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arXiv:cond-mat/9712254 · Physical Review A

Echo in optical lattices: Stimulated revival of breathing oscillations

A. Bulatov, Anatoly B. Kuklov, Boris E. Vugmeister, HERSCHEL A. RABITZ

Published May 1, 1998• 22 citations
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Abstract

We analyze a stimulated revival (echo) effect for the breathing modes of atomic oscillations in optical lattices. The effect arises from the dephasing due to the weak anharmonicity being partly reversed in time by means of additional parametric excitation of the optical lattice. The shape of the echo response is obtained by numerically simulating the equation of motion for the atoms with subsequent averaging over the thermal initial conditions. A qualitative analysis of the phenomenon shows that the suggested echo mechanism combines the features of both spin and phonon echoes.

DOI
10.1103/physreva.57.3788

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We analyze a stimulated revival (echo) effect for the breathing modes of atomic oscillations in optical lattices. The effect arises from the dephasing due to the weak anharmonicity being partly reversed in time by means of additional parametric excitation of the optical lattice. The shape of the echo response is obtained by numerically simulating the equation of motion for the atoms with subsequent averaging over the thermal initial conditions. A qualitative analysis of the phenomenon shows that the suggested echo mechanism combines the features of both spin and phonon echoes.
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.
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 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 perform Raman spectroscopy of optically trapped noninteracting 87Rb^{87}\mathrm{Rb}87Rb atoms, and observe revivals of the atomic coherence at integer multiples of the trap period. The effect of coherence control methods such as echo and dynamical decoupling is investigated experimentally, analytically, and numerically, along with the effect of the anharmonicity of the trapping potential. The latter is shown to be responsible for incompleteness of the revivals. Coherent Raman control of trapped atoms can be useful in the context of free-oscillation atom interferometry and spatial multimode quantum memory.
We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of Anderson et al. [Phys. Rev. Lett. 90, 023001 (2003)] shows that it is a function of the survival probability or fidelity of eigenstates of the motion of the atoms in the trap. The echo coherence and the survival probability display ``system specific'' features, even when the underlying classical dynamics is chaotic. In particular, partial revivals in the echo signal and the survival probability are found for a small shift of the potential. Next, a ``semiclassical'' expression for the averaged echo signal is presented and used to calculate the echo signal for atoms in a light sheet wedge billiard. Revivals in the echo coherence are found in this system, indicating that they may be a generic feature of dipole traps.
In this thesis, I report on experiments with cold 85Rb atoms in a far-detuned one-dimensional optical lattice. These experiments are focused on creating efficient coupling between the quantized vibrational states of atoms in the optical lattice, on controlling and maintaining coherence between the vibrational states, and on developing a spectroscopy method to characterize the decay of coherence. First, I present an experimental study of the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold 85Rb atoms in the optical\nlattice. Experimental results show that a square pulse consisting of lattice displacements and a delay is more efficient than single-step and Gaussian pulses. The square pulse can be seen as an example of coherent control. Numerical calculations are in strong agreement with the experimental results. In addition, it is shown numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices, in which the coupling probability approaches the harmonic\noscillator limit. Next, the effectiveness of these pulses in reviving oscillations of atoms in vibrational superposition states using a pulse-echo technique is examined. Experimental results show that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These echo amplitudes are an order of magnitude larger than the echo amplitudes observed previously for the motional states of atoms in optical lattices.\nWith the aim of the optimized square echo pulse, echo amplitude is measured at much\nlonger times, where a surprising coherence freeze (plateau) is observed. To investigate \nmechanisms responsible for the observed echo decay and the coherence freeze, we developed\na new two-dimensional pump-probe spectroscopy technique to monitor the evolution of frequency-frequency correlations in the system, a necessary input for understanding the decay of coherence. Through this 2D technique, we have characterized the temporal decay of frequency memory and through our simulations we find that coherence freeze is related to the shape of this memory loss function. This technique is general in that it can be applied in a variety of quantum information candidate systems to probe the nature of their decoherence.