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Physical Review A

Transition of laser cooling between standard and Raman optical lattices

R. Zhang, Rachel Sapiro, Natalya V. Morrow, Georg A. Raithel

Published Sep 13, 2006• 2 citations
Publisher

Abstract

Reduced-period optical lattices based on Raman transitions allow for sub-Doppler laser cooling. An important parameter of this Raman optical lattice is the frequency difference ${\ensuremath{\Delta}}_{\mathrm{d}}$ between two virtual energy levels involved in the atom-field interaction scheme. In this work, we use experimental time-of-flight data and quantum simulations to characterize laser cooling in the Raman lattice as a function of ${\ensuremath{\Delta}}_{\mathrm{d}}$. Two different domains of laser cooling are identified. For small ${\ensuremath{\Delta}}_{\mathrm{d}}$, atoms are cooled due to a well-known mechanism that also occurs in standard optical lattices. For large ${\ensuremath{\Delta}}_{\mathrm{d}}$, atoms are cooled based on Raman transitions. We study the transition between the two domains of laser cooling in detail.

DOI
10.1103/physreva.74.033404

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•Jan 1, 1998•1 citation
Reduced-period optical lattices based on Raman transitions allow for sub-Doppler laser cooling. An important parameter of this Raman optical lattice is the frequency difference \ensuremathΔd{\ensuremath{\Delta}}_{\mathrm{d}}\ensuremathΔd​ between two virtual energy levels involved in the atom-field interaction scheme. In this work, we use experimental time-of-flight data and quantum simulations to characterize laser cooling in the Raman lattice as a function of \ensuremathΔd{\ensuremath{\Delta}}_{\mathrm{d}}\ensuremathΔd​. Two different domains of laser cooling are identified. For small \ensuremathΔd{\ensuremath{\Delta}}_{\mathrm{d}}\ensuremathΔd​, atoms are cooled due to a well-known mechanism that also occurs in standard optical lattices. For large \ensuremathΔd{\ensuremath{\Delta}}_{\mathrm{d}}\ensuremathΔd​, atoms are cooled based on Raman transitions. We study the transition between the two domains of laser cooling in detail.
We have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.
It is shown that sub-Doppler cooling occurs in an atom-field geometry that can lead to reduced-period optical lattices. Four optical fields are combined to produce a ``standing wave'' Raman field that drives transitions between two ground state sublevels. In contrast to conventional Sisyphus cooling, sub-Doppler cooling to zero velocity occurs when all fields are polarized in the same direction. Solutions are obtained using both semiclassical and quantum Monte Carlo methods in the case of exact two-photon resonance. The connection of the results with conventional Sisyphus cooling is established using a dressed state basis.
Summary form only given. Laser cooled atoms play a critical role in modern designs of frequency standards such as atomic fountains. Recently, an elegant and efficient method of two-dimensional cooling to the vibrational ground state of a far-off resonance optical lattice has been demonstrated. This method is a variant of Raman sideband cooling based on the Raman transitions between the vibrational manifolds of adjacent Zeeman substates. A static magnetic field is used to tune the Zeeman levels so that Raman resonance occurs on the red sideband and results in cooling. Two circularly polarized fields are used to recycle the atoms for repetitive Raman cooling. Unfortunately, a direct application of this scheme to frequency standards meets with several difficulties. Stimulated by these concepts and results, we propose a new variant of transverse sideband cooling, where these problems are avoided, while still maintaining most of the attractive features. The field configuration used for the optical lattice consists of three linearly polarized beams having equal amplitudes and propagating in the xy plane with angles of 2/spl pi//3 between each other. The polarization vectors of these beams are tilted through a small angle with respect to the z-axis. All the beams have the same frequency far-detuned to the red of the D/sub 2/ resonance line. Raman transitions between vibrational levels of adjacent magnetic substates are induced by the small in-plane component of the field. Two other important requirements for Raman sideband cooling are a uniform energy shift of the magnetic sublevels and optical pumping.
This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.