Photon-Number-Resolved Measurement of an Exciton-Polariton Condensate.

We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.

[1]  S. Reitzenstein,et al.  Photon-Number-Resolving Transition-Edge Sensors for the Metrology of Quantum Light Sources , 2018 .

[2]  I. Savenko,et al.  Kinetic Monte Carlo approach to nonequilibrium bosonic systems , 2017, 1709.06260.

[3]  Christian Schneider,et al.  Exploring the Photon-Number Distribution of Bimodal Microlasers with a Transition Edge Sensor , 2017, Physical Review Applied.

[4]  M. Steger,et al.  Direct measurement of polariton–polariton interaction strength , 2017, Nature Physics.

[5]  A Knorr,et al.  A bright triggered twin-photon source in the solid state , 2016, Nature Communications.

[6]  S. Höfling,et al.  An exciton-polariton laser based on biologically produced fluorescent protein , 2016, Science Advances.

[7]  Patrick Y. Wen,et al.  Bose-Einstein Condensation of Long-Lifetime Polaritons in Thermal Equilibrium. , 2016, Physical review letters.

[8]  T. Ala‐Nissila,et al.  Evolution of Temporal Coherence in Confined Exciton-Polariton Condensates. , 2015, Physical review letters.

[9]  M. Kamp,et al.  Exciton-polariton trapping and potential landscape engineering , 2015, Reports on progress in physics. Physical Society.

[10]  Tim Byrnes,et al.  Exciton–polariton condensates , 2014, Nature Physics.

[11]  S. Brodbeck,et al.  Spatial coherence properties of one dimensional exciton-polariton condensates. , 2014, Physical review letters.

[12]  T. Damm,et al.  Observation of grand-canonical number statistics in a photon Bose-Einstein condensate. , 2013, Physical review letters.

[13]  J. Schmiedmayer,et al.  Prethermalization revealed by the relaxation dynamics of full distribution functions , 2012, 1212.4645.

[14]  S. Brodbeck,et al.  Coherence signatures and density-dependent interaction in a dynamical exciton-polariton condensate , 2012 .

[15]  Sven Höfling,et al.  Power-law decay of the spatial correlation function in exciton-polariton condensates , 2012, Proceedings of the National Academy of Sciences.

[16]  S. Höfling,et al.  From polariton condensates to highly photonic quantum degenerate states of bosonic matter , 2011, Proceedings of the National Academy of Sciences.

[17]  C. Schneider,et al.  Bose-einstein condensation of exciton polaritons in high-Q planar microcavities with GaAs quantum wells , 2010 .

[18]  M. Weitz,et al.  Bose–Einstein condensation of photons in an optical microcavity , 2010, Nature.

[19]  S. Höfling,et al.  Gain-induced trapping of microcavity exciton polariton condensates. , 2010, Physical review letters.

[20]  A. Forchel,et al.  Higher order coherence of exciton-polariton condensates , 2009, 0910.2978.

[21]  M. Bayer,et al.  Higher-Order Photon Bunching in a Semiconductor Microcavity , 2009, Science.

[22]  M. S. Skolnick,et al.  Intrinsic decoherence mechanisms in the microcavity polariton condensate. , 2008, Physical review letters.

[23]  Aaron J. Miller,et al.  Counting near-infrared single-photons with 95% efficiency. , 2008, Optics express.

[24]  B. Deveaud,et al.  Second-order time correlations within a polariton Bose-Einstein condensate in a CdTe microcavity. , 2008, Physical review letters.

[25]  P. Recher,et al.  Coherent zero-state and π-state in an exciton–polariton condensate array , 2007, Nature.

[26]  Isabelle Sagnes,et al.  Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities. , 2007, Physical review letters.

[27]  P. Schwendimann,et al.  Statistics of the polariton condensate , 2007, 0709.4123.

[28]  K. West,et al.  Bose-Einstein Condensation of Microcavity Polaritons in a Trap , 2007, Science.

[29]  J. Dalibard,et al.  Many-Body Physics with Ultracold Gases , 2007, 0704.3011.

[30]  G. Solomon,et al.  Spatial coherence of a polariton condensate. , 2007, Physical review letters.

[31]  V. Savona,et al.  Bose–Einstein condensation of exciton polaritons , 2006, Nature.

[32]  D. Sanvitto,et al.  Dominant effect of polariton-polariton interactions on the coherence of the microcavity optical parametric oscillator. , 2006, Physical review letters.

[33]  S. Girvin,et al.  Resolving photon number states in a superconducting circuit , 2006, Nature.

[34]  E. Demler,et al.  Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids , 2006, cond-mat/0602475.

[35]  Michael Köhl,et al.  Correlations and counting statistics of an atom laser. , 2005, Physical review letters.

[36]  F. Laussy,et al.  Spontaneous coherence buildup in a polariton laser , 2004 .

[37]  Gregor Weihs,et al.  Polariton lasing vs. photon lasing in a semiconductor microcavity , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[38]  V. Kulakovskii,et al.  Polariton parametric scattering processes in semiconductor microcavities observed in continuous wave experiments , 2002 .

[39]  A. Leggett,et al.  Bose-Einstein condensation in the alkali gases: Some fundamental concepts , 2001 .

[40]  C. Piermarocchi,et al.  Role of the exchange of carriers in elastic exciton-exciton scattering in quantum wells , 1998 .

[41]  Sae Woo Nam,et al.  Detection of single infrared, optical, and ultraviolet photons using superconducting transition edge sensors , 1998 .

[42]  A. Forchel,et al.  Weak and strong coupling of photons and excitons in photonic dots , 1998 .

[43]  Stephen M. Barnett,et al.  Methods in Theoretical Quantum Optics , 1997 .

[44]  C. Wieman,et al.  Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay , 1997 .

[45]  Rajeev J Ram,et al.  Nonequilibrium condensates and lasers without inversion: Exciton-polariton lasers. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[46]  Lucio Claudio Andreani,et al.  Quantum well excitons in semiconductor microcavities : unified treatment of weak and strong coupling regimes , 1995 .

[47]  C. Weisbuch,et al.  Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity. , 1992, Physical review letters.

[48]  A. Mann,et al.  Thermal Coherent States and Thermal Squeezed States , 1991 .

[49]  Marlan O. Scully,et al.  Quantum Theory of an Optical Maser. 1. General Theory , 1967 .

[50]  F. Arecchi,et al.  1A4 - Photocount distributions and field statistics , 1966 .

[51]  F. T. Arecchi,et al.  Measurement of the Statistical Distribution of Gaussian and Laser Sources , 1965 .

[52]  W. Marsden I and J , 2012 .

[53]  Jeff Dean,et al.  Time Series , 2009, Encyclopedia of Database Systems.

[54]  S. Pau,et al.  Exciton-Polaritons in Microcavities , 1994 .