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Physical Review Letters

Paramagnetism in a Cesium Optical Lattice

D. R. Meacher, S. Guibal, C. Mennerat-Robilliard, J.-Y. Courtois, K.I. Petsas, G. Grynberg

Published Mar 1, 1995• 27 citations
Publisher

Abstract

We report the observation of paramagnetic behavior of an optical lattice operating on the ${F}_{g}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{\rightarrow}{F}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5$ resonance of cesium. This paramagnetism results from the transfer of population between optical potential wells associated with different magnetic sublevels. The populations are deduced from the amplitudes of stimulated Raman resonances observed in the transmission spectra of probe beams with ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ circular polarizations.

DOI
10.1103/physrevlett.74.1958

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Journal of Experimental and Theoretical Physics•May 1, 2014•3 citations
We report the observation of paramagnetic behavior of an optical lattice operating on the Fg=4\ensuremath→Fe=5{F}_{g}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{\rightarrow}{F}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5Fg​=4\ensuremath→Fe​=5 resonance of cesium. This paramagnetism results from the transfer of population between optical potential wells associated with different magnetic sublevels. The populations are deduced from the amplitudes of stimulated Raman resonances observed in the transmission spectra of probe beams with \ensuremathσ+{\ensuremath{\sigma}}^{+}\ensuremathσ+ and \ensuremathσ\ensuremath−{\ensuremath{\sigma}}^{\ensuremath{-}}\ensuremathσ\ensuremath− circular polarizations.
We show, experimentally and using quantum Monte Carlo simulations, that the quasithermal paramagnetic behavior of cesium atoms in a one-dimensional $\mathrm{lin}\mathrm{\ensuremath{\perp}}\mathrm{lin}$ optical lattice is characterized by a spin temperature of twice the zero-field kinetic temperature. The magnetization is maximum and almost perfect when the Zeeman shift of the extreme magnetic sublevels approximately equals half the maximum light shift. The lifetime of magnetization and the laser-cooling time constant are found to be clearly distinct, the magnetization decay time amounting to at least three times the cooling time. Using simulations we find that the magnetic-dipole correlation time is approximately proportional to the angular momentum FFF of the atoms, while cooling and energy correlation time constants are approximately independent of F.F.F. Our results imply that for large FFF laser cooling within single light-shift potential wells (local cooling) occurs.
We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the 6S1∕2,F=3,mF=06{S}_{1∕2},F=3,{m}_{F}=06S1∕2​,F=3,mF​=0 or 6S1∕2,F=3,mF=36{S}_{1∕2},F=3,{m}_{F}=36S1∕2​,F=3,mF​=3 state by optically pumping atoms trapped in a magneto-optical trap. We use the D1D1D1 resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the mF=0{m}_{F}=0mF​=0 and mF=3{m}_{F}=3mF​=3 cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the mF=0{m}_{F}=0mF​=0 state, it is dissipation and circular dichroism that are important when they are in the mF=3{m}_{F}=3mF​=3 state. Similarly, while the size of the Faraday rotation and the circular dichroism for the mF=0{m}_{F}=0mF​=0 case scales linearly with the applied magnetic field, for the mF=3{m}_{F}=3mF​=3 case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.
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.
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.
The evolution of the populations of the magnetic sublevels of the cesium atom (133Cs isotope) in resonant laser fields with linear polarization is analyzed using the equations for the density matrix. Analytic expressions are derived for stationary populations resulting from laser-induced optical transitions on the hyperfine structure components F g = 3 ↔ F e = 2, 3 and F f = 4 ↔ F e = 3, 4 of lines D1 (62S1/2 → 62P1/2) and D2 (62S1/2 → 62P3/2) depending on the initial values of the populations. The numerical solution of the evolution equations gives the characteristic times of stabilization of the steady regime as functions of laser field intensities and detuning from optical resonance. We determine the sequences of optical transitions increasing (by more than an order of magnitude) the population of the lower sublevel 62S1/2F g = 3 M = 0 of the “clock” microwave transition F g = 3 M = 0 ↔ F f = 4 M = 0 in the cesium frequency standard, which increases the signal intensity in the recording system by the same proportion.