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arXiv:quant-ph/0106032 · Physical Review A

Cesium gas strongly confined in one dimension: Sideband cooling and collisional properties

Isabelle Bouchoule, M. Morinaga, Ch Salomon, Dmitry S. Petrov

Published Feb 1, 2002• 16 citations
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Abstract

We study one-dimensional (1D) sideband cooling of cesium atoms strongly confined in a far-detuned optical lattice. The Lamb-Dicke regime is achieved in the lattice direction whereas the transverse confinement is much weaker. The employed sideband cooling method, first studied by Vuleti\ifmmode \acute{c}\else \'{c}\fi{} et al., uses Raman transitions between Zeeman levels and produces a spin-polarized sample. We present a detailed study of this cooling method and investigate the role of elastic collisions in the system. We accumulate 83(5)% of the atoms in the vibrational ground state of the strongly confined motion, and elastic collisions cool the transverse motion to a temperature of $2.8\ensuremath{\mu}\mathrm{K}=0.7\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{osc}}{/k}_{B},$ where ${\ensuremath{\omega}}_{\mathrm{osc}}$ is the oscillation frequency in the strongly confined direction. The sample then approaches the regime of a quasi-2D cold gas. We analyze the limits of this cooling method and propose a dynamical change of the trapping potential as a mean of cooling the atomic sample to still lower temperatures. Measurements of the rate of thermalization between the weakly and strongly confined degrees of freedom are compatible with the zero-energy scattering resonance observed previously in weak 3D traps. For the explored temperature range the measurements agree with recent calculations of quasi-2D collisions. Transparent analytical models reproduce the expected behavior for ${k}_{B}T\ensuremath{\gg}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{osc}}$ and also for ${k}_{B}T\ensuremath{\ll}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{osc}}$ where the 2D features are prominent.

DOI
10.1103/physreva.65.033402

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We study one-dimensional (1D) sideband cooling of cesium atoms strongly confined in a far-detuned optical lattice. The Lamb-Dicke regime is achieved in the lattice direction whereas the transverse confinement is much weaker. The employed sideband cooling method, first studied by Vuleti\ifmmode \acute{c}\else '{c}\fi{} et al., uses Raman transitions between Zeeman levels and produces a spin-polarized sample. We present a detailed study of this cooling method and investigate the role of elastic collisions in the system. We accumulate 83(5)% of the atoms in the vibrational ground state of the strongly confined motion, and elastic collisions cool the transverse motion to a temperature of 2.8\ensuremathμK=0.7\ensuremath\Elzxh\ensuremathωosc/kB,2.8\ensuremath{\mu}\mathrm{K}=0.7\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{osc}}{/k}_{B},2.8\ensuremathμK=0.7\ensuremath\Elzxh\ensuremathωosc​/kB​, where \ensuremathωosc{\ensuremath{\omega}}_{\mathrm{osc}}\ensuremathωosc​ is the oscillation frequency in the strongly confined direction. The sample then approaches the regime of a quasi-2D cold gas. We analyze the limits of this cooling method and propose a dynamical change of the trapping potential as a mean of cooling the atomic sample to still lower temperatures. Measurements of the rate of thermalization between the weakly and strongly confined degrees of freedom are compatible with the zero-energy scattering resonance observed previously in weak 3D traps. For the explored temperature range the measurements agree with recent calculations of quasi-2D collisions. Transparent analytical models reproduce the expected behavior for kBT\ensuremath≫\ensuremath\Elzxh\ensuremathωosc{k}_{B}T\ensuremath{\gg}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{osc}}kB​T\ensuremath≫\ensuremath\Elzxh\ensuremathωosc​ and also for kBT\ensuremath≪\ensuremath\Elzxh\ensuremathωosc{k}_{B}T\ensuremath{\ll}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{osc}}kB​T\ensuremath≪\ensuremath\Elzxh\ensuremathωosc​ where the 2D features are prominent.
We trap 107{10}^{7}107 cesium atoms in a far red detuned 1D optical lattice. With degenerate Raman sideband cooling we achieve a vibrational ground state population of 80% for the steep trapping direction. Collisional coupling enables us to cool the spin-polarized gas in 3D without loss of atoms to a peak phase space density of 1/1801/1801/180 at a mean temperature of $2.8\ensuremath{\mu}\mathrm{K}$ and a density of $1.4\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\ensuremath{-}3}$.
Sideband laser cooling using stimulated Raman transitions is performed on trapped cesium atoms. The confinement is produced by a far–off-resonance dipole trap consisting of two crossed YAG beams which, by interference, create a one-dimensional optical lattice. In a pure intensity lattice, we measure a 1D temperature of T = 6 μK corresponding to a mean quantum vibrational number of about ⟨ n v ⟩ = 0.75. In a polarization gradient lattice, the final temperature is T = 3.6 μK corresponding to ⟨ n v ⟩ ≃ 2.4.
Sideband laser cooling using stimulated Raman transitions is performed on trapped cesium atoms. The confinement is produced by a far–off-resonance dipole trap consisting of two crossed YAG beams which, by interference, create a one-dimensional optical lattice. In a pure intensity lattice, we measure a 1D temperature of T = 6 μK corresponding to a mean quantum vibrational number of about nv = 0.75. In a polarization gradient lattice, the final temperature is T = 3.6 μK corresponding to nv 2.4.
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.
In the experiment presented in this thesis, Cesium atoms were trapped in a non-dissipative, intensity lattice produced by two Nd:YAG laser beams. Vertically, atoms are confined in independent micro-planes at each intensity maximum. The gaussian shape of the beams provides the horizontal confinement. Thanks to the strong vertical confinement, we could develop an optical sideband cooling method which accumulates about 95\% of the atoms in the ground state of the vertical motion. From this state, which is almost pure, we prepared other pure quantum states and, using an absoption imaging technique, we visualized directly their velocity distribution. First, we produced the first excited state of motion whose velocity distribution is zero for v=0v=0v=0. We also produced non stationary states and visualized the temporal evolution of their velocity distribution. In this way, the evolution of a superposition of the first two vibrationnal states and that of squeezed states have been recorded. Squeezed states are, as the ground state, minimum uncertainty states (ΔpΔz=ℏ/2\Delta p \Delta z=\hbar/2ΔpΔz=ℏ/2), but their velocity distribution is narrower than that of the ground state. A compression of the velocity distribution by a factor 4 has been obtained. By applying the cooling of the vertical motion for a long time, thanks to the energy transfer from the horizontal to the vertical direction provided by the collisions, we cooled the movement in all three directions. In this way, we obtained a temperature T≃3 μT \simeq 3\,\muT≃3μK for which 80\% of the atoms are in the ground state of the vertical movement. The gas thus realized is pratically a two-dimensionnal gas. Finally, the study of thermalization showed that the scattering resonnance at zero energy of Cesium is not affected by the strong vertical confinement.
We discuss binary atomic collisions in a Bose gas tightly confined in one (axial) direction and identify two regimes of scattering. In the quasi-two-dimensional (quasi-2D) regime, where the confinement frequency ${\ensuremath{\omega}}_{0}$ greatly exceeds the gas temperature T,T,T, the scattering rates exhibit 2D features of the particle motion. At temperatures $T\ensuremath{\sim}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}$ one has a confinement-dominated 3D regime, where the confinement can change the momentum dependence of the scattering amplitudes. We describe the collision-induced energy exchange between the axial and radial degrees of freedom and analyze recent experiments on thermalization and spin-relaxation rates in a tightly (axially) confined gas of Cs atoms.