amplification of quantum signals with josephson circuits,” Comptes Rendus Physique 17, 740–755 (2016).
[Crossref]

J. Opt. B: Quantum semiclassical optics (1)

L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B: Quantum semiclassical optics 4, S176 (2002).
[Crossref]

J. Phys. A: Gen. Phys. (1)

J. Radcliffe, “Some properties of coherent spin states,” J. Phys. A: Gen. Phys. 4, 313 (1971).
[Crossref]

Nature (4)

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301 (2010).
[Crossref] [PubMed]

M. H. Devoret and R. J. Schoelkopf, “Amplifying quantum signals with the single-electron transistor,” Nature 406, 1039 (2000).
[Crossref] [PubMed]

J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601 (2017).
[Crossref] [PubMed]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, and et al., “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579 (2017).
[Crossref] [PubMed]

New J. Phys. (2)

S. Gammelmark and K. Mølmer, “Phase transitions and heisenberg limited metrology in an ising chain interacting with a single-mode cavity field,” New J. Phys. 13, 053035 (2011).
[Crossref]

M. Skotiniotis, P. Sekatski, and W. Dür, “Quantum metrology for the ising hamiltonian with transverse magnetic field,” New J. Phys. 17, 073032 (2015).
[Crossref]

Nucl. Phys. (3)

H. J. Lipkin, N. Meshkov, and A. Glick, “Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory,” Nucl. Phys. 62, 188–198 (1965).
[Crossref]

N. Meshkov, A. Glick, and H. Lipkin, “Validity of many-body approximation methods for a solvable model:(ii). linearization procedures,” Nucl. Phys. 62, 199–210 (1965).
[Crossref]

A. Glick, H. Lipkin, and N. Meshkov, “Validity of many-body approximation methods for a solvable model:(iii). diagram summations,” Nucl. Phys. 62, 211–224 (1965).
[Crossref]

Opt. Express (1)

Phys. Lett. A (1)

H. Yuen, “States that give the maximum signal-to-quantum noise ratio for a fixed energy,” Phys. Lett. A 56, 105–106 (1976).
[Crossref]

Phys. Rev. (4)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
[Crossref]

D. A. Glaser, “Some effects of ionizing radiation on the formation of bubbles in liquids,” Phys. Rev. 87, 665 (1952).
[Crossref]

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes. I.,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. i,” Phys. Rev. 160, 1076–1096 (1967).
[Crossref]

Phys. Rev. A (6)

Y. K. Wang and F. Hioe, “Phase transition in the dicke model of superradiance,” Phys. Rev. A 7, 831 (1973).
[Crossref]

J. Vidal, R. Mosseri, and J. Dukelsky, “Entanglement in a first-order quantum phase transition,” Phys. Rev. A 69, 054101 (2004).
[Crossref]

L.-P. Yang, H. X. Tang, and Z. Jacob, “Concept of quantum timing jitter and non-markovian limits in single-photon detection,” Phys. Rev. A 97, 013833 (2018).
[Crossref]

C. T. Lee, “q representation of the atomic coherent states and the origin of fluctuations in superfluorescence,” Phys. Rev. A 30, 3308–3310 (1984).
[Crossref]

F. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972).
[Crossref]

B. Q. Baragiola, R. L. Cook, A. M. Brańczyk, and J. Combes, “N-photon wave packets interacting with an arbitrary quantum system,” Phys. Rev. A 86, 013811 (2012).
[Crossref]

Phys. Rev. B (3)

L. Del Re, M. Fabrizio, and E. Tosatti, “Nonequilibrium and nonhomogeneous phenomena around a first-order quantum phase transition,” Phys. Rev. B 93, 125131 (2016).
[Crossref]

A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, “Antiferromagnetic ising chain in a mixed transverse and longitudinal magnetic field,” Phys. Rev. B 68, 214406 (2003).
[Crossref]

Y. Imry, “Finite-size rounding of a first-order phase transition,” Phys. Rev. B 21, 2042 (1980).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
[Crossref]

Phys. Rev. Lett. (4)

H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, “Decay of loschmidt echo enhanced by quantum criticality,” Phys. Rev. Lett. 96, 140604 (2006).
[Crossref] [PubMed]

U. Gavish, B. Yurke, and Y. Imry, “Generalized constraints on quantum amplification,” Phys. Rev. Lett. 93, 250601 (2004).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

M. Raghunandan, J. Wrachtrup, and H. Weimer, “High-density quantum sensing with dissipative first order transitions,” Phys. Rev. Lett. 120, 150501 (2018).
[Crossref] [PubMed]

Phys. review letters (1)

C. F. Lee and N. F. Johnson, “First-order superradiant phase transitions in a multiqubit cavity system,” Phys. review letters 93, 083001 (2004).
[Crossref]

Proc. Physico-Mathematical Soc. Jpn. 3rd Ser. (1)

K. Husimi, “Some formal properties of the density matrix,” Proc. Physico-Mathematical Soc. Jpn. 3rd Ser. 22, 264–314 (1940).

Rev. scientific instruments (1)

M. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. scientific instruments 82, 071101 (2011).
[Crossref]

Sci. Reports (2)

A. Swatantran, H. Tang, T. Barrett, P. DeCola, and R. Dubayah, “Rapid, high-resolution forest structure and terrain mapping over large areas using single photon lidar,” Sci. Reports 6, 28277 (2016).
[Crossref]

Y. Zhang, L. Yu, J.-Q. Liang, G. Chen, S. Jia, and F. Nori, “Quantum phases in circuit qed with a superconducting qubit array,” Sci. reports 4, 4083 (2014).
[Crossref]

C. Schuck, W. H. Pernice, and H. X. Tang, “Waveguide integrated low noise nbtin nanowire single-photon detectors with milli-hz dark count rate,” Sci. Reports 3, 1893 (2013).
[Crossref]

Science (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, and J. Yao, “Phase transitions in a programmable quantum spin glass simulator,” Science 361, 162–165 (2018).
[Crossref] [PubMed]

The Eur. Phys. J. D (1)

L.-P. Yang, Y. Li, and C. Sun, “Franck-condon effect in central spin system,” The Eur. Phys. J. D 66, 300 (2012).
[Crossref]

Other (4)

B. Korzh, Q. Zhao, S. Frasca, J. Allmaras, T. Autry, E. Bersin, M. Colangelo, G. Crouch, A. Dane, T. Gerrits, and et al., “Demonstrating sub-3 ps temporal resolution in a superconducting nanowire single-photon detector,” arXiv preprint arXiv:1804.06839 (2018).

S. Sachdev, Quantum phase transitions (Wiley Online Library, 2007).

M. A. Nielsen and I. Chuang, “Quantum computation and quantum information,” (2002).

L.-P. Yang and Z. Jacob, Engineering Quantum Phase Transitions for Weak Signal Detection (2018). Under preparation.

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the quantum critical detector (QCD). The bosonic mode (resonant cavity -mode) with frequency ω0 = 1 is the output mode. The spins are immersed in a homogeneous magnetic field along z-axis inducing an energy splitting . The spin-boson coupling λ is in x-direction and the all-to-all spin-spin coupling J is along y-axis. The input weak signal leads to a small time-dependent variation in spin-boson coupling λ(t) and triggers a first-order quantum phase transition if the system is optimally biased around the critical point. The energy pre-stored in the spins transfers to the bosonic mode and realize the amplification in our QCD. (b) Phase diagram of our model and the schematic of the ground-state wave function of each phase. The green, blue, and red lines give the boundaries of the three quantum phases. In the strong-coupling regime J > Jc,II/2 and λ > λ c , II / 2, the QPT between the FN phase and the FS phase (crossing the red line) is of first order. The other two QPTs are of second-order. Here, |0〉 and |α〉 are the vacuum state and coherent state of the bosonic mode. The ground state of the spins in the ferromagnetic phase is a coherent spin state as explained in Appendix B.
Fig. 2
Fig. 2 Numerical demonstration of the phase diagram with the superradiant order parameter ζS = 〈0/N in panel (a) and the magnetic order parameter ζ M , y = S ^ y 2 0 / N 2 in panel (b). The boundaries between different phases are marked out by the blue, the green, and the red lines, which correspond to the three lines in Fig. 1(b) exactly. In this figure, the other parameters are taken as = 1, and both the spin number N and the cutoff for the bosonic mode are set as 40.
Fig. 3
Fig. 3 In (a) and (b), we show the order parameters ζS and ζM,y, respectively, for different spin-spin coupling J. Here, = 1 and both the spin number and the cutoff of the bosonic mode are set as 80. Second-order QPTs occur at λ c , II / 2 = 0.5 for JJc,II/2 = 0.5 and first-order QPTs occur at λ c , I J / 2 for J > Jc,II. The locations of the critical points are marked by the thin black dashed line. In panel (c), we plot ζS with fixed J = 1 > Jc,II for different spin number N. In panel (d), we show that the maximum of the sensitivity diverges with the spin number N verifying the first-order QPT. The polynomial fitting function f(x) = 0.067x2 − 1.881x + 22.62 shows the N2 scaling.
Fig. 4
Fig. 4 The amplification via the first-order dynamical quantum phase transition is shown by the time-dependent quantum gain g(t). The left subplot shows envelope Pe(t) in the time dependent spin-boson coupling λ(t). Here, the spin-spin coupling is set as J = 1 > Jc,II, the time is in a unit of 1/ω0, and amplitude of the small change in the parameter λ(t) is set to be Δλ = 0.01. In the right subplot, we show that the quantum amplification only occurs when λ0 is biased close to critical point λ c , I = J / 2 0.707 with t = 40.
Fig. 5
Fig. 5 Linear scaling of the quantum bosonic amplification with the spin number N for different spin-spin coupling J. The corresponding signal-to-quantum noise ratios are shown in the left subplot. In the right subplot, we shown there is a phase-transition-like behavior in the slope of the maximum gain when J crosses the critical point Jc,II = 0.5. First-order dynamic QPT (blue diamond line) has much higher gain and signal-to-quantum noise ratio than that of second-order QPT.
Fig. 6
Fig. 6 The Husimi Q-functions of the bosonic mode on the ground states of the paramagnetic-normal phase (a), the ferromagnetic-superradiant phase (b), and the ferromagnetic-normal phase (c) are displayed. Here, the other parameters are set as = 1, spin number N = 80, and the bosonic mode cutoff 80.
Fig. 7
Fig. 7 The Husimi Q-functions of the spins for the ground states ρg of the paramagnetic-normal phase (a), the ferromagnetic-superradiant phase (b), and the ferromagnetic-normal phase (c) are displayed. Here, the spherical coordinates (r = Q(θ, ϕ), θ, ϕ) have been transferred to the corresponding Cartesian coordinates (x, y, z). The curves underneath are the contour projections of the corresponding Q-functions in xy-plane. The other parameters are set as = 1, spin number N = 80, and the bosonic mode cutoff 80.

Equations (9)

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H = d ^ d ^ + λ N j = 1 N σ ^ j x ( d ^ + d ^ ) + 2 j = 1 N σ ^ j z J N j < k σ ^ j y σ ^ k y ,
χ ( λ ) = 1 N d d λ d ^ d ^ ,
g ( t ) = d ^ ( t ) d ^ ( t ) / d ^ ( 0 ) d ^ ( 0 ) ,
SQNR = d ^ ( t ) d ^ ( t ) 2 / [ Δ d ^ ( t ) d ^ ( t ) ] 2 ,
S ^ α = 1 2 j = 1 N σ ^ j α , α = x , y , z ,
H = d ^ d ^ + 2 λ N S ^ x ( d ^ + d ^ ) + S ^ z 2 J N S ^ y 2 .
Q ( α ) = 1 π Tr spin [ α | ρ g | α ] ,
Q ( θ , ϕ ) = 2 N + 1 4 π Tr boson [ θ , ϕ | ρ g | θ , ϕ ] ,
| θ , ϕ = e i θ ( S ^ x sin ϕ S ^ y cos ϕ ) | N / 2 , N / 2 .

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