A time frequency analysis of wave packet fractional revivals

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.Comment: 9 pages, 4 figure

Transverse confinement in stochastic cooling of trapped atoms

Stochastic cooling of trapped atoms is considered for a laser-beam configuration with beam waists equal or smaller than the extent of the atomic cloud. It is shown, that various effects appear due to this transverse confinement, among them heating of transverse kinetic energy. Analytical results of the cooling in dependence on size and location of the laser beam are presented for the case of a non-degenerate vapour.Comment: 14 pages, 5 figures, accepted for publication in Journal of Optics

Comparison of Recoil-Induced Resonances (RIR) and Collective Atomic Recoil Laser (CARL)

The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B. Dubetsky and G. Grynberg, Phys. Rev. A {\bf 46}, 1426 (1992)] and the collective atomic recoil laser (CARL) [ R. Bonifacio and L. De Salvo, Nucl. Instrum. Methods A {\bf 341}, 360 (1994)] are compared. Both theories can be used to derive expressions for the gain experienced by a probe field interacting with an ensemble of two-level atoms that are simultaneously driven by a pump field. It is shown that the RIR and CARL formalisms are equivalent. Differences between the RIR and CARL arise because the theories are typically applied for different ranges of the parameters appearing in the theory. The RIR limit considered in this paper is $qP_{0}/M\omega_{q}\gg 1$, while the CARL limit is $qP_{0}/M\omega_{q}\lesssim 1$, where $$ is the magnitude of the difference of the wave vectors of the pump and probe fields, $P_{0}$ is the width of the atomic momentum distribution and $$ is a recoil frequency. The probe gain for a probe-pump detuning equal to zero is analyzed in some detail, in order to understand how the gain arises in a system which, at first glance, might appear to have vanishing gain. Moreover, it is shown that the calculations, carried out in perturbation theory have a range of applicability beyond the recoil problem. Experimental possibilities for observing CARL are discussed.Comment: 16 pages, 1 figure. Submitted to Physical Review

Ferromagnetism in a lattice of Bose condensates

We show that an ensemble of spinor Bose-Einstein condensates confined in a one dimensional optical lattice can undergo a ferromagnetic phase transition and spontaneous magnetization arises due to the magnetic dipole-dipole interaction. This phenomenon is analogous to ferromagnetism in solid state physics, but occurs with bosons instead of fermions.Comment: 4 pages, 2 figure

Keplerian Squeezed States and Rydberg Wave Packets

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments.Comment: accepted for publication in Physical Review

Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms

This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional/full revivals, which occurs on the time scale $t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale $t_{\rm rev}$. These long-term periodicities result in the autocorrelation function at times greater than $t_{\rm rev}$ having a self-similar resemblance to its structure for times less than $t_{\rm rev}$. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.Comment: To appear in Physical Review A, vol. 51, June 199

Wave Packet Echoes in the Motion of Trapped Atoms

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 non-adiabatically shifting the potential and stimulate their reoccurence 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

Elliptical Squeezed States and Rydberg Wave Packets

We present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.Comment: published in Phys. Rev. A, vol. 52, p. 2234, Sept. 199