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Physical Review A

Revivals, damping, and coherence times of atomic wave packets in optical lattices

Renato Ejnisman, Paul Rudy, Han Pu, N. P. Bigelow

Published Nov 1, 1997• 7 citations
Publisher

Abstract

We present a study of the time evolution of wave packets excited in optical lattices. Our model shows that, after a sudden change of the potential well depth, a breathing oscillation is created, in agreement with recently performed experiments. We predict that this motional wave packet should subsequently collapse and revive, with a rich intermediate structure comprised of fractional revivals. Moreover, we estimate the rate of damping of the oscillations due to the interaction of the atoms with light and other experimental constraints.

DOI
10.1103/physreva.56.4331

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Modern Physics Letters B•Apr 10, 2003•0 citations
We present a study of the time evolution of wave packets excited in optical lattices. Our model shows that, after a sudden change of the potential well depth, a breathing oscillation is created, in agreement with recently performed experiments. We predict that this motional wave packet should subsequently collapse and revive, with a rich intermediate structure comprised of fractional revivals. Moreover, we estimate the rate of damping of the oscillations due to the interaction of the atoms with light and other experimental constraints.
We study, experimentally and with quantum Monte-Carlo wave-function simulations, the effects of dispersion and dissipation on two types of spatial wave-packets of atoms in 1D and 3D optical lattices. Breathing-mode oscillations are excited by suddenly changing the potential depth after equilibration of the atoms at the lattice sites. The subsequent breathing-mode oscillations are measured using Bragg scattering. The second type of oscillations is prepared by suddenly shifting the lattice, thus exciting coherent-state-like wave-packets. These sloshing-type oscillations manifest themselves in a periodic photon redistribution between the lattice beams. We measure the resultant intensity exchange, which is a sensitive probe for the wave-packet evolution. For both types of wave-packets we observe an initial collapse within about three to six oscillation periods, a fact which we attribute to dephasing of the components of the wave-packets caused by the anharmonicity of the lattice potential. The initial collapse is followed by revivals of the wave-packets. Dissipation not only reduces the amplitude of these revivals but also modifies their shape and time of occurrence. In shallow lattices we observe that tunneling of the atoms between neighboring potential wells influences the wave-packet oscillations.
We study the effects of dispersion, tunneling, and dissipation on wave-packet oscillations resembling coherent states of atoms in optical lattices. The wave packets are prepared by suddenly shifting the lattice after equilibration of the atoms at the lattice sites. The atoms oscillate in the light-shift potential wells, which exert a force arising from photon redistribution between lattice beams. We measure the resultant periodic intensity exchange between the beams, obtaining information on the wave-packet evolution. We observe a strong impact of dissipation on the overall shape and the time of revivals, as well as a suppression of tunneling by weak magnetic fields.
We experimentally demonstrate and systematically study the stimulated revival (echo) of motional wave packet oscillations. For this purpose, we prepare wave packets in an optical lattice by nonadiabatically shifting the potential and stimulate their reoccurrence by a second shift after a variable time delay. This technique, analogous to spin echoes, enables one even in the presence of strong dephasing to determine the coherence time of the wave packets. We find that for strongly bound atoms it is comparable to the cooling time and much longer than the inverse of the photon scattering rate.
Using Bragg scattering we study classical squeezing and wave packet oscillations of the atomic center-of-mass motion of cesium atoms trapped in 1D and 3D optical lattices. A sudden increase of the potential depth leads to wave packets substantially more localized than in steady state, and subsequent breathing-mode oscillations with a decay rate that under some conditions is remarkably slow. We also study the response of the atoms to parametric driving of the center-of-mass motion. Our results are in agreement with Monte Carlo simulations.
Optical lattices are periodic light shift potentials that are created by the interference of several laser beams. In this dissertation I investigate the motion of atoms in such potentials. The center-of-mass wave-packet motion is initiated by an application of a sudden shift to the lattice potentials. The resulting oscillations are observed using a photon redistribution technique. We first show that by utilizing a real-time feedback loop and shifting the lattice continuously in response to the wave-packet motion, we can increase, alter or damp this motion using different gains of the feedback loop. We further show that by splitting the wave-packet between two adiabatic potentials of the lattice via quantum projection, we can construct an atom interferometer. We observe interference signal when the two components of the original wave-packet overlap. The behavior of the interference is studied as a function of lattice parameters and a consistent theoretical picture is developed. Further, we study how well-to-well tunneling of atoms and sloshing-type wave-pocket dynamics affect each other. We find that in the regions where the well-to-well tunneling is significant, the sloshing type wave-packet oscillations are suppressed. Sloshing-type motion only occurs if the tunneling is sufficiently suppressed with an applied magnetic field. Finally we describe a new type of optical lattice that is based on two-photon Raman transitions. The basic period of this lattice is reduced by a factor of two, compared with traditional lattices. We also show that Sub-Doppler cooling mechanism is present in this lattice. The dissertation is concluded with the presentation of a new experimental set-up for Bose-Einstein Condensate production, which may in the future be used for the study of BEC dynamics in optical lattices.