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Physical Review Letters

Observation of Temporal Behavior of an Atomic Wave Packet Localized in an Optical Potential

Mikio Kozuma, Ken-ichi Nakagawa, Wonho Jhe, Motoichi Ohtsu

Published Apr 1, 1996• 33 citations
Publisher

Abstract

We have investigated the dynamic temporal behavior of atomic motion in a periodic optical potential by detecting a recoil-induced resonance signal. In the slowly moving optical potential, damped oscillations are observed in the transient signal and the oscillation frequency is found to be independent of the moving speed of the potential. By using a Monte Carlo wave-function method, the signal can be attributed to the oscillatory motion of atomic wave packet localized in the potential, where the oscillation frequency corresponds to the energy separation between vibrational levels.

DOI
10.1103/physrevlett.76.2428

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We have investigated the dynamic temporal behavior of atomic motion in a periodic optical potential by detecting a recoil-induced resonance signal. In the slowly moving optical potential, damped oscillations are observed in the transient signal and the oscillation frequency is found to be independent of the moving speed of the potential. By using a Monte Carlo wave-function method, the signal can be attributed to the oscillatory motion of atomic wave packet localized in the potential, where the oscillation frequency corresponds to the energy separation between vibrational levels.
We demonstrate a method to directly observe the dynamics of motion of cold atoms in an optical standing wave using a recoil-induced resonance. By detecting a transient response of this resonance, we observed the interaction between an atomic population grating and a periodic optical potential. Using this method, we investigated the lifetime of the atomic grating under various conditions in the optical potential. As a result, we obtained the appropriate conditions for the long lifetime and observed the narrowest linewidth in the recoil-induced resonance corresponding to the atomic temperature of 4.4\ifmmode\pm\else\textpm\fi{}0.3 \ensuremath{\mu}K for 87Rb^{87}\mathrm{Rb}87Rb atoms.
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.
The dynamic localization of a two-level atom in a periodic potential under the action of spin-orbit coupling and a weak harmonically varying linear force is studied. We consider optical and Zeeman potentials that are either in phase or out of phase in two spinor components, respectively. The expectation value for the position of the atom after one oscillation period of the linear force is recovered in authentic resonances or in pseudoresonances. The frequencies of the linear force corresponding to authentic resonances are determined by the band structure of the periodic potential and are affected by the spin-orbit coupling. The width or dispersion of the wave packet in authentic resonances is usually minimal. The frequencies corresponding to pseudoresonances do not depend on the type of potential and on the strength of the spin-orbit coupling, while the evolution of excitations at the corresponding frequencies is usually accompanied by significant dispersion. Pseudoresonances are determined by the initial phase of the linear force and by the quasimomentum of the wave packet. Due to the spinor nature of the system, the motion of the atom is accompanied by periodic, but not harmonic, spin oscillations. Under the action of spin-orbit coupling the oscillations of the wave packet can be nearly completely suppressed in optical lattices. Dynamic localization in Zeeman lattices is characterized by doubling of the resonant oscillation periods due to band crossing at the boundary of the Brillouin zone. We also show that higher harmonics in the Fourier expansion of the energy band lead to effective dispersion, which can be strong enough to prevent dynamic localization of the Bloch wave packet.
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 abruptly subject laser-cooled 87Rb{}^{87}\mathrm{Rb}87Rb atoms to the one-dimensional, blue-detuned, optical standing-wave potential generated by two crossed probe laser beams and detect the phase change of the probe beam due to cold-atom dynamics. Damped oscillations of the observed phase signal are attributed to a temporal change of the root-mean-square position of the cold atoms relative to the minima of the periodic optical potential. The damping rate is in good agreement with numerical results, which take into account the potential anharmonicity but neglect spontaneous emission. The agreement indicates that the decay is mainly caused by dephasing due to trap anharmonicity. For sufficient low initial temperature, our calculations show quantum revivals of the wave-packet oscillation.
We report an experimental study of atomic motion in the Bloch band of a periodic potential. Our system consists of cold sodium atoms in a far detuned standing wave of near resonant light. We prepare the atoms in the lowest motional band, and then impose phase modulation in order to drive interband transitions. We observe Rabi oscillations between the first and second band as a function of modulation intensity and frequency. We also observe damped oscillations of the population as a function of modulation frequency, which are primarily due to a spread in Rabi frequencies over the Bloch band.