Abstract

We introduce a technique to determine photon correlations of optical light fields in real time. The method is based on ultrafast phase-randomized homodyne detection and allows us to follow the temporal evolution of the second-order correlation function g(2)(0) of a light field. We demonstrate the capabilities of our approach by applying it to a laser diode operated in the threshold region. In particular, we are able to monitor the emission dynamics of the diode switching back and forth between lasing and spontaneous emission with a g(2)(0)-sampling rate of 100 kHz.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

G. Moody, M. Segnon, I. Sagnes, R. Braive, A. Beveratos, I. Robert-Philip, N. Belabas, F. Jahnke, K. L. Silverman, R. P. Mirin, M. J. Stevens, and C. Gies, “Delayed formation of coherence in the emission dynamics of high-q nanolasers,” Optica 5, 395–401 (2018).
[Crossref]

M. Marconi, J. Javaloyes, P. Hamel, F. Raineri, A. Levenson, and A. M. Yacomotti, “Far-from-equilibrium route to superthermal light in bimodal nanolasers,” Phys. Rev. X 8, 011013 (2018).

2017 (2)

H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

J. Kiethe, A. Heuer, and A. Jechow, “Second-order coherence properties of amplified spontaneous emission from a high-power tapered superluminescent diode,” Laser Phys. Lett. 14, 086201 (2017).
[Crossref]

2016 (2)

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
[Crossref]

F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. A. M. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, “Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers,” Nat. Commun. 7, 11540 (2016).
[Crossref] [PubMed]

2015 (2)

T. Wang, G. P. Puccioni, and G. L. Lippi, “Dynamical buildup of lasing in mesoscale devices,” Sci. Rep. 5, 15858 (2015).
[Crossref] [PubMed]

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

2013 (5)

Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, and A. Fiore, “Ultrasensitive n-photon interferometric autocorrelator,” Phys. Rev. Lett. 110, 133605 (2013).
[Crossref] [PubMed]

H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
[Crossref]

J. Arlt, D. Tyndall, B. R. Rae, D. D.-U. Li, J. A. Richardson, and R. K. Henderson, “A study of pile-up in integrated time-correlated single photon counting systems,” Rev. Sci. Instrum. 84, 103105 (2013).
[Crossref] [PubMed]

G. Roumpos and S. T. Cundiff, “Photon number distributions from a diode laser,” Opt. Lett. 38, 139–141 (2013).
[Crossref] [PubMed]

G. Roumpos and S. T. Cundiff, “Multichannel homodyne detection for quantum optical tomography,” J. Opt. Soc. Am. B 30, 1303–1316 (2013).
[Crossref]

2012 (2)

R. Kumar, E. Barrios, A. MacRae, E. Cairns, E. Huntington, and A. Lvovsky, “Versatile wideband balanced detector for quantum optical homodyne tomography,” Opt. Commun. 285, 5259–5267 (2012).
[Crossref]

E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved n-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
[Crossref] [PubMed]

2011 (1)

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2, 366 (2011).
[Crossref] [PubMed]

2010 (5)

2009 (3)

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
[Crossref]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timestime by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

A. I. Lvovsky and M. G. Raymer, “Continuous-variable optical quantum-state tomography,” Rev. Mod. Phys. 81, 299–332 (2009).
[Crossref]

2007 (1)

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007).
[Crossref] [PubMed]

2001 (1)

1997 (1)

D. F. McAlister and M. G. Raymer, “Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection,” Phys. Rev. A 55, R1609–R1612 (1997).
[Crossref]

1995 (1)

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52, R924–R927 (1995).
[Crossref] [PubMed]

1994 (1)

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-qed laser: A comment on the laser–phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
[Crossref] [PubMed]

1991 (1)

1977 (1)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[Crossref]

1972 (1)

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[Crossref]

1963 (1)

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[Crossref]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

Abbaspour, H.

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

Adiyatullin, A. F.

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

Albert, F.

H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
[Crossref]

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2, 366 (2011).
[Crossref] [PubMed]

Allerman, A. A.

Anderson, M. D.

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

Anderson, M. E.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52, R924–R927 (1995).
[Crossref] [PubMed]

André, R.

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

Arlt, J.

J. Arlt, D. Tyndall, B. R. Rae, D. D.-U. Li, J. A. Richardson, and R. K. Henderson, “A study of pile-up in integrated time-correlated single photon counting systems,” Rev. Sci. Instrum. 84, 103105 (2013).
[Crossref] [PubMed]

Aßmann, M.

F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. A. M. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, “Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers,” Nat. Commun. 7, 11540 (2016).
[Crossref] [PubMed]

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

M. Aßmann, F. Veit, J.-S. Tempel, T. Berstermann, H. Stolz, M. van der Poel, J. M. Hvam, and M. Bayer, “Measuring the dynamics of second-order photon correlation functions inside a pulse with picosecond time resolution,” Opt. Express 18, 20229–20241 (2010).
[Crossref]

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
[Crossref]

Ates, S.

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007).
[Crossref] [PubMed]

Avenhaus, M.

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Baek, B.

Barrios, E.

R. Kumar, E. Barrios, A. MacRae, E. Cairns, E. Huntington, and A. Lvovsky, “Versatile wideband balanced detector for quantum optical homodyne tomography,” Opt. Commun. 285, 5259–5267 (2012).
[Crossref]

Bayer, M.

F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. A. M. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, “Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers,” Nat. Commun. 7, 11540 (2016).
[Crossref] [PubMed]

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

M. Aßmann, F. Veit, J.-S. Tempel, T. Berstermann, H. Stolz, M. van der Poel, J. M. Hvam, and M. Bayer, “Measuring the dynamics of second-order photon correlation functions inside a pulse with picosecond time resolution,” Opt. Express 18, 20229–20241 (2010).
[Crossref]

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
[Crossref]

Belabas, N.

Berggren, K. K.

Berstermann, T.

Beveratos, A.

Blansett, E. L.

Boggavarapu, D.

M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, “Photon-number statistics from the phase-averaged quadrature-field distribution: Theory and ultrafast measurement,” Phys. Rev. A 52, R924–R927 (1995).
[Crossref] [PubMed]

Boitier, F.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timestime by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Braive, R.

Busi, P. V.

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

Cairns, E.

R. Kumar, E. Barrios, A. MacRae, E. Cairns, E. Huntington, and A. Lvovsky, “Versatile wideband balanced detector for quantum optical homodyne tomography,” Opt. Commun. 285, 5259–5267 (2012).
[Crossref]

Carmichael, H. J.

P. R. Rice and H. J. Carmichael, “Photon statistics of a cavity-qed laser: A comment on the laser–phase-transition analogy,” Phys. Rev. A 50, 4318–4329 (1994).
[Crossref] [PubMed]

Chekhova, M. V.

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

Cundiff, S. T.

Dagenais, M.

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39, 691–695 (1977).
[Crossref]

Dauler, E. A.

del Valle, E.

E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved n-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
[Crossref] [PubMed]

Deveaud, B.

A. F. Adiyatullin, M. D. Anderson, P. V. Busi, H. Abbaspour, R. André, M. T. Portella-Oberli, and B. Deveaud, “Temporally resolved second-order photon correlations of exciton-polariton bose-einstein condensate formation,” Appl. Phys. Lett. 107, 221107 (2015).
[Crossref]

Eckardt, A.

H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

Elson, E.

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[Crossref]

Fabre, C.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timestime by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Fiore, A.

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H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
[Crossref]

H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
[Crossref]

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2, 366 (2011).
[Crossref] [PubMed]

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007).
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J. Arlt, D. Tyndall, B. R. Rae, D. D.-U. Li, J. A. Richardson, and R. K. Henderson, “A study of pile-up in integrated time-correlated single photon counting systems,” Rev. Sci. Instrum. 84, 103105 (2013).
[Crossref] [PubMed]

Robert-Philip, I.

Rosencher, E.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timestime by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Roumpos, G.

Roy, R.

Sagnes, I.

Schlottmann, E.

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
[Crossref]

Schneider, C.

H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. A. M. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, “Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers,” Nat. Commun. 7, 11540 (2016).
[Crossref] [PubMed]

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
[Crossref]

H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
[Crossref]

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2, 366 (2011).
[Crossref] [PubMed]

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Serkland, D. K.

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M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

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Stevens, M. J.

Stolz, H.

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E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved n-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
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J. Arlt, D. Tyndall, B. R. Rae, D. D.-U. Li, J. A. Richardson, and R. K. Henderson, “A study of pile-up in integrated time-correlated single photon counting systems,” Rev. Sci. Instrum. 84, 103105 (2013).
[Crossref] [PubMed]

Ulrich, S. M.

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007).
[Crossref] [PubMed]

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Veit, F.

M. Aßmann, F. Veit, J.-S. Tempel, T. Berstermann, H. Stolz, M. van der Poel, J. M. Hvam, and M. Bayer, “Measuring the dynamics of second-order photon correlation functions inside a pulse with picosecond time resolution,” Opt. Express 18, 20229–20241 (2010).
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M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
[Crossref]

Vorberg, D.

H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

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T. Wang, G. P. Puccioni, and G. L. Lippi, “Dynamical buildup of lasing in mesoscale devices,” Sci. Rep. 5, 15858 (2015).
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D. Magde, E. Elson, and W. W. Webb, “Thermodynamic fluctuations in a reacting system—measurement by fluorescence correlation spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[Crossref]

Wiersig, J.

H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. A. M. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, “Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers,” Nat. Commun. 7, 11540 (2016).
[Crossref] [PubMed]

H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
[Crossref]

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007).
[Crossref] [PubMed]

Wolters, J.

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
[Crossref]

Worschech, L.

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2, 366 (2011).
[Crossref] [PubMed]

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

Yacomotti, A. M.

M. Marconi, J. Javaloyes, P. Hamel, F. Raineri, A. Levenson, and A. M. Yacomotti, “Far-from-equilibrium route to superthermal light in bimodal nanolasers,” Phys. Rev. X 8, 011013 (2018).

Zhou, Z.

Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, and A. Fiore, “Ultrasensitive n-photon interferometric autocorrelator,” Phys. Rev. Lett. 110, 133605 (2013).
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Nat. Commun. (2)

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Commun. 2, 366 (2011).
[Crossref] [PubMed]

F. Jahnke, C. Gies, M. Aßmann, M. Bayer, H. A. M. Leymann, A. Foerster, J. Wiersig, C. Schneider, M. Kamp, and S. Höfling, “Giant photon bunching, superradiant pulse emission and excitation trapping in quantum-dot nanolasers,” Nat. Commun. 7, 11540 (2016).
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Nat. Phys. (1)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timestime by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Nature (1)

R. Hanbury Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature 178, 1046–1048 (1956).
[Crossref]

New J. Phys. (1)

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
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[Crossref]

Phys. Rev. B (1)

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

Phys. Rev. Lett. (6)

S. M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, and P. Michler, “Photon statistics of semiconductor microcavity lasers,” Phys. Rev. Lett. 98, 043906 (2007).
[Crossref] [PubMed]

M. Avenhaus, K. Laiho, M. V. Chekhova, and C. Silberhorn, “Accessing higher order correlations in quantum optical states by time multiplexing,” Phys. Rev. Lett. 104, 063602 (2010).
[Crossref] [PubMed]

E. del Valle, A. Gonzalez-Tudela, F. P. Laussy, C. Tejedor, and M. J. Hartmann, “Theory of frequency-filtered and time-resolved n-photon correlations,” Phys. Rev. Lett. 109, 183601 (2012).
[Crossref] [PubMed]

Z. Zhou, G. Frucci, F. Mattioli, A. Gaggero, R. Leoni, S. Jahanmirinejad, T. B. Hoang, and A. Fiore, “Ultrasensitive n-photon interferometric autocorrelator,” Phys. Rev. Lett. 110, 133605 (2013).
[Crossref] [PubMed]

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H. A. M. Leymann, D. Vorberg, T. Lettau, C. Hopfmann, C. Schneider, M. Kamp, S. Höfling, R. Ketzmerick, J. Wiersig, S. Reitzenstein, and A. Eckardt, “Pump-power-driven mode switching in a microcavity device and its relation to bose-einstein condensation,” Phys. Rev. X 7, 021045 (2017).

M. Marconi, J. Javaloyes, P. Hamel, F. Raineri, A. Levenson, and A. M. Yacomotti, “Far-from-equilibrium route to superthermal light in bimodal nanolasers,” Phys. Rev. X 8, 011013 (2018).

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J. Arlt, D. Tyndall, B. R. Rae, D. D.-U. Li, J. A. Richardson, and R. K. Henderson, “A study of pile-up in integrated time-correlated single photon counting systems,” Rev. Sci. Instrum. 84, 103105 (2013).
[Crossref] [PubMed]

Sci. Rep. (1)

T. Wang, G. P. Puccioni, and G. L. Lippi, “Dynamical buildup of lasing in mesoscale devices,” Sci. Rep. 5, 15858 (2015).
[Crossref] [PubMed]

Science (1)

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Schematic of the homodyne detection setup. LO: local oscillator; PBS: polarizing beam splitter; HWP: half-wave plate.
Fig. 2
Fig. 2 Time-averaged emitted photon number (black dots) and second-order correlation function 〈g(2)(0)〉 (red dots) plotted against the drive current across the lasing threshold region. Red and blue solid lines denote the thermal and coherent limit of 〈g(2)(0)〉, respectively. The open red dots mark the drive currents investigated in more detail in Fig. 3.
Fig. 3
Fig. 3 Time traces of the emitted photon numbers (black) and g(2)(0) values (red) for different diode laser drive currents. From top to bottom, the currents used are 62 mA and 75 mA with the lasing threshold It=70.5 mA between them. Above threshold, higher photon numbers are correlated with lower g(2)(0) values and vice versa.
Fig. 4
Fig. 4 Histograms of the distribution of the values of the second-order correlation function for different drive currents. Note that the spacings of drive currents along the z-axis are not equidistant. The datasets used for Fig. 3 are marked in red.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

g ( 2 ) ( τ , t ) = a ^ ( t ) a ^ ( t + τ ) a ^ ( t + τ ) a ^ ( t ) a ^ ( t ) a ^ ( t ) a ^ ( t + τ ) a ^ ( t + τ ) ,
q ^ ϕ = 1 2 ( e i ϕ a ^ + e i ϕ a ^ )
a ^ ± = 1 2 ( e i ϕ a ^ LO ± a ^ S )
Q ^ = a ^ LO ( e i ϕ a ^ S + e i ϕ a ^ S ) .
g ( 2 ) ( τ = 0 , t ) = a ^ S a ^ S a ^ S a ^ S a ^ S a ^ S 2
Q ^ 2 = a ^ LO 2 ( 2 a ^ S a ^ S + 1 )
Q ^ 4 = a ^ LO 4 ( 6 a ^ S a ^ S a ^ S a ^ S + 12 a ^ S a ^ S + 3 )

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