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

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

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

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Spectral line shape of resonant four-wave mixing induced by broad-bandwidth lasers

We present a theoretical and experimental study of the line shape of resonant four-wave mixing induced by broad-bandwidth laser radiation that revises the theory of Meacher, Smith, Ewart, and Cooper (MSEC) [Phys. Rev. A 46, 2718 (1992)]. We adopt the same method as MSEC but correct for an invalid integral used to average over the distribution of atomic velocities. The revised theory predicts a Voigt line shape composed of a homogeneous, Lorentzian component, defined by the collisional rate Γ, and an inhomogeneous, Doppler component, which is a squared Gaussian. The width of the inhomogeneous component is reduced by a factor of √2 compared to the simple Doppler width predicted by MSEC. In the limit of dominant Doppler broadening, the width of the homogeneous component is predicted to be 4Γ, whereas in the limit of dominant homogeneous broadening, the predicted width is 2Γ. An experimental measurement is reported of the line shape of the four-wave-mixing signal using a broad-bandwidth, "modeless", laser resonant with the Q1 (6) line of the A2 Σ - X2 Π(0,0) system of the hydroxyl radical. The measured widths of the Voigt components were found to be consistent with the predictions of the revised theory

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