Photon thermalization via laser cooling of atoms

Abstract

Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that noninteracting photons can thermalize with the atoms to a grand canonical ensemble with a nonzero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser-cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential nearly equal to the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare-earth atoms. With the addition of photon-photon interactions, this system could provide a platform for exploring many-body physics.arXiv:1712.08643v2 [quant-ph]

Theory of Bose condensation of light via laser cooling of atoms

“…These populations are significantly lower than would be predicted by a single temperature equal to the atom temperature (see Fig. 5 in [40]). Thus, for a fixed n tot and T , the mode occupation of the lower modes is significantly higher than in the untruncated case, which increases the transition temperature.…”

“…The Boltzman factor is picked up by each pair of p i and p i satisfying the energy conservation condition K(p i ) − K(p i ) = (ω L − ω q lm ) when summing over the atomic momentum distribution. This equilibration condition can be understood within the framework of photon thermalization with a parametrically coupled bath [40,[51][52][53], where the conservation of the total number of cavity plus laser photons during the scattering processes imposes a nonzero chemical potential ω L to the cavity photons. For ω q lm > ω L , one…”

“…Based on the theoretical tools developed in Ref. [40], assuming perfect cavity mirrors, the detailed balance condition is modified by the loss caused by scattering of the cavity photons into the free-space modes to…”

“…On the other hand, interactions between atoms and optical cavities have made possible novel atom-cooling mechanisms [30][31][32][33][34][35][36][37][38] as well as peculiar states of light [39]. We recently found a different photon thermalization mechanism that occurs in Doppler laser cooling of a high optical depth atomic ensemble [40], which requires neither matter-matter nor effective photon-photon interactions. Here we show that this thermalization mechanism can lead to Bose condensation of photons.…”

Radiation in equilibrium with plasma and plasma effects on cosmic microwave background

“…[3,4]), it is not the case in general [5,6]. Chemical potential is related to constraints on the number of particles and such situations can be realized, for example, in semiconductors [5][6][7][8], where the number of photons is related to the number of electrons and holes; in plasmas when scattering dominates over absorption and thus the number of photons conserved [9]; in dye filled microcavities [10,11]; and in other systems [12][13][14]. Third, there are geometrical and finiteness effects restricting the number of available k modes.…”