Few emitters in a cavity: from cooperative emission to individualization

We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well-distinguished statistical properties of the emitted radiation. For small cavity decay rates, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared with the emitter–cavity coupling) and for a few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady-state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows us to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-the-art techniques of Q-switch of resonant cavities, allied with the recent capability of tuning single emitters in and out of resonance, suggest this system to be a versatile source of different quantum states of light.

[1]  Oliver G. Schmidt,et al.  In situ laser microprocessing of single self-assembled quantum dots and optical microcavities , 2007 .

[2]  A. Poddubny,et al.  Nonlinear emission spectra of quantum dots strongly coupled to a photonic mode , 2010, 1007.0244.

[3]  Detlef Hommel,et al.  Superradiance of quantum dots , 2007 .

[4]  A. Lemaître,et al.  Continuous-wave versus time-resolved measurements of Purcell-factors for quantum dots in semiconductor microcavities , 2009, 0906.0750.

[5]  V. Sandoghdar,et al.  A scanning microcavity for in-situ control of single-molecule emission , 2010, 1005.0236.

[6]  S. Huant,et al.  “Deterministic” quantum plasmonics. , 2010, Nano letters.

[7]  R. Loudon.  REVIEW ARTICLE: Non-classical effects in the statistical properties of light , 1980 .

[8]  Andrei Faraon,et al.  Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity , 2010, 1012.3815.

[9]  A Lemaître,et al.  Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity. , 2004, Physical review letters.

[10]  H. Carmichael.  Statistical Methods in Quantum Optics 2 , 2008 .

[11]  Bose-Einstein partition distribution in microcavity quantum superradiance , 2001 .

[12]  Young-Shin Park,et al.  Cavity QED with diamond nanocrystals and silica microspheres. , 2006, Nano letters.

[13]  A. Auffèves,et al.  Pure emitter dephasing: A resource for advanced solid-state single-photon sources , 2008, 0808.0820.

[14]  F. Jelezko,et al.  Creation efficiency of nitrogen-vacancy centres in diamond , 2010 .

[15]  V. Kulakovskii,et al.  Strong coupling in a single quantum dot–semiconductor microcavity system , 2004, Nature.

[16]  W. Scott,et al.  Group Theory. , 1964 .

[17]  Cristiano Ciuti,et al.  Extracavity quantum vacuum radiation from a single qubit , 2009, 0906.2706.

[18]  Serge Haroche,et al.  Superradiance: An essay on the theory of collective spontaneous emission , 1982 .

[19]  M. Holland,et al.  Steady-state superradiance with alkaline-earth-metal atoms , 2009, 0912.0690.

[20]  H. Weinfurter,et al.  Single photon emission from SiV centres in diamond produced by ion implantation , 2006 .

[21]  E. Kapon,et al.  Single-Photon Emission from Site-Controlled Pyramidal Quantum Dots , 2004 .

[22]  U. Banin,et al.  Cavity QED with semiconductor nanocrystals , 2006 .

[23]  E. Pike,et al.  The effect of atomic number fluctuations on photon antibunching in resonance fluorescence , 1977 .

[24]  Dirk Englund,et al.  Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade , 2008, 0804.2740.

[25]  F. Laussy,et al.  Entanglement and lasing with two quantum dots in a microcavity , 2007 .

[26]  J Wrachtrup,et al.  Strong coupling of a spin ensemble to a superconducting resonator. , 2010, Physical review letters.

[27]  F. Jelezko,et al.  Engineering single photon emitters by ion implantation in diamond. , 2009, Applied physics letters.

[28]  K. Mølmer,et al.  Wave-function approach to dissipative processes in quantum optics. , 1992, Physical review letters.

[29]  F. Laussy,et al.  Luminescence spectra of quantum dots in microcavities. II. Fermions , 2008, 0812.2694.

[30]  M. Holland,et al.  Intensity fluctuations in steady-state superradiance , 2010, 1005.0866.

[31]  R. Bonifacio,et al.  Quantum Statistical Theory of Superradiance. II , 1971 .

[32]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[33]  S. Combrie,et al.  GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55 microm. , 2008, Optics letters.

[34]  Ulrike Woggon,et al.  Photon statistics in the cooperative spontaneous emission. , 2009, Optics express.

[35]  Andrew G. Glen,et al.  APPL , 2001 .

[36]  H. Carmichael.  Statistical Methods in Quantum Optics 1 , 1999 .

[37]  G. Rupper,et al.  Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity , 2004, Nature.

[38]  L. DiCarlo,et al.  Demonstration of two-qubit algorithms with a superconducting quantum processor , 2009, Nature.

[39]  S. Gulde,et al.  Quantum nature of a strongly coupled single quantum dot–cavity system , 2007, Nature.

[40]  V. Sandoghdar,et al.  Near-infrared single-photons from aligned molecules in ultrathin crystalline films at room temperature. , 2010, Optics express.

[41]  Markus Sauer,et al.  Measuring the number of independent emitters in single-molecule fluorescence images and trajectories using coincident photons. , 2002, Analytical chemistry.

[42]  R. Dicke.  Coherence in Spontaneous Radiation Processes , 1954 .

[43]  Yoshinori Tanaka,et al.  Dynamic increase and decrease of photonic crystal nanocavity Q factors for optical pulse control. , 2008, Optics express.

[44]  Ronald Hanson,et al.  Fabrication and Characterization of Two-Dimensional Photonic Crystal Microcavities in Nanocrystalline Diamond , 2007 .

[45]  De Martini F,et al.  Bose-einstein partition statistics in superradiant spontaneous emission , 2000, Physical review letters.

[46]  L. Andreani,et al.  Controlling the dynamics of a coupled atom-cavity system by pure dephasing , 2010, 1002.3753.

[47]  F. Laussy,et al.  Effect of pure dephasing on the Jaynes-Cummings nonlinearities. , 2009, Optics express.

[48]  John Rarity,et al.  INTENSITY FLUCTUATION SPECTROSCOPY OF SMALL NUMBERS OF DYE MOLECULES IN A MICROCAVITY , 1998 .

[49]  Huan-Cheng Chang,et al.  Quantifying the number of color centers in single fluorescent nanodiamonds by photon correlation spectroscopy and Monte Carlo simulation , 2009 .

[50]  C. Schneider,et al.  Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system. , 2010, Nature materials.

[51]  R. Brouri,et al.  Photon antibunching in the fluorescence of individual color centers in diamond. , 2000, Optics letters.

[52]  D. Bouwmeester,et al.  Self-tuned quantum dot gain in photonic crystal lasers. , 2005, Physical review letters.

[53]  D. Walls,et al.  Intensity Correlations in Resonance Fluorescence with Atomic Number Fluctuations , 1978 .

[54]  H. Carmichael,et al.  Stochastic initiation of superradiance in a cavity: An approximation scheme within quantum trajectory theory , 2002 .

[55]  Engineering chromium-related single photon emitters in single crystal diamonds , 2010, 1009.5844.

[56]  M. Kaniber,et al.  Mutual coupling of two semiconductor quantum dots via an optical nanocavity , 2009, 0912.3685.

[57]  A. Dousse,et al.  Origin of the optical emission within the cavity mode of coupled quantum dot-cavity systems. , 2009, Physical review letters.

[58]  F. Arecchi,et al.  Atomic coherent states in quantum optics , 1972 .

[59]  M. Amann,et al.  Investigation of the nonresonant dot-cavity coupling in two-dimensional photonic crystal nanocavities , 2008, 0802.2008.

[60]  James E. Butler,et al.  Observation of whispering gallery modes in nanocrystalline diamond microdisks , 2007 .

[61]  이동욱.  12. M & A , 2000 .

[62]  H. Gibbs,et al.  Single-Pulse Superfluorescence in Cesium , 1977 .

[63]  U. Woggon,et al.  Superradiance and subradiance in an inhomogeneously broadened ensemble of two-level systems coupled to a low-Q cavity. , 2005, Physical review letters.

[64]  P. J. Harding,et al.  Dynamical ultrafast all-optical switching of planar GaAs/AlAs photonic microcavities , 2007, 0706.2385.

[65]  A Lemaître,et al.  Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography. , 2008, Physical review letters.

[66]  Mario Dagenais,et al.  Photon Antibunching in Resonance Fluorescence , 1977 .