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Physical Review A

Two-dimensional Sisyphus cooling in a three-beam laser configuration

Kirstine Berg‐Sørensen

Published Jun 1, 1994• 6 citations
Publisher

Abstract

Calculations on the steady-state distribution of atoms cooled in three coplanar laser beams are presented. For this three-beam configuration, the achievements of Sisyphus cooling are independent of fluctuations in the relative time phases between the beams. The atomic motion is quantized and the steady-state solution of the density-matrix equations is found within a secular approximation. We obtain a minimum width of the cooled momentum distributions on the order of six photon momenta.

DOI
10.1103/physreva.49.r4297

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Calculations on the steady-state distribution of atoms cooled in three coplanar laser beams are presented. For this three-beam configuration, the achievements of Sisyphus cooling are independent of fluctuations in the relative time phases between the beams. The atomic motion is quantized and the steady-state solution of the density-matrix equations is found within a secular approximation. We obtain a minimum width of the cooled momentum distributions on the order of six photon momenta.
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.
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.
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In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and results of the first realized three dimensional Brownian motor in optical lattices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three dimensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brownian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice.
We demonstrate the possibility of three-dimensional cooling of neutral atoms by illuminating them with two counterpropagating laser beams of mutually orthogonal linear polarization, where one of the lasers is a speckle field, i.e., a highly disordered but stationary coherent light field. This configuration gives rise to atom cooling in the transverse plane via a Sisyphus cooling mechanism similar to the one known in standard two-dimensional optical lattices formed by several plane laser waves. However, striking differences occur in the spatial diffusion coefficients as well as in local properties of the trapped atoms.