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Europhysics Letters (EPL)

Cooling and Tunnelling of Atoms in a 2D Laser Field

Kirstine Berg‐Sørensen, Yvan Castin, Klaus Mølmer, Jean Dalibard

Published Jun 20, 1993• 31 citations
Publisher

Abstract

We present a quantum treatment of Sisyphus cooling in two dimensions. The steady state is given by the populations of the energy eigenstates for the atomic motion in the potential created by the atom-light interaction. In addition to characterizing the momentum and position distributions, we show that resonant tunnelling between adjacent optical potential wells leads to a sizable variation of the lowest-energy state population, as a function of the field parameters.

DOI
10.1209/0295-5075/22/9/005

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Cambridge University Press eBooks•Jan 5, 2016•0 citations
We present a quantum treatment of Sisyphus cooling in two dimensions. The steady state is given by the populations of the energy eigenstates for the atomic motion in the potential created by the atom-light interaction. In addition to characterizing the momentum and position distributions, we show that resonant tunnelling between adjacent optical potential wells leads to a sizable variation of the lowest-energy state population, as a function of the field parameters.
We present theoretical descriptions of Sisyphus cooling in a two-dimensional laser configuration, based on semiclassical as well as quantum approaches. A detailed comparison of these various approaches and a discussion of their range of validity are given. Features of the cooled atomic distribution such as channeling of the atoms along specific lines in momentum space and the observability of tunneling induced resonances in the population of the ground state of the atomic motion in the optical potential wells are discussed.
We present a quantum treatment of laser cooling of neutral atoms. The cooling mechanism studied is the "Sisyphus" process for 1-dimensional optical molasses. We first derive the energy eigenstates for the atom moving in the potential associated with the light-shifts due to the laser. Then, taking into account optical pumping, we calculate the steady-state populations of these quantum levels in the secular approximation. This approach allows us to determine the atomic eigenfrequencies in the optical wells, as well as momentum and position distributions. In particular, the minimum r.m.s. atomic momentum is ≃ 6 single-photon momenta; this result was not accessible to previous semi-classical treatments.
The quantum-mechanical transport properties of cold atoms in an optical lattice are described in terms of an analytically tractable model. The atoms are cooled down to the lowest energy band in the periodic optical potential, in the tight- binding limit. The transport mechanisms are coherent tunneling through potential barriers, and momentum recoil at optical pumping. Expressions are obtained for the time-dependent population distributions over the energy eigenstates and over localized states. These expressions are modified in the presence of a dark atomic state, that is uncoupled to the field.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗{\mathrm{He}}^{*}He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav){(E}_{\mathrm{av}})(Eav​) for purely Sisyphus cooling is comparable to the minimum value of Eav{E}_{\mathrm{av}}Eav​ with Doppler cooling alone.
Cold atoms in optical lattices are an ideal test bed to explore ratchet physics. This is largely due to the extreme tunability of optical lattice systems, which allows one to precisely control the shape of the potential and of any applied force, as well as to vary at will the level of dissipation. Since the very first demonstration of directed motion in a cold atom system by Mennerat-Robilliard et al. (1999), a number of experimental investigations with cold atoms in optical lattices have explored different aspects of the physics of ratchets. Here, the focus is first on the experiments in the classical regime which explored the relationship between symmetry and transport in a.c. driven ratchets. Experiments in the full quantum Hamiltonian regime are then described, and the unique features of such a regime highlighted. Ratchets in dissipative optical lattices Dissipative optical lattices Optical lattices are periodic potentials for atoms created by the interference of two or more laser fields.The detuning between the laser fields and the nearest atomic transition will emerge as a key parameter to describe the light–atom interaction. It is thus important to distinguish two very different situations: the case of fardetuned laser fields, and the case of near-resonant laser fields. For far-detuned laser fields, a purely conservative potential is produced. As will be discussed in the following sections, far-detuned optical lattices are ideal to model Hamiltonian systems. In the case of near-resonant laser fields, the interaction between the laser and the atoms may lead, under appropriate conditions, to dissipative dynamics. That is, for an appropriately arranged set of near-resonant optical lattices, a dissipative optical lattice, is produced, where the set of laser fields produce at once the periodic potential acting on the atoms and the cooling mechanism, which decreases their kinetic energy and lead to the trapping of the atoms at the bottom of potential wells. The principles behind the cooling mechanism, termed Sisyphus cooling for reasons which will become apparent in the following discussion, can be captured by considering the minimal configuration of a one-dimensional optical lattice and a J g = 1 / 2 → J e = 3 / 2 atomic transition. This is the simplest configuration in which Sisyphus cooling takes place.