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Physical Review A

Condensation state of photons in a Kerr nonlinear blackbody

Ze Cheng

Published Sep 17, 2009• 12 citations
Publisher

Abstract

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 $Q$ 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.

DOI
10.1103/physreva.80.033826

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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.
A photon blackbody field in Kerr nonlinear crystal is a squeezed thermal radiation state in which there is a new kind of quasi particle, the nonpolariton. A nonpolariton is a condensate of virtual nonpolar phonons, with a bare photon acting as the nucleus of condensation. The propagation velocity of nonpolaritons is a monotonically increasing function of temperature, and the noise of one quadrature phase in the squeezed thermal radiation state can be below the noise level in the vacuum state. The photon system undergoes a second-order phase transition from the normal to the squeezed thermal radiation state.
We find that the photon system in the black body filled in its interior by a Kerr-nonlinear crystal is in a squeezed thermal radiation state, in which the photon system possesses a new kind of quasiparticles - nonpolaritons. The existence of nonpolaritons should be manifested by observing the predicted temperature dependence of the velocity and squeezing of nonpolaritons. The propagation velocity and noise properties of nonpolaritons constitute potentially novel and significant effects in solid-state quantum optics and hence these effects should have extensive application to fields of science and technology.
In the present paper, a charged oscillator in a harmonic potential well interacting with a Kerr-nonlinear blackbody is investigated. A quantum Langevin equation is derived. It is shown that below a transition temperature Tc, the memory function is a decreasing function of the Kerr-nonlinear coefficient. In the large-cutoff limit, the free-energy shift is a complicated function of temperature which is no longer a simply T2-dependent function. The energy level shift of an oscillator in a normal blackbody is negative, while in our Kerr-nonlinear blackbody, only near zero temperature is the corresponding energy level shift negative. As the temperature increases to the transition temperature Tc, the corresponding energy level shift becomes a large positive value. Above Tc, our results are the same as those found in a normal blackbody.
In this paper we propose a model of polariton condensation with Kerr-type nonlinear photons. We introduce a generalized Dicke Hamiltonian to describe our system. By constructing the partition function as a path integral, the analytical and numerical solutions are presented. On the mean-field level, it is shown that the polariton condensation can occur and the Kerr nonlinearity affects the character of the polariton condensate. As the nonlinear coefficient increases, the condensate evolves from more photon-like to more exciton-like. Although the photon nonlinearity gives rise to a chemical potential greater than the photon energy, the quasiparticle excitation spectrum is still fully gapped. For the condensate collective excitations, the nonlinearity destroys the Goldstone modes and mixes the phase modes with the amplitude modes, resulting four non-zero-frequency collective modes. In addition, the influence of the photon-exciton detuning on the polariton condensate is also discussed.
A reservoir theory has been used to investigate the spontaneous emission of a two-level atom in a Kerr nonlinear blackbody. It is found that the atomic decay rate is a monotonically increasing function of absolute temperature. Below a transition temperature Tc{T}_{c}Tc​, the spontaneous emission is always inhibited compared to that in a nonabsorbing linear medium. It is also found that the inhibition of spontaneous emission is a monotonically decreasing function of the Kerr nonlinear coefficient. The inhibition of spontaneous emission is interpreted on the basis of a physical mechanism.