Condensation Of Photons Research Articles

Dynamics of Phase Coherence Onset in Bose Condensates of Photons by Incoherent Phonon Emission

Recent experiments with photons equilibrating inside a dye medium in a cavity have raised the question of whether Bose condensation can occur in a system with only incoherent interaction with phonons in a bath but without particle-particle interaction. Analytical calculations analogous to those done for a system with particle-particle interactions indicate that a system of bosons interacting only with incoherent phonons can indeed undergo Bose condensation and furthermore can exhibit spontaneous amplification of quantum coherence. We review the basic theory for these calculations.

When does single-mode lasing become a condensation phenomenon?

We present a generic route to classical light condensation (LC) in linear photonic mode systems, such as cw lasers, with different grounds from regular Bose-Einstein condensation (BEC). LC is based on weighting the modes in a noisy environment (spontaneous emission, etc.) in a loss-gain scale, rather than in photon energy. It is characterized by a sharp transition from a multi- to single-mode oscillation. The study uses a linear multivariate Langevin formulation which gives a mode occupation hierarchy that functions like Bose-Einstein statistics. Condensation occurs when the spectral filtering has near the lowest-loss mode a power law dependence with exponent smaller than 1. We then discuss how condensation can occur in photon systems, its relation to lasing and the difficulties to observe regular photon-BEC in laser cavities. We raise the possibility that experiments on photon condensation in optical cavities fall in a classical LC or lasing category rather than being a thermal-quantum BEC phenomenon.

Phase Transition and Superfluid of Photons and Photon Pairs in a Two-Dimensional Optical Microcavity

We analyze the ground-state properties and the excitation spectrum of Bose—Einstein condensates of photons and PPs in a two-dimensional optical microcavity. First, using the variational method, we discuss the ground-state phase transition of the two-component system. We also investigate the energy gap between the ground state and the first excited state. Moreover, by investigating the excitation spectrum, we also illustrate how the superfluid behavior of photons and PPs can be associated with the phase transition of the system.

Coupled condensates of excitons and photons in the trap

The properties of traps for exciton polaritons in a semiconductor optical microcavity with an embedded quantum well were considered. The two-component Bose condensate of photons and excitons was described by a coupled system of equations similar to the Gross-Pitaevskii equations, and analytical solutions in the Thomas-Fermi approximation were obtained for traps with weak exciton confinement. For strong confinement, condensate behavior was investigated numerically, and spatial profiles of coupled condensates of excitons and photons (which appear to be different in general case) were determined.

Temperature dependence of the energy-level shift induced by the Bose—Einstein condensation of photons

We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose—Einstein condensation of photons. It is found that below the critical temperature Tc, the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T. Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.

Bose—Einstein Condensation of Photons and Photon Pairs

We investigate the Bose-Einstein condensation of photons and photon pairs in a two-dimension optical microcavity. We find that in the paraxial approximation, the mixed gas of photons and photon pairs is formally equivalent to a two dimension system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phase. We also discuss the quantum phase transition of the system and obtain the critical point analytically. Moreover, we find that the quantum phase transition of the system can be interpreted as second harmonic generation.

Thermalization of a two-dimensional photon gas in a polymeric host matrix

We investigate thermodynamic properties of a two-dimensional photon gas confined by a dye-filled optical microcavity. A thermally equilibrated state of the photon gas is achieved by radiative coupling to a heat bath that is realized with dye molecules embedded in a polymer at room temperature. The chemical potential of the gas is freely adjustable. The optical microcavity consisting of two curved mirrors induces both a non-vanishing effective photon mass and a harmonic trapping potential for the photons. While previous experiments of our group have used liquid dye solutions, the measurements described here are based on dye molecules incorporated into a polymer host matrix. The solid state material allows a simplified operation of the experimental scheme. We furthermore describe studies of fluorescence properties of dye-doped polymers, and verify the applicability of Kennard–Stepanov theory in this system. In the future, dye-based solid state systems hold promise for the realization of single-mode light sources in thermal equilibrium based on Bose–Einstein condensation of photons, as well as for solar energy concentrators.

Difference in Bose-Einstein condensation of conserved and unconserved particles

The peculiarities in the Bose-Einstein condensation of particles and quasiparticles are discussed. The difference between the condensation of conserved and unconserved particles is analyzed. A classification of quasiparticles is given. The emphasis is made on the ability of particles and quasiparticles to condense. Illustrations include: general Bose-condensed atomic systems, such as ensembles of trapped atoms, Bose gases with conserved and unconserved number of atoms, vibrating atoms in double-well lattices, Holstein-Primakoff magnons, Schwinger bosons, slave bosons, and the condensation of singletons and triplons. The basic difference is that the system of particles, whose total number is conserved, can form equilibrium as well as nonequilibrium condensates, while unconserved particles can condense only in a nonequilibrium system subject to external pumping supporting the density of these particles sufficient for their condensation. The examples of such a nonequilibrium condensation of unconserved particles are the Bose-Einstein condensation of excitons, polaritons, and photons. Elementary collective excitations, such as bogolons and phonons, being self-consistently defined, do not condense. Magnons cannot condense in equilibrium systems. Controversies, existing in literature with regard to the Bose-Einstein condensation of some quasiparticles, are explained. Pushing a system out of equilibrium may favor the condensation of unconserved quasiparticles, but suppresses the condensate fraction of conserved particles.

Photon condensation in circuit quantum electrodynamics by engineered dissipation

We study photon condensation phenomena in a driven and dissipative array of superconducting microwave resonators. Specifically, we show that by using an appropriately designed coupling of microwave photons to superconducting qubits, an effective dissipative mechanism can be engineered, which scatters photons towards low-momentum states while conserving their number. This mimics a tunable coupling of bosons to a low-temperature bath, and leads to the formation of a stationary photon condensate in the presence of losses and under continuous-driving conditions. In this paper, we propose a realistic experimental setup to observe this effect in two or multiple coupled cavities, and study the characteristics of such an out-of-equilibrium condensate, which arise from the competition between pumping and dissipation processes.

Does Bose-Einstein condensation of CMB photons cancelμdistortions created by dissipation of sound waves in the early Universe?

The difference in the adiabatic indices of photons and non-relativistic baryonic matter in the early Universe causes the electron temperature to be slightly lower than the radiation temperature. Thermalization of photons with a colder plasma results in the accumulation of photons in the Rayleigh-Jeans tail, aided by stimulated recoil, while the higher frequency spectrum tries to approach Planck spectrum at the electron temperature $T_{\gamma}^{final}=\Te<T_{\gamma}^{initial}$; i.e., Bose-Einstein condensation of photons occurs. We find new solutions of the Kompaneets equation describing this effect. No actual condensate is, in reality, possible since the process is very slow and photons drifting to low frequencies are efficiently absorbed by bremsstrahlung and double Compton processes. The spectral distortions created by Bose-Einstein condensation of photons are within an order of magnitude (for the present range of allowed cosmological parameters), with exactly the same spectrum but opposite in sign, of those created by diffusion damping of the acoustic waves on small scales corresponding to comoving wavenumbers $45< k< 10^4\, Mpc^{-1}$. The initial perturbations on these scales are completely unobservable today due to their being erased completely by Silk damping. There is partial cancellation of these two distortions, leading to suppression of $\mu$ distortions expected in the standard model of cosmology. The net distortion depends on the scalar power index $n_S$ and its running $d n_S/d\ln k$, and may vanish for special values of parameters, for example, for a running spectrum with, $n_S=1,d n_S/d\ln k=-0.038$. We arrive at an intriguing conclusion: even a null result, non-detection of $\mu$-type distortion at a sensitivity of $10^{-9}$, gives a quantitative measure of the primordial small-scale power spectrum.

Temperature Dependence of Atomic Decay Rate

We investigate the decay rate of an atom in a two-dimensional optical microcavity in which there exists a Bose-Einstein condensation of photons. It is found that below the critical temperature Tc, the atomic decay rate depends on the absolute temperature T. Especially, at absolute zero temperature almost all photons are in the condensate state, and the atom can be approximately treated as if it is in vacuum.

Bose-Einstein Condensate-Hidden Riches for New Forms of Technology and Energy Generation; Potential for Glimpse into Inner Reality

Abstract With the announcement of t he recent successful production of a Bose-Einstein condensate (BEC) of photons, a circle has been completed which started in 1925 with the vision of Albert Einstein and Satyendra Nath Bose – a sustained macroscopic condensed state of matter where all atoms are in the same lowest quantum state. The creation of an all-optical BEC, involving a surprisingly straightforward “tabletop” method which bypasses the normally requisite laser/evaporative cooling equipment and ultra-high vacuum chambers necessary for production of the standard delicate atomic BEC, elevates this phenomenon to a new level well beyond its current perception as mere laboratory curiosity. Accordingly, this development certainly heralds eventual incorporation of atomic and photon BECs as standard operating components of energy-efficient mechanical, optical and electrical systems, implying novel ingenious engineering protocols amenable to all the tools of non-linear and quantum optics. Pointing towards such a promising technological future are the suggestion that a photon BEC could serve as a new high-energy ultra-violet (UV) laser photon source, as well as the recent unprecedented implementation of a closed-loop atom circuit (toroidal atomic BEC) demonstrating precise control of superfluid current flow, forecasting the coveted development of an atomic SQUID. Perhaps more significantly, the new highly robust and manageable optical BEC will allow heretofore unfathomable precise probing of the atomic and nano-levels of nature, affording novel high-quality testing procedures of the major foundations of quantum mechanics itself. Such a primary advancement, providing a clearer glimpse into the microscopic realms, may present us as never before with an unprecedented view of the quantum engine that underpins physical reality itself and help place the contextual nature of entanglement and quantum superposition on a firmer foundation. Thus, further progress in achieving mastery over the precise flexible manipulation of BEC states could demonstrate that quantum contextuality might be an unsuspected over-arching archetypal principle in nature, leading to new insight in regards to the interpretation of quantum mechanics as applied to all levels of nature. Moreover, it will be shown that this concealed and hence heretofore unsuspected contextual aspect of natural laws, as exemplified by the dynamics underlying BEC structure, could be brought to bear to account for physical anomalies inexplicable using current paradigms, such as the claimed energy yields from low-energy nuclear reactions (as represented by the so-called process of “cold fusion”), making this phenomenon more tractable and rendered less controversial.

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.

Bose-Einstein condensate of cavity exciton polaritons in a trap

The properties of traps for exciton polaritons in a semiconductor microcavity with an embedded quantum well have been considered. The behavior of the two-component Bose-Einstein condensate of photons and excitons described by the coupled system of Gross-Pitaevskii equations has been investigated. The analytical solutions for weak-confinement traps have been found in the Thomas-Fermi approximation. In the case of strong confinement, the behavior of the condensate has been investigated and constraints on the possible values of the chemical potential of the system have been obtained. The wavefunctions and generally different spatial profiles of the coupled photon and exciton condensates have been found.

Bose-Einstein condensation of photons in a 'white-wall' photon box

Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, has been observed in cold atomic gases and solid-state physics quasiparticles. In contrast, photons do not show this phase transition usually, because in Planck's blackbody radiation the particle number is not conserved and at low temperature the photons disappear in the walls of the system. Here we report on the realization of a photon Bose-Einstein condensate in a dye-filled optical microcavity, which acts as a "white-wall" photon box. The cavity mirrors provide a trapping potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped massive bosons. Thermalization of the photon gas is reached in a number conserving way by multiple scattering off the dye molecules. Signatures for a BEC upon increased photon density are: a spectral distribution that shows Bose-Einstein distributed photon energies with a macroscopically populated peak on top of a broad thermal wing, the observed threshold of the phase transition showing the predicted absolute value and scaling with resonator geometry, and condensation appearing at the trap centre even for a spatially displaced pump spot.

From exciton to photon condensation via polariton in electron-holephoton systems

We present a unified theoretical description of the quantum condensates in the electron-hole-photon (ehp) systems, which covers all condensates of exciton, polariton, and photon. To build such model, a phenomenological mean-field treatment for the exciton condensation is employed and extended to include the photon degree of freedom. We clarify changes from exciton/polariton condensations in the low-density limit to photon condensation in the high-density limit as a function of the detuning and the density. Clear change in the microscopic quantities are also found; the carrier distribution function shows broadening in the momentum space, and the minimal excitation energy for breaking an electron-hole (eh) pair increases even in the high density limit. Along this change, relative motion of electron and hole is confined within a tiny radius. In other words, the Wannier-type exciton-polariton picture is replaced by the Frenkel-type. This indicates that the smallest length scale of the system (corresponding to some ultraviolet cutoff) plays important roles due to the presence of coupling between carriers and coherent photons. These features show a remarkable contrast from the scenario of BEC-BCS crossover in the eh systems.

Bose–Einstein condensation of photons in an optical microcavity

Bose-Einstein condensation (BEC)-the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density-has been observed in several physical systems, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state. Theoretical works have considered thermalization processes that conserve photon number (a prerequisite for BEC), involving Compton scattering with a gas of thermal electrons or photon-photon scattering in a nonlinear resonator configuration. Number-conserving thermalization was experimentally observed for a two-dimensional photon gas in a dye-filled optical microcavity, which acts as a 'white-wall' box. Here we report the observation of a Bose-Einstein condensate of photons in this system. The cavity mirrors provide both a confining potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped, massive bosons. The photons thermalize to the temperature of the dye solution (room temperature) by multiple scattering with the dye molecules. Upon increasing the photon density, we observe the following BEC signatures: the photon energies have a Bose-Einstein distribution with a massively populated ground-state mode on top of a broad thermal wing; the phase transition occurs at the expected photon density and exhibits the predicted dependence on cavity geometry; and the ground-state mode emerges even for a spatially displaced pump spot. The prospects of the observed effects include studies of extremely weakly interacting low-dimensional Bose gases and new coherent ultraviolet sources.

Particles of light

Bose–Einstein condensation, which demonstrates the wave nature of material particles, now offers further illumination of wave–particle duality: it has been observed in light itself. See Letter p.545 Bose–Einstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. However, it becomes theoretically possible in the presence of thermalization processes that conserve photon number. Martin Weitz and colleagues have now realized such conditions experimentally, observing Bose–Einstein condensation of photons in a dye-filled optical microcavity. The effect is of interest for fundamental studies and may lead to new coherent ultraviolet sources.

Thermalization of a two-dimensional photonic gas in a ‘white wall’ photon box

Bose-Einstein condensation, the macroscopic accumulation of bosonic particles in the energetic ground state below a critical temperature, has been demonstrated in several physical systems. The perhaps best known example of a bosonic gas, blackbody radiation, however exhibits no Bose-Einstein condensation at low temperatures. Instead of collectively occupying the lowest energy mode, the photons disappear in the cavity walls when the temperature is lowered - corresponding to a vanishing chemical potential. Here we report on evidence for a thermalised two-dimensional photon gas with freely adjustable chemical potential. Our experiment is based on a dye filled optical microresonator, acting as a 'white-wall' box for photons. Thermalisation 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. As a striking example for the unusual system properties, we demonstrate a yet unobserved light concentration effect into the centre of the confining potential, an effect with prospects for increasing the efficiency of diffuse solar light collection.

Influence of temperature on the Bose condensation of photons and excitons in optic microcavity

In this paper, an exciton-photon model is created in an optic microcavity, and then in Bose condensation (BC), the variations of chemical potential range and number density of particles with temperature and position are studied in cases: constant width and varying width. Taking a semiconductor optic microcavity GaAs as example, the influence of temperature on BC is analyzed. The result shows that the range of chemical potential is related to dielectric function and microcavity width, while the number densities of photons and excitons and the sum of both particle numbers are related not only to them but also to temperature. The theoretical temperature of BC of GaAs is close to the experimental value. The densities of photons and excitons are almost equal, and their distributions are restricted to r=0 when BC occurs. With the reduction of temperature the number densities of both particles increase and their distributions expand, and the number of photons is more than that of excitons no matter how the width of optic microcavity changes.