571 research outputs found
Phase Coherence in a Driven Double-Well System
We analyze the dynamics of the molecular field incoherently pumped by the
photoassociation of fermionic atoms and coupled by quantum tunnelling in a
double-well potential. The relative phase distribution of the molecular modes
in each well and their phase coherence are shown to build up owing to quantum
mechanical fluctuations starting from the vacuum state. We identify three
qualitatively different steady-state phase distributions, depending on the
ratio of the molecule-molecule interaction strength to interwell tunnelling,
and examine the crossover from a phase-coherent regime to a phase-incoherent
regime as this ratio increases.Comment: 5 pages, 2 figure
Quantum dynamics of cavity assisted photoassociation of Bose-Einstein condensed atoms
We explore the quantum dynamics of photoassociation of Bose-Einstein
condensed atoms into molecules using an optical cavity field. Inside of an
optical resonator, photoassociation of quantum degenerate atoms involves the
interaction of three coupled quantum fields for the atoms, molecules, and the
photons. The feedback created by a high-Q optical cavity causes the cavity
field to become a dynamical quantity whose behavior is linked in a nonlinear
manner to the atoms inside and where vacuum fluctuations have a more important
role than in free space. We develop and compare several methods for calculating
the dynamics of the atom-molecule conversion process with a coherently driven
cavity field. We first introduce an alternate operator representation for the
Hamiltonian from which we derive an improved form of mean field theory and an
approximate solution of the Heisenberg-Langevin (HL) equations that properly
accounts for quantum noise in the cavity field. It is shown that our improved
mean field theory corrects several deficiencies in traditional mean field
theory based on expectation values of annihilation/creation operators. Also, we
show by direct comparison to numerical solutions of the density matrix
equations that our approximate quantum solution of HL equations gives an
accurate description of weakly or undriven cavities where mean field theories
break down
Phase Conjugation of a Quantum-Degenerate Atomic Fermi Beam
We discuss the possibility of phase-conjugation of an atomic Fermi field via
nonlinear wave mixing in an ultracold gas. It is shown that for a beam of
fermions incident on an atomic phase-conjugate mirror, a time reversed backward
propagating fermionic beam is generated similar to the case in nonlinear
optics. By adopting an operational definition of the phase, we show that it is
possible to infer the presence of the phase-conjugate field by the loss of the
interference pattern in an atomic interferometer
Molecule formation as a diagnostic tool for second order correlations of ultra-cold gases
We calculate the momentum distribution and the second-order correlation
function in momentum space, for molecular dimers
that are coherently formed from an ultracold atomic gas by photoassociation or
a Feshbach resonance. We investigate using perturbation theory how the quantum
statistics of the molecules depend on the initial state of the atoms by
considering three different initial states: a Bose-Einstein condensate (BEC), a
normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The
cases of strong and weak coupling to the molecular field are discussed. It is
found that BEC and BCS states give rise to an essentially coherent molecular
field with a momentum distribution determined by the zero-point motion in the
confining potential. On the other hand, a normal Fermi gas and the unpaired
atoms in the BCS state give rise to a molecular field with a broad momentum
distribution and thermal number statistics. It is shown that the first-order
correlations of the molecules can be used to measure second-order correlations
of the initial atomic state.Comment: revtex, 15 pages,8 figure
Diffraction of ultra-cold fermions by quantized light fields: Standing versus traveling waves
We study the diffraction of quantum degenerate fermionic atoms off of
quantized light fields in an optical cavity. We compare the case of a linear
cavity with standing wave modes to that of a ring cavity with two
counter-propagating traveling wave modes. It is found that the dynamics of the
atoms strongly depends on the quantization procedure for the cavity field. For
standing waves, no correlations develop between the cavity field and the atoms.
Consequently, standing wave Fock states yield the same results as a classical
standing wave field while coherent states give rise to a collapse and revivals
in the scattering of the atoms. In contrast, for traveling waves the scattering
results in quantum entanglement of the radiation field and the atoms. This
leads to a collapse and revival of the scattering probability even for Fock
states. The Pauli Exclusion Principle manifests itself as an additional
dephasing of the scattering probability
Transient cosmic acceleration from interacting fluids
Recent investigations seem to favor a cosmological dynamics according to
which the accelerated expansion of the Universe may have already peaked and is
now slowing down again \cite{sastaro}. As a consequence, the cosmic
acceleration may be a transient phenomenon. We investigate a toy model that
reproduces such a background behavior as the result of a time-dependent
coupling in the dark sector which implies a cancelation of the "bare"
cosmological constant. With the help of a statistical analysis of Supernova
Type Ia (SNIa) data we demonstrate that for a certain parameter combination a
transient accelerating phase emerges as a pure interaction effect.Comment: Latex file, 23 pages, 21 figures in eps format. Discussion enlarged,
new subsection on scalar field dynamics included, accepted for publication in
JCAP
Testing homogeneity with galaxy number counts : light-cone metric and general low-redshift expansion for a central observer in a matter dominated isotropic universe without cosmological constant
As an alternative to dark energy it has been suggested that we may be at the
center of an inhomogeneous isotropic universe described by a
Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to
test this hypothesis we calculate the general analytical formula to fifth order
for the redshift spherical shell mass. Using the same analytical method we
write the metric in the light-cone by introducing a gauge invariant quantity
which together with the luminosity distance completely
determine the light-cone geometry of a LTB model.Comment: 13 page
Measuring dark energy spatial inhomogeneity with supernova data
The gravitational lensing distortion of distant sources by the large-scale
distribution of matter in the Universe has been extensively studied. In
contrast, very little is known about the effects due to the large-scale
distribution of dark energy. We discuss the use of Type Ia supernovae as probes
of the spatial inhomogeneity and anisotropy of dark energy. We show that a
shallow, almost all-sky survey can limit rms dark energy fluctuations at the
horizon scale down to a fractional energy density of ~10^-4Comment: 4 pages; PRL submitte
Boson-Fermion coherence in a spherically symmetric harmonic trap
We consider the photoassociation of a low-density gas of quantum-degenerate
trapped fermionic atoms into bosonic molecules in a spherically symmetric
harmonic potential. For a dilute system and the photoassociation coupling
energy small compared to the level separation of the trap, only those fermions
in the single shell with Fermi energy are coupled to the bosonic molecular
field. Introducing a collective pseudo-spin operator formalism we show that
this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum
optics, with an additional pairing interaction. By exact diagonalization of the
Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi
system, and study the dynamics of the coherent coupling between atoms and
molecules. In a semiclassical description of the system, the pairing
interaction between fermions is shown to result in a self-trapping transition
in the photoassociation, with a sudden suppression of the coherent oscillations
between atoms and molecules. We also show that the full quantum dynamics of the
system is dominated by quantum fluctuations in the vicinity of the
self-trapping solution.Comment: 16 pages, 14 figure
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