Phase-space-density limitation in laser cooling without spontaneous emission

Abstract

We study the possibility to enhance the phase space density of non-interacting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the particle motion is more reliable than semi-classical description which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position-momentum phase space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum of the position-momentum phase space density, can only increase by a factor M for M -level particles. This bound comes from a transfer between the external and internal degrees of freedom. Therefore, it is impossible to increase the position-momentum phase space density in the same internal state.

Limitations for field-enhanced atom interferometry

“…We will deals with non relativistic atom interferometry (see [75] for a more general case). Several methods exists to study the evolution: using a plane wave or a gaussian wavepacket decomposition [76,77], sometimes linked with a path integrals formulation [8,9], or using the density matrix [78] or Wigner function evolution [58,[79][80][81][82]). Obviously, all methods leads to the same final results but the choice is made depending on the context.…”

“…(1). Under such circumstances, that fortunately are the most usual ones, the quantum phasespace (Wigner) distribution evolves under the same (Liouville's) equation than the classical phase-space distribution [82,86]. The fact that the evolution is given by the classical evolution is also directly visible using the evolution operator between the time t i and t f that, in the 2 levels caseÛ (t i , t f ) =…”

“…We should also deal with the π or π/2 light pulses. The general case of the interaction with lights can be complicated because correlations may appear between internal and external variables invalidating the Blochequation or the simple semi-classical approaches [82,86]. However, because it is not the main focus of our article to deal with these issues, we will restrict ourselves to ideal case of quasi-instantaneous light pulse and with no momentum transfer created by the pulses.…”

“…In our case, in addition, we deal with higher order terms, such as the third order ones (r 2 z and z 3 ones). The theory is more complex and generally no more linked to the classical world with for instance negative values for the Wigner function [82,86]. Fortunately, if the extra terms are considered as a perturbation L 1 on the Lagrangian L = L 0 + L 1 , the phase shift δφ introduced into the final wavefunction, by the perturbation L 1 , is given simply (to the first order) by the integral of the perturbation along the classical unperturbed path Γ 0 [87][88][89]:…”

Entropy transfer from a quantum particle to a classical coherent light field

“…Moreover, it is often stated that the coherent light field is not perturbed, and hence does not absorb entropy, because the quantum counterpart to the laser field, the coherent state, is unaffected by the absorption of photons by the gas. However, there are some studies that predict entropy removal from the gas via interaction with the laser field [9][10][11][12][13]. In an effort to further understand the underlying physics of laser cooling and optical pumping, we propose a simple Gedanken experiment that probes the change of a light field that coherently interacts with a particle containing nonzero initial entropy.…”