714 research outputs found
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 , while the CARL
limit is , where is the magnitude of the
difference of the wave vectors of the pump and probe fields, 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
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