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Optical feedback-induced dynamics and nonclassical photon statistics of semiconductor microcavity laser

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Abstract

We study a coherently driven semiconductor laser cavity containing a single quantum dot(QD) (as gain medium) with optical feedback under Markovian approximation. We have obtained coupled operator equations for the model Hamiltonian using standard input-output formalism of cavity-QED and have found that these equations do not have any finite steady state solutions. We have also used an exact numerical framework based on Matlab platform qotoolbox, to compute the temporal dynamics of the mean excitation number of laser cavity mode under high feedback coupling regime. We have further studied the photon correlations of both the cavity mode as well as external feedback mode to feedback identify the laser parameters and coupling strength that give the nonclassical sub-Poissonian photon statistics. This work is useful for coherent control of photon statistics and photon correlations in the semiconductor laser with optical feedback.

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References

  1. E.T. Jaynes, F.W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89–109 (1965)

    Article  Google Scholar 

  2. S. Haroche, J.M. Raimond, Radiative properties of Rydberg states in resonant cavities. Adv. Atomic Mol. Opt. Phys. 20, 347–411 (1985)

    Article  ADS  Google Scholar 

  3. R.J. Thompson, G. Rempe, H.J. Kimble, Observation of normal-mode splitting for an atom in an optical cavity. Phys. Rev. Lett. 68, 1132–1135 (1992)

    Article  ADS  Google Scholar 

  4. E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58, 2059–2062 (1987)

    Article  ADS  Google Scholar 

  5. J.M. Gerard, D. Barrier, J.Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, T. Rivera, Quantum boxes as active probes for photonic microstructures: the pillar microcavity case. Appl. Phys. Lett. 69, 449–451 (1996)

    Article  ADS  Google Scholar 

  6. K.M. Birnbaum, A. Boca, R. Miller, A.D. Boozer, T.E. Northup, H.J. Kimble, Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005)

    Article  ADS  Google Scholar 

  7. H.J. Carmichael, Photon Antibunching and Squeezing for a Single Atom in a Resonant Cavity. Phys. Rev. Lett. 55, 2790–2793 (1985)

    Article  ADS  Google Scholar 

  8. C.M. Savage, Photon Antibunching and Squeezing for a Single Atom in a Resonant Cavity. Phys. Rev. Lett. 60, 1828–1831 (1988)

    Article  ADS  Google Scholar 

  9. H.J. Carmichael, R.J. Brecha, M.G. Raizen, H.J. Kimble, P.R. Rice, linewidth averaging for coupled atomic and cavity-mode oscillators. Phys. Rev. A 40, 5516–5519 (1989)

    Article  ADS  Google Scholar 

  10. M.D. Lukin, S.F. Yelin, M. Fleischhauer, Entanglement of Atomic Ensembles by Trapping Correlated Photon States. Phys. Rev. Lett. 84, 4232–4235 (1999)

    Article  ADS  Google Scholar 

  11. P. Li, Y. Gu, Q. Gong, G. Guo, Generation of two-mode entanglement between separated cavities. J. Opt. Soc. Am. B 26, 189–193 (2009)

    Article  ADS  Google Scholar 

  12. H.M. Wiseman, G.J. Milburn, All-optical versus electro-optical quantum-limited feedback. Phys. Rev. A 49, 4110–4125 (1994)

    Article  ADS  Google Scholar 

  13. K. Jacobs, X. Wang, H.M. Wiseman, Coherent feedback that beats all measurement-based feedback protocols. New J. Phys. 16, 073036 (2014)

    Article  ADS  MATH  Google Scholar 

  14. J.M. Horowitz, K. Jacobs, Quantum effects improve the energy efficiency of feedback control. Phys. Rev. E 89, 042134 (2014)

    Article  ADS  Google Scholar 

  15. N. Yamamoto, Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information. Phys. Rev. X 4, 041029 (2014)

    Google Scholar 

  16. S. Roy, I.R. Petersen, E.H. Huntington, Coherent-classical estimation for linear quantum systems. Automatica 82, 109–117 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. R.J. Nelson, Y. Weinstein, D. Cory, S. Lloyd, Experimental Demonstration of Fully Coherent Quantum Feedback. Phys. Rev. Lett. 85, 3045–3048 (2000)

    Article  ADS  Google Scholar 

  18. S. Iida, M. Yukawa, H. Yonezawa, N. Yamamoto, A. Furusawa, Experimental Demonstration of Coherent Feedback Control on Optical Field Squeezing. IEEE Trans. Autom. Control 57, 2045–2050 (2012)

    Article  Google Scholar 

  19. Y. Zhou, X. Jia, F. Li, J. Yu, C. Xie, K. Peng, Quantum Coherent Feedback Control for Generation System of Optical Entangled State. Sci. Rep. 5, 11132 (2015)

    Article  ADS  Google Scholar 

  20. D. Wang, C. Xia, Q. Wang, Y. Wu, F. Liu, Y. Zhang, M. Xiao, Feedback-optimized extraordinary optical transmission of continuous-variable entangled states. Phys. Rev. B 91, 121406(R) (2015)

    Article  ADS  Google Scholar 

  21. J. Kerckhoff, R.W. Andrews, H.S. Ku, W.F. Kindel, K. Cicak, R.W. Simmonds, K.W. Lehnert, Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network. Phys. Rev. X 3, 02013 (2013)

    Google Scholar 

  22. H. Mabuchi, Coherent-feedback quantum control with a dynamic compensator. Phys. Rev. A 78, 032323 (2008)

    Article  ADS  Google Scholar 

  23. J. Kerckhoff, K.W. Lehnert, Superconducting Microwave Multivibrator Produced by Coherent Feedback. Phys. Rev. Lett. 109, 153602–153605 (2012)

    Article  ADS  Google Scholar 

  24. M. Sarovar, D.B. Soh, J. Cox, C. Brif, C.T. DeRose, R. Camacho, P. Davids, Silicon nanophotonics for scalable quantum coherent feedback networks. EPJ Quantum Technol. 3, 14 (2016)

    Article  Google Scholar 

  25. M. Hirose, P. Cappellaro, Coherent feedback control of a single qubit in diamond. Nature (London) 532, 77–80 (2016)

    Article  ADS  Google Scholar 

  26. R. Lang, K. Kobayashi, External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. 16, 347–355 (1980)

    Article  ADS  Google Scholar 

  27. T. Heil, I. Fischer, W. Elsaber, B. Krauskopf, K. Green, A. Gavrielides, Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms. Phys. Rev. E 67, 066214 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  28. G.H.M. van Tartwijk, D. Lenstra, Semiconductor lasers with optical injection and feedback. Quantum Semiclass. Opt. 7, 87–143 (1995)

    Article  ADS  Google Scholar 

  29. A.M. Levine, G.H.M. van Tartwijk, D. Lenstra, T. Erneux, Diode lasers with optical feedback: stability of the maximum gain mode. Phys. Rev. A 52, R3436–R3439 (1995)

    Article  ADS  Google Scholar 

  30. M.C. Soriano, J. Garcia-Ojalvo, C.R. Mirasso, I. Fische, Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers. Rev. Mod. Phys. 85, 421–470 (2013)

    Article  ADS  Google Scholar 

  31. S. Franz, L. Benjamin, H. Sven Moritz, C. Alexander, S. Eckehard, L. Kathy, K. Andreas, Feedback-Induced Steady-State Light Bunching Above the Lasing Threshold. Phys. Rev. A 89, 041801 (2014)

    Article  Google Scholar 

  32. V. del Elena, P.L. Fabrice, T. Carlos, Luminescence spectra of quantum dots in microcavities. II. Fermions. Phys. Rev. B 79, 235326 (2009)

    Article  Google Scholar 

  33. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, Y. Arakawa, Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system. Nat. Phys. 6, 279–283 (2010)

    Article  Google Scholar 

  34. S. Strauf, K. Hennessy, M.T. Rakher, Y.-S. Choi, A. Badolato, L.C. Andreani, E.L. Hu, P.M. Petroff, D. Bouwmeester, Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers. Phys. Rev. Lett. 96, 127404 (2006)

    Article  ADS  Google Scholar 

  35. S.M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, P. Michler, Self-Tuned Quantum Dot Gain in Photonic Crystal Lasers. Phys. Rev. Lett. 96, 127404 (2006)

    Article  Google Scholar 

  36. S.M. Ulrich, C. Gies, S. Ates, J. Wiersig, S. Reitzenstein, C. Hofmann, A. Löffler, A. Forchel, F. Jahnke, P. Michler, Photon Statistics of Semiconductor Microcavity Lasers. Phys. Rev. Lett. 98, 043906 (2007)

    Article  ADS  Google Scholar 

  37. Z.G. Xie, S. Gotzinger, W. Fang, H. Cao, G.S. Solomon, Influence of a Single Quantum Dot State on the Characteristics of a Microdisk Laser. Phys. Rev. Lett. 98, 117401 (2007)

    Article  ADS  Google Scholar 

  38. S. Reitzenstein, C. Böckler, A. Bazhenov, A. Gorbunov, A. Löffler, M. Kamp, V.D. Kulakovskii, A. Forchel, Single quantum dot controlled lasing effects in high-Q micropillar cavities. Opt. Express 16, 4848–4857 (2008)

    Article  ADS  Google Scholar 

  39. Jelena Vuckovic, Matthew Pelton, Axel Scherer, Yoshihisa Yamamoto, Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics. Phys. Rev. A 66, 023808 (2002)

    Article  ADS  Google Scholar 

  40. Gunnar Björk, Anders Karlsson, Yoshihisa Yamamoto, Definition of a laser threshold. Phys. Rev. A 50, 1675–1680 (1994)

    Article  ADS  Google Scholar 

  41. C. Joshi, U. Akram, G.J. Milburn, An all-optical feedback assisted steady state of an optomechanical array. New J. Phys. 16, 1367–2630 (2014)

    Article  Google Scholar 

  42. J. Li, G. Li, S. Zippilli, D. Vitali, T. Zhang, Enhanced entanglement of two different mechanical resonators via coherent feedback. Phys. Rev. A 95, 043819 (2017)

    Article  ADS  Google Scholar 

  43. A.F. Kockum, G. Johansson, F. Nori, Decoherence-Free Interaction between Giant Atoms in Waveguide Quantum Electrodynamics. Phys. Rev. Lett. 120, 140404 (2018)

    Article  ADS  Google Scholar 

  44. A.L. Grimsmo, A.S. Parkins, B.-S. Skagerstam, Rapid steady-state convergence for quantum systems using time-delayed feedback control. New J. Phys. 16, 065004 (2014)

    Article  ADS  MATH  Google Scholar 

  45. J. Kabuss, D.O. Krimer, S. Rotter, K. Stannigel, A. Knorr, A. Carmele, Analytical study of quantum-feedback-enhanced Rabi oscillations. Phys. Rev. A 92, (2015)

  46. P. Guimond, H. Pichler, A. Rauschenbeutel, P. Zoller, Chiral quantum optics with V-level atoms and coherent quantum feedback. Phys. Rev. A 94, 033829 (2016)

    Article  ADS  Google Scholar 

  47. D. Chen, Z. Fang, H. Cai, J. Geng, R. Qu, Instabilities in a grating feedback external cavity semiconductor laser. Opt. Express 16, 17014–17020 (2008)

    Article  ADS  Google Scholar 

  48. A. Wicht, M. Rudolf, P. Huke, R.H. Rinkleff, K. Danzmann, Grating enhanced external cavity diode laser. Appl. Phys. B 78, 137–144 (2004)

    Article  ADS  Google Scholar 

  49. U. Dorner, P. Zoller, Laser-driven atoms in half-cavities. Phys. Rev. A 66, 023816 (2002)

    Article  ADS  Google Scholar 

  50. M.J. Collett, C.W. Gardiner, Squeezing of intracavity and traveling-wave light fields produced in parametric amplification. Phys. Rev. A 30, 1386 (1984)

    Article  ADS  Google Scholar 

  51. C. W. Gardiner, Handbook of Stochastic Methods, (Springer,Berlin,1983)

  52. M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997)

    Book  Google Scholar 

  53. P. Meystre, M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin Heidelberg, 2007)

    Book  MATH  Google Scholar 

  54. E.A. Sete, H. Eleuch, Sumanta D, Semiconductor cavity QED with squeezed light: Nonlinear regime. Phys. Rev. A 84, 053817 (2011)

    Article  ADS  Google Scholar 

  55. S.K. Singh, C.H.O. Raymond, Quantum correlations of quadratic optomechanical oscillator. J. Opt. Soc. Am. B 31, 2390 (2014)

    Article  ADS  Google Scholar 

  56. S.M. Tan, A computational toolbox for quantum and atomic optics. J. Opt. B. 1, 424–432 (1999)

    Article  ADS  Google Scholar 

  57. S.K. Singh, Quantum dynamics and nonclassical photon statistics of coherently driven Raman transition in bimodal cavity. J. Modern Opt. 56, 562–570 (2019)

    Article  ADS  Google Scholar 

  58. P.D. Nation, J.R. Johansson, QuTiP: Quantum toolbox in Python, http://code.google.com/p/qutip, 2011

  59. P. Michler, A. Kiraz, C. Becher, W.V. Schoenfeld, P.M. Petroff, L. Zhang, E. Hu, A. Imamoglu, A Quantum Dot Single-Photon Turnstile Device. Science 22, 2282–2285 (2000)

    Article  ADS  Google Scholar 

  60. H.I. Veena, M. Rekha, P. Anshu, Low Threshold Quantum Dot Lasers. J. Phys. Chem. Lett. 7, 1244–1248 (2016)

    Article  Google Scholar 

  61. J. Wiersig, C. Gies, F. Jahnke, S. Reitzenstein, A. Forchel, Direct observation of correlations between individual photon emission events of a microcavity laser. Nature 460, 245–249 (2009)

    Article  ADS  Google Scholar 

  62. Y. Guo, C. Peng, Xiaomin G, Photon statistics and bunching of a chaotic semiconductor laser. Opt. Express 26, 5991–6000 (2018)

    Article  ADS  Google Scholar 

  63. F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Hofling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, I. Kanter, Observing chaos for quantum-dot microlasers with external feedback. Nat. Commun. 2, 366 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  65. W. Vogel, Dirk Gunnar Welsch, Quantum Optics, Wiley(Third Edition)

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Singh, S.K. Optical feedback-induced dynamics and nonclassical photon statistics of semiconductor microcavity laser. Appl. Phys. B 127, 90 (2021). https://doi.org/10.1007/s00340-021-07632-7

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