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Laser Physics

Kinetic model of the bichromatic dark trap for atoms

I. V. Krasnov

Published Jul 27, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1555-6611/aa786c

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Bichromatic dark trap immersed in a buffer gas with an admixture of resonant atoms

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arXiv:1307.2883•Physical Review A•Sep 30, 2013•34 citations
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.
Abstract The quasiclassical kinetic theory of optical forces has been applied to describe the kinetics of accumulation, deep trapping and cooling of particles in a bichromatic dark trap (BDT), which is placed into a reservoir with a thermal gas at room temperature containing an admixture of resonant atoms. BDT (proposed in our previous works, Krasnov 2016 Laser Phys. 26 105 501, 2017 27 085 501) is a multiple-optical-beam dark trap, in which rectified gradient forces in a bichromatic light field are used to manipulate the particles. The purpose of the present study is to investigate the possibility of direct BDT loading from the equilibrium gas mixture which will result in trapping and cooling of a sufficiently great amount of atoms by BDT. We derived a reduced Fokker-Planck equation in the energy space (for the Wigner particle distribution function) including the collision term. This equation takes into account the optical trapping force, its quantum fluctuations, particle loss from the trap and weakly-dissipative nature of BDT. Its asymptotic solution allows one to describe the particle kinetics and obtain explicit formulas for the main characteristics of BDT (particle capture rate into BDT, temperature and number of the trapped particles). Ultimately, we demonstrate the high efficiency of the particle accumulation in BDT. In particular, the concentration of the trapped particles (with the temperature at least by four orders of magnitude lower than the room temperature) has been shown to be able to exceed the concentration of the ‘hot’ untrapped particles by several dozens of times, and it has been demonstrated that the accumulation efficiency can reach the values of the order of 10 3 .
The theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.
Abstract A novel mechanism of the formation of a deep optical superlattice (OSL) for three-dimensional (3D) trapping of resonant impurity atoms immersed in a transparent cold buffer gas is proposed and investigated theoretically. This mechanism is associated with the joint action of two factors of different physical nature: rectification effect of the gradient force of light pressure and effect of the light induced drift (LID) of atoms (a consequence of the difference in gas-kinetic cross sections of excited and unexcited atoms). Such a situation can be realised when a gas mixture is irradiated by a bichromatic combined light beam which is a special coaxial superposition of cosine-Gaussian optical beams. Here, the RcGF creates a periodic 1D array of deep potential wells (OSL) along the beam axes, and an effective force, causing LID, pulls resonant particles into the combined light beam and provides their transverse (with respect to the beam axes) confinement in OSL. As a result, there can occur a giant accumulation of impurity particles in the OSL cells, accompanied by a strong spatial particle localization far away from the walls of the reservoir, in which the gas mixture is located.
The semiclassical dynamics of atoms, when the atoms are confined inside a standing-wave high-finesse resonator, is theoretically studied. The atoms are cooled by scattering processes in which the photons of a transverse laser are coherently scattered into the cavity mode. We derive a Fokker-Planck equation for the atomic center-of-mass variables which allows us to determine the equations of motion in the semiclassical limit for any value of the intensity of the laser field. We extract its prediction for the dynamics when the resonator is essentially in the vacuum state and the atoms are cooled by scattering photons into the cavity mode, which then decays. Its predictions for the stationary atomic distribution are compared with the ones of the Fokker-Planck equation by Domokos et al. [J. Phys. B 34, 187 (2001)], which has been derived under different assumptions. We find full agreement in the considered parameter regime.