Kinetic model of the bichromatic dark trap for atoms

Abstract

A kinetic model of atom confinement in a bichromatic dark trap (BDT) is developed with the goal of describing its dissipative properties. The operating principle of the deep BDT is based on using the combination of multiple bichromatic cosine–Gaussian optical beams (CGBs) for creating high-potential barriers, which is described in our previous work (Krasnov 2016 Laser Phys. 26 105501). In the indicated work, particle motion in the BDT is described in terms of classical trajectories. In the present study, particle motion is analyzed by means of the Wigner function (phase-space distribution function (DF)), which allows one to properly take into account the quantum fluctuations of optical forces. Besides, we consider an improved scheme of the BDT, where CGBs create, apart from plane potential barriers, a narrow cooling layer. We find an asymptotic solution of the Fokker–Planck equation for the DF and show that the DF of particles deeply trapped in a BDT with a cooling layer is the Tsallis distribution with the effective temperature, which can be considerably lower than in a BDT without a cooling layer. Moreover, it can be adjusted by slightly changing the CGBs’ radii. We also study the effect of particle escape from the trap due to the scattering of resonant photons and show that the particle lifetime in a BDT can exceed several tens of hours when it is limited by photon scattering.