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Physical Review A

Temperature and magnetism of gray optical lattices

K.I. Petsas, J.-Y. Courtois, G. Grynberg

Published Apr 1, 1996• 18 citations
Publisher

Abstract

We present a theoretical investigation of the temperature and of the magnetization of atoms in one-dimensional ``gray'' optical lattices. Such lattices consist of counterpropagating beams having crossed linear polarizations, tuned on the blue side of a J\ensuremath{\rightarrow}J or a J\ensuremath{\rightarrow}J-1 transition, and a static longitudinal magnetic field. The variation of the atomic temperature with the magnetic field recently observed (an increase at low magnetic field; a decrease towards an asymptotic value at high magnetic field) is found for any atomic transition admitting one or two uncoupled states. This change of behavior of the temperature results from a qualitative change of the cooling mechanism and is correlated with a transition from paramagnetism to antiparamagnetism in the optical lattice. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2533

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We present a theoretical investigation of the temperature and of the magnetization of atoms in one-dimensional ``gray'' optical lattices. Such lattices consist of counterpropagating beams having crossed linear polarizations, tuned on the blue side of a J\ensuremath{\rightarrow}J or a J\ensuremath{\rightarrow}J-1 transition, and a static longitudinal magnetic field. The variation of the atomic temperature with the magnetic field recently observed (an increase at low magnetic field; a decrease towards an asymptotic value at high magnetic field) is found for any atomic transition admitting one or two uncoupled states. This change of behavior of the temperature results from a qualitative change of the cooling mechanism and is correlated with a transition from paramagnetism to antiparamagnetism in the optical lattice. \textcopyright{} 1996 The American Physical Society.
The motion of atoms in a dark magneto-optical lattice is considered. This lattice is formed by a nonuniformly polarized laser field in the presence of a static magnetic field. Cold atoms are localized in the vicinity of points where dark states are not destroyed by a magnetic field. As a result, the optical interaction tends to zero (dark or gray lattices). Depending on the field configuration, such a lattice can exhibit one, two, or three-dimensional periodicity. It is shown that in 1D and 2D, mark magneto- optical lattices the effects connected with the Bose- statistics of particles can be observed under the temperature 10-5 - 10-6K and densities 1011 - 1012cm-3, those are usual for current experiments on laser cooling.
The probe-transmission spectrum of a one-dimensional optical lattice is calculated. The optical lattice consists of atoms that are cooled by a pair of counterpropagating, linearly polarized fields, whose frequency \ensuremath{\omega} is detuned to the blue side of an atomic transition. A weak probe field of frequency ${\mathrm{\ensuremath{\omega}}}^{\ensuremath{'}}$ is assumed to be propagating in the same direction as one of the cooling fields. It is shown that, owing to the existence of dark and gray states in the lattice, the probe-transmission spectrum exhibits interesting features that are qualitatively different from those of a ``normal'' optical lattice with red-detuned cooling fields. Examples of these features include subrecoil linewidths and reversed absorption-amplification sidebands. It is shown that by monitoring the magnitudes of resonance signals in the spectrum, one can gain information on the evolution of the dark-state population in the lattice.
The motion of atoms in a dark magneto-optical lattice is considered. This lattice is formed by a non-uniformly polarized laser field in the presence of a static magnetic field. Cold atoms are localized in the vicinity of points where dark states are not destroyed by a magnetic field. As a result, the optical interaction tends to zero (dark or grey lattices). Depending on the field configuration such a lattice can exhibit one-dimensional (1D) or two-dimensional (2D) periodicity. It is shown that in 1D and 2D dark magneto-optical lattices the effects connected with the Bose statistics of particles can be observed under temperatures 10 -5 -10 -6 K and densities 10 11 -10 12 cm -3 , i.e. those that are usual for current experiments on laser cooling.
The magnetization and lifetimes of atoms in gray optical lattices exhibit modulations as functions of an applied B field that are attributed to tunneling resonances between neighboring lattice wells. Expanding on previous observations, we show how these modulations depend on well depth, and we derive spin temperatures for the system. A band-structure-based model and quantum Monte Carlo wave-function simulations are used to explain these results. We predict subrecoil structures in the velocity distributions; these structures undergo systematic variations when the applied magnetic field is varied. Dramatically different behaviors for bosonic and fermionic spin systems are found and explained.
We present a new type of lattice for trapping cold atoms in nearly-dark states where they weakly interact with light. The periodic potential is obtained with fields in a lin ⊥ lin configuration tuned on the blue side of a J → J transition and in the presence of a uniform static magnetic field. A numerical analysis performed for J = 4 demonstrates the occurrence of very small absorption widths and large populations in the lowest vibrational states. These lattices should be interesting for increasing the atomic density and for observing delocalized atomic wave functions.
Summary form only given. We have performed a detailed study of the steady-state temperature and other parameters in a three-dimensional optical lattice for a wide range of detunings. Specifically we have investigated the situation with the detuned blue light of a J-J transition, and configurations where several allowed transitions may influence the results. We load a chirp cooled Cs-beam into a magneto-optical trap, cool the atoms in an optical molasses and load them into a four-beam three-dimensional optical lattice. The lattice beams are detuned below the transition between the states 6s/sup 2/S/sub 1/2/, F=4 and 6p/sup 2/P/sub 3/2/, F' =5, at 852 nm. The detuning is varied from -5/spl Gamma/ (where /spl Gamma//2/spl pi/=5.22 MHz is the natural linewidth of the transition) all the way to the F=4/spl rarr/F'=4 transition, located -48.3/spl Gamma/ away. For each detuning we let the atoms equilibrate in the lattice, and measure the steady-state temperature by a time of flight technique.