Photon Gas Research Articles

An analogy of the size distribution of business firms with Bose–Einstein statistics

We approach the size distribution of business firms by proposing an analogy of the firms’ ranking with a boson gas, identifying the annual revenue of the firms with energy. We found that Bose–Einstein statistics fits very well to the empirical cumulative distribution function for the firms’ ranking for different countries. The fitted values for the temperature-like parameter are compared between countries and with an index of economic development, and we found that our results support the hypothesis that the temperature of the economy can be associated with the level of economic development of a country. Moreover, for most of the countries the value obtained for the fugacity-like parameter is close to 1, suggesting that the analogy could correspond to a photon gas in which the number of particles is not conserved; this is indeed the case for real-world firms’ dynamics, where new firms arrive in the economy and other firms disappear, either by merging with others or through bankruptcy.

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.

Electromagnetically induced transparency with single atoms in a cavity

Optical nonlinearities offer unique possibilities for the control of light with light. A prominent example is electromagnetically induced transparency (EIT), where the transmission of a probe beam through an optically dense medium is manipulated by means of a control beam. Scaling such experiments into the quantum domain with one (or just a few) particles of light and matter will allow for the implementation of quantum computing protocols with atoms and photons, or the realization of strongly interacting photon gases exhibiting quantum phase transitions of light. Reaching these aims is challenging and requires an enhanced matter-light interaction, as provided by cavity quantum electrodynamics. Here we demonstrate EIT with a single atom quasi-permanently trapped inside a high-finesse optical cavity. The atom acts as a quantum-optical transistor with the ability to coherently control the transmission of light through the cavity. We investigate the scaling of EIT when the atom number is increased one-by-one. The measured spectra are in excellent agreement with a theoretical model. Merging EIT with cavity quantum electrodynamics and single quanta of matter is likely to become the cornerstone for novel applications, such as dynamic control of the photon statistics of propagating light fields or the engineering of Fock state superpositions of flying light pulses.

Thermodynamics of a photon gas with an invariant energy scale

Quantum Gravity framework motivates us to find new theories in which an observer independent finite energy upper bound (preferably Planck Energy) exists. We have studied the modifications in the thermodynamical properties of a photon gas in such a scenario where we have an invariant energy scale. We show that the density of states and the entropy in such a framework are less than the corresponding quantities in Einstein's Special Relativity (SR) theory. This result can be interpreted as a consequence of the deformed Lorentz symmetry present in the particular model we have considered.

On the thermodynamics of moving bodies

We model the situation in which a photon detector moves with constant velocity in a Minkowski heat-bath by considering an Unruh-DeWitt detector, with variable energy gap ℏω, moving on a brane, at a non-zero (Unruh) temperature T due to acceleration in an orthogonal direction. We compute the angular response for a 2-brane. At low velocity we find agreement with the standard Doppler shift formula in the limit ℏω ≫ T in which the photon gas is classical; otherwise there is a discrepancy. At relativistic velocities our result disagrees with the standard formula even when ℏω ≫ T, and above a critical velocity there is no response from the detector within a 'backward' cone. We discuss potential implications for observations of the cosmic microwave background radiation. [Talk given by JGR at this 1st Mediterranean Conference in Classical and Quantum Gravity].

Radiative heat exchange between spherical particles caused by fluctuation electromagnetic field

Expressions for the rate of radiative heat exchange between two spherical particles with temperatures T1 and T2 spaced by distance R in an equilibrium photon gas with temperature T3 is obtained for the first time in a dipole approximation within the framework of fluctuation electrodynamics.

Dissipation-induced Tonks-Girardeau gas of polaritons

A scheme for the generation of a Tonks-Girardeau gas of photons with purely dissipative interaction is described. We put forward a master equation approach for the description of stationary light in atomic four-level media and show that, under suitable conditions, two particle decays are the dominant photon loss mechanism. These dissipative two-photon losses increase the interaction strength by at least one order of magnitude as compared to dispersive two-photon processes and can drive the photons into the Tonks-Girardeau regime. Different scenarios for the observation of fermionic correlations between photons in the Tonks-Girardeau gas regime are discussed.

Breakdown of the isotropy of diffuse radiation as a consequence of its diffraction at multidimensional regular structures

This article is devoted to the results of an experimental test of the theoretical assumption that the basic axiomatic postulate of statistical physics according to which it is equally probable for a closed system to reside in any of the microstates accessible to it may be invalid for nonergodic cases. In the course of photometric experiments for the purpose of recording the predicted loss of isotropy by a diffuse light field when it came into contact with a two-dimensional phase-type diffraction grating, a significant deviation from Lambert's law was detected when the diffuse photon gas was scattered by the grating surface. This caused angular anisotropy of the radiation fluxes to appear in the initially homogeneous light field. These results provide a basis for revising the determination of the most probable macrostate of a closed system.

Cadmium stress in wheat seedlings: growth, cadmium accumulation and photosynthesis

Seedlings of wheat (Triticum aestivum L.) cultivars Jing 411, Jinmai 30 and Yangmai 10 were exposed to 0, 10, 20, 30, 40 or 50 μM of CdCl2 in a solution culture experiment. The effects of cadmium (Cd) stress on wheat growth, leaf photon energy conversion, gas exchange, and Cd accumulation in wheat seedlings were investigated. Gas exchange was monitored at 3, 9, 24 days after treatment (DAT). Growth parameters, chlorophyll content, leaf chlorophyll fluorescence, and Cd concentration in shoot and root were measured at 24 DAT. Seedling growth, gas exchange, chlorophyll content, chlorophyll fluorescence parameters were generally depressed by Cd stress, especially under the high Cd concentrations. Cd concentration and accumulation in both shoots and roots increased with increasing external Cd concentrations. Relationships between corrected parameters of growth, photosynthesis and fluorescence and corrected Cd concentrations in shoots and roots could be explained by the regression model Y = K/(1 + exp(a + bX)). Jing 411 was found to be Cd tolerant considering parameters of chlorophyll content, photosynthesis and chlorophyll fluorescence in which less Cd translocation was from roots into shoots. The high Cd concentrations were in shoots and roots in Yangmai 10 which has been found to be a relative Cd tolerant cultivar in terms of most growth parameters.

Quantum information transmission between two qubits through an intermediary photon gas

The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.

On parton distributions in a photon gas

In some cases it may be useful to know parton distributions in a photon gas. This may be relevant, e.g., for the analysis of interactions of high energy cosmic ray particles with the cosmic microwave background radiation. The latter can be considered as a gas of photons with an almost perfect blackbody spectrum. An approach to finding such parton distributions is described. The survival probability of ultra-high energy neutrinos traveling through this radiation is calculated.

Three-loop hard-thermal-loop free energy for QED

We calculate the free energy of a hot gas of electrons and photons to three loops using the hard-thermal-loop perturbation theory reorganization of finite-temperature perturbation theory. We calculate the free energy through three loops by expanding in a power series in ${m}_{D}/T$, ${m}_{f}/T$, and ${e}^{2}$, where ${m}_{D}$ and ${m}_{f}$ are thermal masses and $e$ is the coupling constant. We demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, $e\ensuremath{\sim}2$. The reorganization is gauge invariant by construction, and due to cancellation among various contributions, we obtain a completely analytic result for the resummed thermodynamic potential at three loops. Finally, we compare our result with similar calculations that use the $\ensuremath{\Phi}$-derivable approach.

Density matrix of strongly coupled quantum dot – microcavity system

Any two-level quantum system can be used as a quantum bit (qubit)-the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.

The correct theory of photon gas

The correct theoretical analysis of the generally accepted foundations of theory of photon (quantum) gas is proposed. The principle of the unity of formal logic and of rational dialectics is the correct methodological basis of the analysis. The new results– the correct quantum-statistical foundations– obtained within the framework of the formulated master equation taking into consideration both the quantum states of the radiating molecule and the quantum states of the photon gas in the isolated macroscopic systems “molecule + molecular gas + monochromatic photon gas” are as follows: (a) Planck’s, Einstein’s, and Bose’s works on the theory of photon (quantum) gas contain logical errors; (b) photon (quantum) gas being born by radiating molecule obeys “Gibbs statistics”: equilibrium photon (quantum) gas is described by Gibbs quantum canonical distribution; (c) Planck function (“Bose’s distribution”) is an consequence of Gibbs quantum canonical distribution; (d) Einstein coefficients (i.e. the coefficients of spontaneous emission, induced emission and absorption) are equal to each other. Keywords: quantum theory, statistical physics, heat radiation, Planck function, photon gas

Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.

Crystallization of strongly interacting photons in a nonlinear optical fibre

Understanding strongly correlated quantum systems is a central problem in many areas of physics. The collective behaviour of interacting particles gives rise to diverse fundamental phenomena such as confinement in quantum chromodynamics, electron fractionalization in the quantum Hall regime and phase transitions in unconventional superconductors and quantum magnets. Such systems typically involve massive particles, but optical photons can also interact with one another in a nonlinear medium. In practice, however, such interactions are often very weak. Here we describe a technique that enables the creation of a strongly correlated quantum gas of photons using one-dimensional optical systems with tight field confinement and coherent photon trapping techniques. The confinement enables the generation of large, tunable optical nonlinearities via the interaction of photons with a nearby cold atomic gas. In its extreme, we show that a quantum light field can undergo fermionization in such one-dimensional media, which can be probed via standard photon correlation measurements. Interactions between photons are typically extremely weak. But when light pulses are confined to an optical waveguide and manipulated with nearby cold atoms, strongly interacting photons can be created that may even undergo crystallization, as is now shown theoretically.

Recent progress in thermodynamics of radiation—exergy of radiation, effective temperature of photon and entropy constant of photon

The recent progress on thermodynamic properties of spectral radiant energy in the field of thermodynamics of radiation is reviewed. The effective temperature of photon Tλ representing the energy quality of photon is introduced. The relation between Tλ and the wavelength λ is given as λTλ =c3=5.33016×10−3 m·K. The entropy constant of photon is given as sλ=3.72680×10−23 J/K. The exergy, entropy and enthalpy of the spectral blackbody radiation, the equilibrium cavity radiation, the radiation flux in open system are discussed by using Tλ and sλ, as well as the entropy change in the process of the state transformation of photon gas. By analyzing the exergy of spectral radiation, the exergy efficiency of spectral radiant energy available for photosynthesis is proved to be higher than that of light energy. The method for the irreversible loss of exergy calculation in radiant energy converters is also discussed.

On the statistical-mechanical meaning of the Bousso bound

The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property holds, emerging when the attempt is made to apply the bound to thin layers of matter. This property consists of the existence of an ultimate lower limit l* to the thickness of the slices for which a statistical-mechanical description is viable, depending l* on the thermodynamical variables which define the state of the system locally. This limiting scale, found to be in general much larger than the Planck scale (so that no Planck scale physics must be necessarily invoked to justify it), appears not related to gravity and this suggests that the generalized entropy bound is likely to be rooted on conventional flat-spacetime statistical mechanics, with the maximum admitted entropy being however actually determined also by gravity. Some examples of ideal fluids are considered in order to identify the mechanisms which can set a lower limit to the statistical-mechanical description and these systems are found to respect the lower limiting scale l*. The photon gas, in particular, appears to seemingly saturate this limiting scale and the consequence is drawn that for systems consisting of a single slice of a photon gas with thickness l*, the generalized Bousso bound is saturated. It is argued that this seems to open the way to a peculiar understanding of black hole entropy: if an entropy can meaningfully (i.e. with a second law) be assigned to a black hole, the value A/4 for it (where A is the area of the black hole) is required simply by (conventional) statistical mechanics coupled to general relativity.

Analytical Solutions for Expanding Fireballs

Many models of gamma-ray bursts (GRBs) as well as of soft gamma repeaters (SGRs) involve a fireball — an optically thick concentration of radiation energy with a high ratio of energy density to rest mass. We study the asymptotic behavior of an ultrarelativistic fireball consisting of electron-positron pairs and photons. We show that in the ultrarelativistic limit, after photons decouple from the pairs, the photon distribution function remains a blackbody spectrum in some appropriate Lorentz frame, allowing us to define an effective Lorentz factor and temperature for the photon gas. We also study the freezing out of electron-positron pairs and their asymptotic Lorentz factor γ∞. The dependence of these quantities on initial conditions can be described by simple scaling laws. We apply our results to SGR 1806-20 and find that the energy carried by electron-positron pairs is higher than calculated by former estimates, but is still an order of magnitude short of the minimum energy required to produce the observed afterglow. A viable solution of the energy budget is that the fireball is loaded by baryons or electromagnetic flux.

Information rates of radiation as a photon gas

The information rates achievable with a photon-gas model of electromagnetic radiation are studied. At any frequency, information rates over the photon-gas model essentially coincide with the Shannon capacity when the signal-to-noise ratio is below a threshold. Only above the threshold does the photon gas incur in a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds $40\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ for radio frequencies and vanishes at higher frequencies.