Abstract

Spin squeezing has received much attention due to the interesting physics and important applications such as quantum metrology and quantum information processing. We here present a scheme to engineer stable spin squeezing in an array of nitrogen vacancy centers (NVCs) coupled to a rectangular hollow metallic waveguide. The remarkable feature of the waveguide as the common environment media is that one can switch on/off either the waveguide induced dipole-dipole interactions or correlated spontaneous emissions among the NVCs by designing their spatial separation. It permits us to achieve a dissipative Dicke model after the dipole-dipole interactions vanish due to destructive interference. With the external driving lasers on each NVC, a second-order phase transition is triggered, separating the steady state into two phases with and without collective spin squeezing. Supplying a physical realization of the dissipative Dicke model, our study gives a bridge between the generation of the stable spin squeezing and the phase transition physics.

© 2017 Optical Society of America

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2016 (6)

Q. S. Tan, H. Y. Lu, and S. Yi, “Spin squeezing of a dipolar Bose gas in a double-well potential,” Phys. Rev. A 93, 013606 (2016).
[Crossref]

D. Kajtoch and E. Witkowska, “Spin squeezing in dipolar spinor condensates,” Phys. Rev. A 93, 023627 (2016).
[Crossref]

T. Opatrný, H. Saberi, E. Brion, and K. Mølmer, “Counterdiabatic driving in spin squeezing and Dicke-state preparation,” Phys. Rev. A 93, 023815 (2016).
[Crossref]

T. Pichler, T. Caneva, S. Montangero, M. D. Lukin, and T. Calarco, “Noise-resistant optimal spin squeezing via quantum control,” Phys. Rev. A 93, 013851 (2016).
[Crossref]

P. B. Li, Z. L. Xiang, P. Rabl, and F. Nori, “Hybrid quantum device with nitrogen-vacancy centers in diamond coupled to carbon nanotubes,” Phys. Rev. Lett. 117, 015502 (2016).
[Crossref] [PubMed]

C. Chen, C. J. Yang, and J. H. An, “Exact decoherence-free state of two distant quantum systems in a non-Markovian environment,” Phys. Rev. A 93, 062122 (2016).
[Crossref]

2015 (4)

E. Bermúdezureña, C. Gonzalezballestero, M. Geiselmann, R. Marty, I. P. Radko, T. Holmgaard, Y. Alaverdyan, E. Moreno, F. J. Garcívidal, and S. I. Bozhevolnyi, “Coupling of individual quantum emitters to channel plasmons,” Nat. Commun. 6, 7883 (2015).
[Crossref]

J. B. You, W. L. Yang, Z. Y. Xu, A. H. Chan, and C. H. Oh, “Phase transition of light in circuit-QED lattices coupled to nitrogen-vacancy centers in diamond,” Phys. Rev. B 90, 195112 (2015).
[Crossref]

W. L. Yang, J. H. An, C. J. Zhang, C. Y. Chen, and C. H. Oh, “Dynamics of quantum correlation between separated nitrogen-vacancy centers embedded in plasmonic waveguide,” Sci. Rep. 5, 15513 (2015).
[Crossref] [PubMed]

L. N. Wu, G. R. Jin, and L. You, “Spin squeezing of the non-Hermitian one-axis twisting model,” Phys. Rev. A 92, 033826 (2015).
[Crossref]

2014 (3)

E. Wolfe and S. F. Yelin, “Certifying separability in symmetric mixed states of N qubits, and superradiance,” Phys. Rev. Lett. 112, 140402 (2014).
[Crossref] [PubMed]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Nanophotonics. Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 6205 (2014).
[Crossref]

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref] [PubMed]

2013 (9)

E. Shahmoon and G. Kurizki, “Nonradiative interaction and entanglement between distant atoms,” Phys. Rev. A 87, 033831 (2013).
[Crossref]

T. A. González and D. Porras, “Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics,” Phys. Rev. Lett. 110, 691 (2013).

Y. Lin, J. P. Gaebler, F. Reiter, T. R. Tan, R. Bowler, A. S. Sørensen, D. Leibfried, and D. J. Wineland, “Dissipative production of a maximally entangled steady state of two quantum bits,” Nature 504, 415 (2013).
[Crossref] [PubMed]

J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2013).
[Crossref]

A. Bermudez, T. Schaetz, and M. B. Plenio, “Dissipation-assisted quantum information processing with trapped ions,” Phys. Rev. Lett. 110, 110502 (2013).
[Crossref] [PubMed]

E. G. D. Torre, J. Otterbach, E. Demler, V. Vuletic, and M. D. Lukin, “Dissipative preparation of spin squeezed atomic ensembles in a steady state,” Phys. Rev. Lett. 110, 120402 (2013).
[Crossref] [PubMed]

W. L. Yang, J. H. An, C. J. Zhang, M. Feng, and C. H. Oh, “Preservation of quantum correlation between separated nitrogen-vacancy centers embedded in photonic-crystal cavities,” Phys. Rev. A 87, 022312 (2013).
[Crossref]

C. G. Yale, B. B. Buckley, D. J. Christle, G Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, “All-optical control of a solid-state spin using coherent dark states,” PNAS 110, 7595 (2013).
[Crossref] [PubMed]

H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, and L. Childress, “Heralded entanglement between solid-state qubits separated by three metres,” Nature 497, 86 (2013).
[Crossref] [PubMed]

2012 (3)

D. Porras and J. J. G. Ripoll, “Shaping an itinerant quantum field into a multimode squeezed vacuum by dissipation,” Phys. Rev. Lett. 108, 043602 (2012).
[Crossref] [PubMed]

P. B. Li, S. Y. Gao, H. R. Li, S. L. Ma, and F. L. Li, “Dissipative preparation of entangled states between two spatially separated nitrogen-vacancy centers,” Phys. Rev. A 85, 042306 (2012).
[Crossref]

G. Watanabe and H. Mäkelä, “Dissipation-induced squeezing,” Phys. Rev. A 85, 023604 (2012).
[Crossref]

2011 (9)

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
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Figures (5)

Fig. 1
Fig. 1 (a) An array of NVCs is coupled to the vacuum field of a rectangular hollow metallic waveguide. The NVCs are further driven individually by external laser fields. (b) Crystal structure of the NVC in diamond. (c) Energy level structure for the NVC: the qubit is encoded in the states |ms = −1〉 and |A2〉 with transition frequency ω0, and Deg is Zeeman splitting.
Fig. 2
Fig. 2 Husimi’s Q function on the Bloch sphere (top panels) and in the plane perpendicular to the MSD (bottom panels). The red arrow represents the MSD. The parameters are N = 50, δ = 0, Ω/(Γ11N) = 0, 0.3, 0.4, and 0.5 in (a1) and (b1), (a2) and (b2), (a3) and (b3), and (a4) and (b4), respectively.
Fig. 3
Fig. 3 Polar angle θ0 in (a) and squeezing parameter 1/ξR in (b) versus the driving strength Ω for different N. The parameter δ = 0 is used.
Fig. 4
Fig. 4 Density plots of the squeezing parameter 1/ξR in the parameter space {δ,Ω} for different N.
Fig. 5
Fig. 5 Time evolution of the squeezing parameter 1/ξR for different initial states |N/2, m〉. The parameters are N = 60, δ = 0, and Ω/ (Γ0N) = 0.446.

Equations (9)

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H ^ S = i = 1 N [ ω 0 2 σ ^ i z + Ω σ ^ i x cos ( ω d t ) ] ,
H ^ E = k ω k a k a ^ k ,
H ^ I = i = 1 N k σ ^ i x ( g k i a ^ k + g k i * a ^ k ) ,
ρ ˙ ( t ) = i [ H ^ S , ρ ( t ) ] + i , j = 1 N γ i j 2 [ 2 σ ^ i ρ ( t ) σ ^ j + { σ ^ i + σ ^ j , ρ ( t ) } ] ,
Δ i j = Γ 11 ζ ω 11 c sin z i j ζ , γ i j = Γ 11 ζ ω 11 c cos z i j ζ ,
ρ ˙ ( t ) = i [ δ S ^ z + Ω S ^ x , ρ ( t ) ] + Γ 0 2 [ 2 S ^ ρ ( t ) S ^ + { S ^ + S ^ , ρ ( t ) } ] ,
ρ ( ) = A m , n = 0 N a m n ( g * ) m g n S ^ m S ^ + n ,
Q ( θ , φ ) = 2 j + 1 4 π θ , φ | ρ | θ , φ ,
ξ R = 2 j ( Δ S n ) min / | Tr ( ρ S ^ ) | ,

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