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Europhysics Letters (EPL)

Designing Optical Lattices: An Investigation with Cesium Atoms

Philippe Verkerk, D. R. Meacher, A. B. Coates, J.-Y. Courtois, S. Guibal, Brahim Lounis, Ch Salomon, G. Grynberg

Published Apr 20, 1994• 45 citations
Publisher

Abstract

We present a method for creating three-dimensional optical lattices starting from well-known one-dimensional configurations. This method is applied to the case of the lin ⊥ lin molasses and gives rise to optical potentials having orthorhombic symmetry. The vibrational frequencies of cesium atoms in these optical potentials are measured and found to be in good agreement with theoretical predictions. The experiment also shows that the localisation of atoms in the lowest bound levels involves relaxation times which can be as large as 30 ms.

DOI
10.1209/0295-5075/26/3/003

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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.

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Europhysics Letters (EPL)•Nov 15, 1998•15 citations
We present a method for creating three-dimensional optical lattices starting from well-known one-dimensional configurations. This method is applied to the case of the lin ⊥ lin molasses and gives rise to optical potentials having orthorhombic symmetry. The vibrational frequencies of cesium atoms in these optical potentials are measured and found to be in good agreement with theoretical predictions. The experiment also shows that the localisation of atoms in the lowest bound levels involves relaxation times which can be as large as 30 ms.
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.
Quantization of atomic motion is observed in two- and three-dimensional cesium optical molasses by stimulated Raman spectroscopy. A new geometry is used with the minimum number of laser beams, so that the topography of the optical potential is not sensitive to phase drifts of the molasses beams. The deepest potential wells are located on a hexagonal lattice in two dimensions and on a body-centered-cubic lattice in three dimensions. They correspond to purely circularly polarized light, allowing a Lamb-Dicke narrowing of the transitions between vibrational levels to occur.
We present an experimental investigation of a three-dimensional (3D) optical lattice where the light polarization is linear at the bottom of the potential wells instead of being circular as in previous studies. In the present situation, optical pumping induces frequent transitions between differently light-shifted Zeeman sublevels (jumping regime). However, narrow vibrational lines are still observed as a result from a motional narrowing-like phenomenon taking place in this lattice. The atomic kinetic temperature is investigated and shown to be lower than in a standard 3D lin ⊥ lin optical lattice.
A complete laser cooling setup was built, with focus on threedimensional near-resonant optical lattices for cesium. These consist of regularly ordered micropotentials, created by the interference of four laser beams. One key feature of optical lattices is an inherent ”Sisyphus cooling” process. It efficiently extracts kinetic energy from the atoms, leading to equilibrium temperatures of a few µK. The corresponding kinetic energy is lower than the depth of the potential wells, so that atoms can be trapped. We performed detailed studies of the cooling processes in optical lattices by using the time-of-flight and absorption-imaging techniques. We investigated the dependence of the equilibrium temperature on the optical lattice parameters, such as detuning, optical potential and lattice geometry. The presence of neighbouring transitions in the cesium hyperfine level structure was used to break symmetries in order to identify, which role “red” and “blue” transitions play in the cooling. We also examined the limits for the cooling process in optical lattices, and the possible difference in steady-state velocity distributions for different directions. Moreover, in collaboration with ´Ecole Normale Sup´erieure in Paris, numerical simulations were performed in order to get more insight in the cooling dynamics of optical lattices. Optical lattices can keep atoms almost perfectly isolated from the environment and have therefore been suggested as a platform for a host of possible experiments aimed at coherent quantum manipulations, such as spin-squeezing and the implementation of quantum logic-gates. We developed a novel way to trap two different cesium ground states in two distinct, interpenetrating optical lattices, and to change the distance between sites of one lattice relative to sites of the other lattice. This is a first step towards the implementation of quantum simulation schemes in optical lattices.
We report temperature measurements of atoms trapped in a three-dimensional (3D) optical lattice, a well-defined laser-cooling situation that can be treated with currently available theoretical tools. We also obtain fluorescence spectra from a 3D optical lattice, from which we obtain quantitative information about the trapping atoms, including the oscillation frequencies, spatial localization, and a temperature, which is in good agreement with our direct measurements. For comparison we study a 1D lattice using the same atom (cesium).