Photon Gas Research Articles

Thermalization kinetics of light: From laser dynamics to equilibrium condensation of photons

We report a time-resolved study of the thermalization dynamics and the lasing to photon Bose-Einstein condensation crossover by in-\textit{situ} monitoring the photon kinetics in a dye microcavity. When the equilibration of the light to the dye temperature by absorption and re-emission is faster than photon loss in the cavity, the optical spectrum becomes Bose-Einstein distributed and photons accumulate at low-energy states, forming a Bose-Einstein condensate. The thermalization of the photon gas and its evolution from nonequilibrium initial distributions to condensation is monitored in real-time. In contrast, if photons leave the cavity before they thermalize, the system operates as a laser.

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: III. Galactic far-infrared radiation

Using the three-component spectral model describing the FIRAS average continuum spectra, the exact analytical expressions for thermodynamic and radiative functions of Galactic far-infrared radiation are obtained. The COBE FIRAS instrument data in the 0.15–2.88 THz frequency interval at the mean temperatures of T1 = 17.72 K, T2 = 14 K and T3 = 6.73 K are used for calculating the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, total emissivity, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume and pressure for the warm, intermediate-temperature and very cold components of the Galactic continuum spectra. The generalized Stefan-Boltzmann law for warm, intermediate-temperature and very cold components is constructed. The temperature dependence of each component is determined by the formula IS–B(T) = σ′T6. This result is important when we construct the cosmological models of radiative transfer that can be applied inside the Galaxy. Within the framework of the three-component spectral model, the total number of photons in our Galaxy and the total radiation power (total luminosity) emitted from a surface of the Galaxy are calculated. Their values are NGtotal = 1.3780 × 1068 and IGtotal(T) = 1.0482 × 1036 W. Other radiative and thermodynamic properties of the Galactic far-infrared radiation (photon gas) of the Galaxy are calculated. The expressions for astrophysical parameters, such as the entropy density/Boltzmann constant and number density of the Galactic far-infrared photons are obtained. We assume that the obtained analytical expressions for thermodynamic and radiative functions may be useful for describing the continuum spectra of the far-infrared radiation for other galaxies.

Spectroscopic analysis of the phase diagram of Yang-Mills-Higgs theory

Yang-Mills-Higgs theory, being the standard-model Higgs sector for a suitable choice of gauge and custodial group, offers a rich set of physics. In particular, in some region of its parameter space it has QCD-like behavior, while in some other region it is Higgs-like. Therefore, it is possible to study a plethora of phenomena within a single theory. Here, the physics of the standard-model version is studied using lattice gauge theory. To this end, the low-lying spectrum in several different channels is obtained for more than 140 different sets of bare parameters throughout the phase diagram. The theory shows quite different behaviors in the different regions, from almost Yang-Mills-like to the one of an essentially free gas of massive photons. Especially, not always is the behavior as naively expected.

Homoclinic accretion solutions in the Schwarzschild–anti–de Sitter space-time

The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild-anti-de Sitter spacetime. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultra-hard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michel's solutions in the Schwarzschild spacetime. In contrast to that global solutions should not exist for matter models with a non-vanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.

Fluctuations in particle number for a photon gas

The fluctuation-compressibility theorem of statistical mechanics states that fluctuations in particle number are proportional to the isothermal compressibility. Given that the compressibility of a photon gas does not exist, this seems to suggest that fluctuations in photon number similarly do not exist. However, it is shown here that the fluctuation-compressibility theorem does not hold for photons and, in fact, that fluctuations do exist.

Thermalization and breakdown of thermalization in photon condensates

We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot ``phase diagrams'' distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence ${g}^{(2)}$ and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.

Effects of dissipation on the superfluid–Mott-insulator transition of photons

We investigate the superfluid--Mott-insulator transition of a two-dimensional photon gas in a dye-filled optical microcavity and in the presence of a periodic potential. We show that in the random-phase approximation the effects of the dye molecules, which generally lead to dissipation in the photonic system, can be captured by two dimensionless parameters that only depend on dye-specific properties. Within the mean-field approximation, we demonstrate that one of these parameters decreases the size of the Mott lobes in the phase diagram. By considering also Gaussian fluctuations, we show that the coupling with the dye molecules results in a finite lifetime of the quasiparticle and quasihole excitations in the Mott lobes. Moreover, we show that there are number fluctuations in the Mott lobes even at zero temperature and therefore that the true Mott-insulating state never exists if the interactions with the dye are included.

Light Red Shift in Cosmic Background Photon Gas

There is a stable cosmic background photon gas fulfilled in our universe and a very weak damping force is acting on every traveling photon, then the light red shift has been observed at a large distance. When a photon travels in the cosmic background photon gas, its frequency continually lowers and at last diminishes in the photon gas as a low velocity one. The decay factor of traveling photons has been estimated; the light red shift is nonlinear in space, and our visual field is finite although the universe is infinite.

Thermal Ground State and Nonthermal Probes

The Euclidean formulation of SU(2) Yang-Mills thermodynamics admits periodic, (anti)self-dual solutions to the fundamental, classical equation of motion which possess one unit of topological charge: (anti)calorons. A spatial coarse graining over the central region in a pair of such localised field configurations with trivial holonomy generates an inert adjoint scalar fieldϕ, effectively describing the pure quantum part of the thermal ground state in the induced quantum field theory. Here we show for the limit of zero holonomy how (anti)calorons associate a temperature independent electric permittivity and magnetic permeability to the thermal ground state ofSU2CMB, the Yang-Mills theory conjectured to underlie the fundamental description of thermal photon gases.

Cosmological perturbations in the (1 + 3 + 6)-dimensional space-times

Cosmological perturbations in the (1+3+6)-dimensional space-times including photon gas without viscous processes are studied on the basis of Abbott et al.'s formalism. Space-times consist of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section). The inner space expands initially and contracts later. Abbott et al. derived only power-type solutions in the small wave-number limit which appear at the final stage of the space-times. In this paper, we derive not only small wave-number solutions, but also large wave-number solutions. It is found that the latter solutions depend on the two wave-numbers k_r and k_R (which are defined in the outer and inner spaces, respectively), and that the k_r-dependent and k_R-dependent parts dominate the total perturbations when (k_r/r(t))/(k_R/R(t)) >> 1 or << 1, respectively, where r(t) and R(t) are the scale-factors in the outer and inner spaces. By comparing the behaviors of these perturbations, moreover, changes in the spectrum of perturbations in the outer space with time are discussed.

Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral

In this article, we discuss some well-known theoretical models where an observer-independent energy scale or a length scale is present. The presence of this invariant scale necessarily deforms the Lorentz symmetry. We study different aspects and features of such theories about how modifications arise due to this cutoff scale. First we study the formulation of energy-momentum tensor for a perfect fluid in doubly special relativity (DSR), where an energy scale is present. Then we go on to study modifications in thermodynamic properties of photon gas in DSR. Finally we discuss some models with generalized uncertainty principle (GUP).

Bose-Einstein condensation of photons with nonlocal nonlinearity in a dye-doped graded-index microcavity

We consider a microcavity made by a graded-index (GRIN) glass, doped by dye molecules, placed within two planar mirrors and study Bose-Einstein condensation (BEC) of photons. The presence of the mirrors leads to an effective photon mass, and the index grading provides an effective trapping frequency; the photon gas becomes formally equivalent to a two dimensional Bose gas trapped in an isotropic harmonic potential. The inclusion of nonlinear effects provides an effective interaction between photons. We discuss, in particular, thermal lensing effects and nonlocal nonlinearity, and quantitatively compare our results with the reported experimental data.

On photon emission and absorption from electronic transitions in an ideal potential well

Within the one-electron approximation, we investigate, in a new way, the main aspects of photon emission and absorption processes from electronic transitions in an ideal one-dimensional potential well. As a matter of fact, we calculate a lower bound for the absolute temperature of the involved photon gas. In addition, a lower bound for the electron Fermi energy is determined.

Thermodynamics of a photon gas in nonlinear electrodynamics

In this paper we analyze the thermodynamic properties of a photon gas under the influence of a background electromagnetic field in the context of any nonlinear electrodynamics. Neglecting the self-interaction of photons, we obtain a general expression for the grand canonical potential. Particularizing for the case when the background field is uniform, we determine the pressure and the energy density for the photon gas. Although the pressure and the energy density change when compared with the standard case, the relationship between them remains unaltered, namely ρ=3p. Finally, we apply the developed formulation to the cases of Heisenberg–Euler and Born–Infeld nonlinear electrodynamics. For the Heisenberg–Euler case, we show that our formalism recovers the results obtained with the 2-loop thermal effective action approach.

Exact Solutions of the Kompaneets Equation for Photon “Comptonization” Kinetics

The nonlinear Kompaneets equation for the evolution of the spectrum of a photon gas with Compton scattering in a rarefied nonrelativistic electron plasma (i.e., the “comptonization” of the radiation) is examined. Exact solutions of this equation are obtained by separation of variables. The solutions are expressed in terms of transcendental Heun and Bessel functions.

Satyendra Nath Bose and nanophotonics

ITMO University, Saint-Petersburg, 197101, RussiaAbstract. This paper is devoted to the 90th anniversary of the 1924 publication of the seminalpaperbyBosetitled “Planck’slawandthehypothesisonlightquanta”(ZeitschriftfurPhysik26,178–181). The paper has been the cornerstone quantum statistical physics. Remarkably, theverystartingideaisthediscretenessofphasespaceexpressedintheformofthedensityofstates.Boseconsidered equilibrium electromagnetic radiation as gas of photons and, therefore, introducedthe photon density of states notion into the physics though without using directly the term “den-sity of states.” Today, engineering photon density of states to modify light-matter interaction innanostructures including both spontaneous emission and spontaneous scattering of photons con-stitutes the solid part of nanophotonics.

Effect of the Minimal Length on the Thermodynamics of Ultra-Relativistic Ideal Fermi Gas

Based on the generalized uncertainty principle, the thermodynamics of Fermi gas in high density, high pressure and high temperature are calculated. As the temperature and density increases, the energy and entropy becomes saturated and the pressure blows up without any bound. Using the conservation equation of the Robertson—Walker cosmology, we find that, when the energy exceeds the EH = β0−1/2c2Mp, the expansion cannot be driven by the photon gas and the fermion gas. This requires some new physical mechanism related to quantum gravity, such as tachyons and dilatons.

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: II. Extragalactic far infrared background radiation

Using the three-component spectral model describing the FIRAS average continuum spectra, the analytical expressions for the temperature dependence of the thermodynamic and radiative functions of the galactic far-infrared radiation are obtained. The COBE FIRAS instrument data in the 0.15 - 2.88 THz frequency interval at the mean temperatures T = 17.72 K, T = 14 K, and T =6.73 K are used for calculating the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, total emissivity, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume and pressure for the warm, intermediate-temperature and very cold components of the Galactic continuum spectra. The generalized Stefan-Boltzmann laws for the warm, intermediate-temperature and very cold components are constructed. This result is important when we construct the cosmological models of radiative transfer in the inner Galaxy. Within the framework of the three- component spectral model, the total number of photons in our Galaxy and the total radiation power (total luminosity) emitted from the surface of the Galaxy are calculated. Other radiative and thermodynamic properties of the galactic far-infrared radiation (photon gas) for the Galaxy are presented. The expressions for astrophysical parameters, such as the entropy density/Boltzmann constant, and number density of the galactic far-infrared photons are obtained. We assume that the obtained analytical expressions for thermodynamic and radiative functions may be useful for describing the continuum spectra of the far-infrared radiation for outer galaxies.

Heat and Gravitation: The Action Principle

This first article of a series formulates the thermodynamics of ideal gases in a constant gravitational field in terms of an action principle that is closely integrated with thermodynamics. The theory, in its simplest form, does not deviate from standard practice, but it lays the foundations for a more systematic approach to the various extensions, such as the incorporation of radiation, the consideration of mixtures and the integration with General Relativity. We study the interaction between an ideal gas and the photon gas, and propose a new approach to this problem. We study the propagation of sound in a vertical, isothermal column and are led to suggest that the theory is incomplete, and to ask whether the true equilibrium state of an ideal gas may turn out be adiabatic, in which case the role of solar radiation is merely to compensate for the loss of energy by radiation into the cosmos. An experiment with a centrifuge is proposed, to determine the influence of gravitation on the equilibrium distribution with a very high degree of precision.

A scheme to observe universal breathing mode and Berezinskii–Kosterlitz–Thouless phase transition in a two-dimensional photon gas

A system of two-dimensional photon gas has recently been realized experimentally. We show that this setup can be used to observe a universal breathing mode of photon gas and a modification in the experimental setup would open up a possibility of observing the Berezinskii–Kosterlitz–Thouless (BKT) phase transition in such a system. Furthermore, the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.