Bose–Einstein condensation of paraxial light

Photons, due to the virtually vanishing photon–photon interaction, constitute to very good approximation an ideal Bose gas, but owing to the vanishing chemical potential a (free) photon gas does not show Bose–Einstein condensation. However, this is not necessarily true for a lower-dimensional photon gas. By means of a fluorescence induced thermalization process in an optical microcavity one can achieve a thermal photon gas with freely adjustable chemical potential. Experimentally, we have observed thermalization and subsequently Bose–Einstein condensation of the photon gas at room temperature. In this paper, we give a detailed description of the experiment, which is based on a dye-filled optical microcavity, acting as a white-wall box for photons. Thermalization is achieved in a photon number-conserving way by photon scattering off the dye molecules, and the cavity mirrors both provide an effective photon mass and a confining potential-key prerequisites for the Bose–Einstein condensation of photons. The experimental results are in good agreement with both a statistical and a simple rate equation model, describing the properties of the thermalized photon gas.

[1]  Alfons Penzkofer,et al.  Fluorescence Behaviour of Highly Concentrated Rhodamine 6G Solutions , 1987 .

[2]  S. Viefers,et al.  Effective photon-photon interaction in a two-dimensional "photon fluid" (20 pages) , 2003, physics/0309065.

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

[4]  Douglas Magde,et al.  Fluorescence Quantum Yields and Their Relation to Lifetimes of Rhodamine 6G and Fluorescein in Nine Solvents: Improved Absolute Standards for Quantum Yields¶ , 2002, Photochemistry and photobiology.

[5]  D. Solnyshkov,et al.  Formation of an exciton polariton condensate: thermodynamic versus kinetic regimes. , 2008, Physical review letters.

[6]  S. Noda,et al.  Full three-dimensional photonic bandgap crystals at near-infrared wavelengths , 2000, Science.

[7]  J. Hickmann,et al.  Weak-wave advancement in nearly collinear four-wave mixing. , 2002, Optics express.

[8]  B. Levit,et al.  Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser. , 2010, Optics express.

[9]  R. Chiao.  Bogoliubov dispersion relation for a `photon fluid': Is this a superfluid? 1 It is a great pleasure , 1999, quant-ph/9908060.

[10]  K. Helmerson,et al.  Observation of a 2D Bose gas: from thermal to quasicondensate to superfluid. , 2008, Physical review letters.

[11]  Meschede,et al.  Suppression of spontaneous decay at optical frequencies: Test of vacuum-field anisotropy in confined space. , 1987, Physical review letters.

[12]  T. Wassmer.  6 , 1900, EXILE.

[13]  Alfons Penzkofer,et al.  Fluorescence quenching of rhodamine 6G in methanol at high concentration , 1986 .

[14]  D. Kleppner,et al.  Inhibited spontaneous emission by a Rydberg atom. , 1985, Physical review letters.

[15]  Maira Amezcua,et al.  Quantum Optics , 2012 .

[16]  Loudon,et al.  Spontaneous emission in the optical microscopic cavity. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[17]  K. B. Davis,et al.  Bose-Einstein Condensation in a Gas of Sodium Atoms , 1995, EQEC'96. 1996 European Quantum Electronic Conference.

[18]  Erich P. Ippen,et al.  Rapid photobleaching of organic laser dyes in continuously operated devices , 1971 .

[19]  Dynamics of atom-mediated photon-photon scattering , 2000, physics/0002014.

[20]  Michael Kasha,et al.  Characterization of electronic transitions in complex molecules , 1950 .

[21]  Markus Greiner,et al.  Emergence of a molecular Bose–Einstein condensate from a Fermi gas , 2003, Nature.

[22]  Eberhard E. Müller.  Bose-Einstein condensation of free photons in thermal equilibrium , 1986 .

[23]  A. Chao,et al.  Effect of nuclear deformation on high-energy proton--nucleus scattering , 1975 .

[24]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[25]  A. Meyer,et al.  Luminescent Solar Concentrators--a review of recent results. , 2008, Optics express.

[26]  C. Wieman,et al.  Bose-Einstein Condensation in Atomic Gases , 1999 .

[27]  C. Sackett,et al.  Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number , 1997 .

[28]  B. Richards,et al.  Measurement method for photoluminescent quantum yields of fluorescent organic dyes in polymethyl methacrylate for luminescent solar concentrators. , 2009, Applied optics.

[29]  Knox,et al.  Universal relationship between optical emission and absorption of complex systems: An alternative approach. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[30]  E. H. Kennard.  On The Thermodynamics of Fluorescence , 1918 .

[31]  G. Ozin,et al.  Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres , 2000, Nature.

[32]  T. Anan,et al.  Controlling spontaneous emission and threshold-less laser oscillation with optical microcavities , 1992 .

[33]  Low-dimensional trapped gases , 2004, cond-mat/0409230.

[34]  Joseph Georges,et al.  FLUORESCENCE QUANTUM YIELD OF RHODAMINE 6G IN ETHANOL AS A FUNCTION OF CONCENTRATION USING THERMAL LENS SPECTROMETRY , 1996 .

[35]  Mark Kac,et al.  The ideal Bose-Einstein gas, revisited , 1977 .

[36]  M. Weitz,et al.  Bose‐Einstein‐Kondensat aus Licht , 2011 .

[37]  Fluctuations in Ideal and Interacting Bose–Einstein Condensates: From the Laser Phase Transition Analogy to Squeezed States and Bogoliubov Quasiparticles ⁎ , 2006, cond-mat/0605507.

[38]  Gunnar Björk,et al.  Micro-cavity semiconductor lasers with controlled spontaneous emission , 1992 .

[39]  Frank Vewinger,et al.  Bose–Einstein condensation of photons in an optical microcavity , 2010, Nature.

[40]  De Martini F,et al.  Anomalous spontaneous-stimulated-decay phase transition and zero-threshold laser action in a microscopic cavity. , 1988, Physical review letters.

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

[42]  K. N. Dollman,et al.  - 1 , 1743 .

[43]  A. Lempicki,et al.  Long-pulse laser emission from rhodamine 6G , 1970 .

[44]  S. Kimura,et al.  磁場中でのS=1/2 擬一次元Ising様反強磁性体に関する新しい規則化 , 2008 .

[45]  R. H. Brown,et al.  A Test of a New Type of Stellar Interferometer on Sirius , 1956, Nature.

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

[47]  E. Purcell,et al.  The Question of Correlation between Photons in Coherent Light Rays , 1956, Nature.

[48]  L Angelani,et al.  Condensation in disordered lasers: theory, 3D+1 simulations, and experiments. , 2008, Physical review letters.

[49]  M. Planck.  Ueber das Gesetz der Energieverteilung im Normalspectrum , 1901 .

[50]  H. Kogelnik,et al.  Laser beams and resonators. , 1966, Applied optics.

[51]  I. Carusotto,et al.  Superfluidity of polaritons in semiconductor microcavities , 2009 .

[52]  B. Englert,et al.  Cavity quantum electrodynamics , 2006 .

[53]  P. Mataloni,et al.  Microcavity quantum superradiance , 2000 .

[54]  M. Dunn,et al.  Refractive indices and thermo-optical properties of dye laser solvents , 1987 .

[55]  Thermalization of a two-dimensional photonic gas in a `white wall' photon box , 2010, 1004.2956.

[56]  M. Wouters,et al.  Quantized vortices in an exciton–polariton condensate , 2008 .

[57]  Bose.  Plancks Gesetz und Lichtquantenhypothese , 1924 .

[58]  D. Goswami,et al.  Solvent effect on two-photon absorption and fluorescence of rhodamine dyes , 2009, Journal of photochemistry and photobiology. A, Chemistry.

[59]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[60]  H. Yokoyama,et al.  Rate equation analysis of microcavity lasers , 1989 .

[61]  Condensation of classical nonlinear waves. , 2005, Physical review letters.

[62]  W. Mullin.  A Study of Bose-Einstein Condensation in a Two-Dimensional Trapped Gas , 1997, cond-mat/9709077.

[63]  Valérie Doya,et al.  Condensation and thermalization of classsical optical waves in a waveguide , 2011 .

[64]  P. Mataloni,et al.  Anomalous spontaneous emission time in a microscopic optical cavity. , 1987, Physical review letters.

[65]  W. Zurek,et al.  Dissipative optical flow in a nonlinear Fabry-Pérot cavity. , 2001, Physical review letters.

[66]  B. B. Snavely,et al.  cw OPERATION OF AN ORGANIC DYE SOLUTION LASER , 1970 .

[67]  D. Haar,et al.  Fluctuations in the population of the ground state of Bose Systems , 1970 .

[68]  G. Aeppli,et al.  Proceedings of the International School of Physics Enrico Fermi , 1994 .

[69]  J. C. Martínez,et al.  Semiclassical quantization of the electromagnetic field confined in a Kerr-effect nonlinear cavity , 2006 .

[70]  Bose-Einstein condensation in a harmonic potential , 1996, cond-mat/9610005.

[71]  Baptiste Battelier,et al.  Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas , 2006, Nature.

[72]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[73]  R. Loudon,et al.  Spontaneous emission in microcavities , 2007 .

[74]  R. L. Campbell,et al.  Can a Bose gas be saturated? , 2011, Physical review letters.

[75]  D. Meschede,et al.  Radiating atoms in confined space: From spontaneous emission to micromasers , 1992 .

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

[77]  J. Lakowicz.  Principles of fluorescence spectroscopy , 1983 .

[78]  S. Jochim,et al.  Bose-Einstein Condensation of Molecules , 2003, Science.

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

[80]  M. S. Zubairy,et al.  Quantum optics: Frontmatter , 1997 .