135 research outputs found
Detection of vorticity in Bose-Einstein condensed gases by matter-wave interference
A phase-slip in the fringes of an interference pattern is an unmistakable
characteristic of vorticity. We show dramatic two-dimensional simulations of
interference between expanding condensate clouds with and without vorticity. In
this way, vortices may be detected even when the core itself cannot be
resolved.Comment: 3 pages, RevTeX, plus 6 PostScript figure
Quantum Noise and Superluminal Propagation
Causal "superluminal" effects have recently been observed and discussed in
various contexts. The question arises whether such effects could be observed
with extremely weak pulses, and what would prevent the observation of an
"optical tachyon." Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett., vol.
81, 2190 (1998)] have argued that quantum noise will preclude the observation
of a superluminal group velocity when the pulse consists of one or a few
photons. In this paper we reconsider this question both in a general framework
and in the specific example, suggested by Chiao, Kozhekin, and Kurizki [Phys.
Rev. Lett., vol. 77, 1254 (1996)], of off-resonant, short-pulse propagation in
an optical amplifier. We derive in the case of the amplifier a signal-to-noise
ratio that is consistent with the general ARS conclusions when we impose their
criteria for distinguishing between superluminal propagation and propagation at
the speed c. However, results consistent with the semiclassical arguments of
CKK are obtained if weaker criteria are imposed, in which case the signal can
exceed the noise without being "exponentially large." We show that the quantum
fluctuations of the field considered by ARS are closely related to
superfluorescence noise. More generally we consider the implications of
unitarity for superluminal propagation and quantum noise and study, in addition
to the complete and truncated wavepackets considered by ARS, the residual
wavepacket formed by their difference. This leads to the conclusion that the
noise is mostly luminal and delayed with respect to the superluminal signal. In
the limit of a very weak incident signal pulse, the superluminal signal will be
dominated by the noise part, and the signal-to-noise ratio will therefore be
very small.Comment: 30 pages, 1 figure, eps
Quantum State Reconstruction of a Bose-Einstein Condensate
We propose a tomographic scheme to reconstruct the quantum state of a
Bose-Einstein condensate, exploiting the radiation field as a probe and
considering the atomic internal degrees of freedom. The density matrix in the
number state basis can be directly retrieved from the atom counting
probabilities.Comment: 11 pages, LaTeX file, no figures, to appear in Europhysics Letter
Generalized Pseudopotentials for Higher Partial Wave Scattering
We derive a generalized zero-range pseudopotential applicable to all partial
wave solutions to the Schroedinger equation based on a delta-shell potential in
the limit that the shell radius approaches zero. This properly models all
higher order multipole moments not accounted for with a monopolar delta
function at the origin, as used in the familiar Fermi pseudopotential for
s-wave scattering. By making the strength of the potential energy dependent, we
derive self-consistent solutions for the entire energy spectrum of the
realistic potential. We apply this to study two particles in an isotropic
harmonic trap, interacting through a central potential, and derive analytic
expressions for the energy eigenstates and eigenvalues.Comment: RevTeX 4 pages, 1 figure, final published versio
A Knob for Changing Light Propagation from Subluminal to Superluminal
We show how the application of a coupling field connecting the two lower
metastable states of a lambda-system can produce a variety of new results on
the propagation of a weak electromagnetic pulse. In principle the light
propagation can be changed from subluminal to superluminal. The negative group
index results from the regions of anomalous dispersion and gain in
susceptibility.Comment: 6 pages,5 figures, typed in RevTeX, accepted in Phys. Rev.
Pseudopotential model of ultracold atomic collisions in quasi-one- and two-dimensional traps
We describe a model for s-wave collisions between ground state atoms in
optical lattices, considering especially the limits of quasi-one and two
dimensional axisymmetric harmonic confinement. When the atomic interactions are
modelled by an s-wave Fermi-pseudopotential, the relative motion energy
eigenvalues can easily be obtained. The results show that except for a bound
state, the trap eigenvalues are consistent with one- and two- dimensional
scattering with renormalized scattering amplitudes. For absolute scattering
lengths large compared with the tightest trap width, our model predicts a novel
bound state of low energy and nearly-isotropic wavefunction extending on the
order of the tightest trap width.Comment: 9 pages, 8 figures; submitted to Phys. Rev.
Entanglement of two interacting bosons in a two dimensional isotropic harmonic trap
We compute the pair entanglement between two interacting bosons in a two
dimensional (2D)isotropic harmonic trap. The interaction potential is modeled
by a 2D regularized pseudo-potential. By analytically decomposing the wave
function into the single particle basis, we show the dependency of the pair
entanglement on the scattering length. Our results turn out to be in good
agreements with earlier results using a quasi-2D geometry.Comment: 5 figure
Feshbach resonances in a quasi-2D atomic gas
Strongly confining an ultracold atomic gas in one direction to create a
quasi-2D system alters the scattering properties of this gas. We investigate
the effects of confinement on Feshbach scattering resonances and show that
strong confinement results in a shift in the position of the Feshbach resonance
as a function of the magnetic field. This shift, as well as the change of the
width of the resonance, are computed. We find that the resonance is strongly
damped in the thermal gas, but in the condensate the resonance remains sharp
due to many-body effects. We introduce a 2D model system, suited for the study
of resonant superfluidity, and having the same scattering properties as the
tightly confined real system near a Feshbach resonance. Exact relations are
derived between measurable quantities and the model parameters.Comment: 8 pages, 2 figure
Group velocity control in the ultraviolet domain via interacting dark-state resonances
The propagation of a weak probe field in a laser-driven four-level atomic
system is investigated. We choose mercury as our model system, where the probe
transition is in the ultraviolet region. A high-resolution peak appears in the
optical spectra due to the presence of interacting dark resonances. We show
that this narrow peak leads to superluminal light propagation with strong
absorption, and thus by itself is only of limited interest. But if in addition
a weak incoherent pump field is applied to the probe transition, then the peak
structure can be changed such that both sub- and superluminal light propagation
or a negative group velocity can be achieved without absorption, controlled by
the incoherent pumping strength
Transparent Anomalous Dispersion and Superluminal Light Pulse Propagation at a Negative Group Velocity
Anomalous dispersion cannot occur in a transparent passive medium where
electromagnetic radiation is being absorbed at all frequencies, as pointed out
by Landau and Lifshitz. Here we show, both theoretically and experimentally,
that transparent linear anomalous dispersion can occur when a gain doublet is
present. Therefore, a superluminal light pulse propagation can be observed even
at a negative group velocity through a transparent medium with almost no pulse
distortion. Consequently, a {\it negative transit time} is experimentally
observed resulting in the peak of the incident light pulse to exit the medium
even before entering it. This counterintuitive effect is a direct result of the
{\it rephasing} process owing to the wave nature of light and is not at odds
with either causality or Einstein's theory of special relativity.Comment: 12 journal pages, 9 figure
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