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Journal of Nonlinear Optical Physics & Materials

Thermodynamic properties of coherent photons in self-focusing nonlinear waveguides

Ze Cheng

Published Mar 1, 2019• 0 citations
Publisher

Abstract

We study the thermodynamic properties of coherent photons in self-focusing nonlinear waveguides. The equation of the superfluid state of photons has been derived. There is a transition temperature [Formula: see text], above which the photon gas is in the coherent state, but below which the photon gas is in the superfluid state. At [Formula: see text], the photon system undergoes a first-order phase transition from the coherent to the superfluid state. To determine the fugacity [Formula: see text] and the transition temperature [Formula: see text] of the photon gas, we numerically solve the equation of the superfluid state of photons. The fugacity [Formula: see text] is a monotonically decreasing function of temperature [Formula: see text] and light intensity [Formula: see text]. The transition temperature [Formula: see text] is a monotonically decreasing function of light intensity [Formula: see text].

DOI
10.1142/s0218863519500061

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We study the thermodynamic properties of coherent photons in self-focusing nonlinear waveguides. The equation of the superfluid state of photons has been derived. There is a transition temperature [Formula: see text], above which the photon gas is in the coherent state, but below which the photon gas is in the superfluid state. At [Formula: see text], the photon system undergoes a first-order phase transition from the coherent to the superfluid state. To determine the fugacity [Formula: see text] and the transition temperature [Formula: see text] of the photon gas, we numerically solve the equation of the superfluid state of photons. The fugacity [Formula: see text] is a monotonically decreasing function of temperature [Formula: see text] and light intensity [Formula: see text]. The transition temperature [Formula: see text] is a monotonically decreasing function of light intensity [Formula: see text].
The cause of the phenomenon of self-focusing of intense laser beams is the nonlinear intensity dependent refractive index of optical materials. This property which leads to the self-focusing can be interpreted as an attractive force in between the photons thereby increasing the photon density. For large enough densities the photon gas may undergo Bose-Einstein condensation and if the attractive force is strong enough may even become a superfluid through a second order phase transition. This mechanism not possible for free photons is possible inside optical materials with a large refractive index because there the photons can be viewed as massive quasiparticles having a velocity less than the velocity of light. With the large dielectric constants of certain ferroelectric substances valid in the range of microwave frequencies the envisioned process might even work with microwave photons. This would make possible the generation of very intense highly coherent microwave beams. I .
Within the framework of quantum field theory, we show that the photon system in a blackbody whose interior is filled by a Kerr nonlinear crystal is in a condensation state. In the condensation state, bare photons with opposite wave vectors and helicities are bound into pairs and unpaired bare photons are transformed into a new kind of quasiparticle, the nonpolariton. The photon-pair system is a condensate and the nonpolariton system is a boson gas. At zero temperature the condensate possesses a largest persistent energy density. The persistent energy density of the condensate is a monotonically decreasing function of temperature and Kerr nonlinear coefficient. The QQQ function of a Kerr nonlinear blackbody at any temperature is derived analytically. In the transition from the normal to the condensation state, the phase symmetry of the photon system is spontaneously broken.
The problem of photonic phase transition for the system of a two-level atomic ensemble interacting with a quantized single-mode electromagnetic field in the presence of optical collisions (OCs) is considered. We have shown that for large and negative atom-field detuning a photonic field exhibits high-temperature second-order phase transition to superradiant state under thermalization condition for coupled atom-light states. Such a transition can be connected with superfluid (coherent) properties of photonlike low branch (LB) polaritons. We discuss the application of metallic cylindrical waveguide for observing predicted effects.
Due to their photonic components, exciton-polariton systems provide a convenient platform to study the coherence properties of weakly-interacting Bose gases. In particular, optical interferometry enables the measurement of the first-order coherence function which provides information about the intrinsic correlations of the system. In this paper, we derive a universal curve for the coherent fraction of a noninteracting, equilibrium, homogeneous, two-dimensional Bose gas, with density expressed in units of the observation area, and compare to recent experimental results. Although there is a sharp transition from normal to superfluid phases in the thermodynamic limit, the coherent fraction of the gas varies continuously across this transition due to the finite system size. We find that the theory agrees nearly perfectly with the experimental data in the low-density limit with no free parameters other than the effective temperature, highly constrained by the measurements. At higher density, the experiments are consistent with standard weakly-interacting Bose gas theory. By having a theory that treats both the optical diffraction and Bose coherence, we can clearly see the effect of the quantum statistics on the coherence.
Based on the density operator's coherent state representation [Phys. Lett.A252, 281 (1999)], we extend the well-known Bose distribution's partition function Ξ [Formula: see text] for ideal photon gas [Formula: see text] to that of an assembly of photon gas interacting with nonlinear medium described by the Hamiltonian [Formula: see text], where A=(a1,a2,…,an), Ω is a symmetric matrix, and we report that the corresponding partition function is [Formula: see text] As a result, the generalized Bose distribution and thermodynamic functions are derived.