616 research outputs found
Functional Wigner representation of BEC quantum dynamics
We develop a method of simulating the full quantum field dynamics of
multi-mode multi-component Bose-Einstein condensates in a trap. We use the
truncated Wigner representation to obtain a probabilistic theory that can be
sampled. This method produces c-number stochastic equations which may be solved
using conventional stochastic methods. The technique is valid for large mode
occupation numbers. We give a detailed derivation of methods of functional
Wigner representation appropriate for quantum fields. Our approach describes
spatial evolution of spinor components and properly accounts for nonlinear
losses. Such techniques are applicable to calculating the leading quantum
corrections, including effects like quantum squeezing, entanglement, EPR
correlations and interactions with engineered nonlinear reservoirs. By using a
consistent expansion in the inverse density, we are able to explain an
inconsistency in the nonlinear loss equations found by earlier authors
Electromagnetic quantization in dispersive inhomogeneous nonlinear dielectrics
A technique of canonical quantization in a general dispersive nonlinear dielectric medium is presented. The medium can be inhomogeneous and anisotropic. The fields are expanded in a slowly varying envelope approximation to allow quantization. An arbitrary number of envelopes is included, assuming lossless propagation in each relevant frequency band. The resulting Lagrangian and Hamiltonian agree with known propagation equations and expressions for the dispersive energy. The central result of the theory is an expansion of the quantum Hamiltonian in terms of annihilation and creation operators corresponding to group-velocity photon-polariton excitations in the dielectric
Critical fluctuations in an optical parametric oscillator: when light behaves like magnetism
We study the nondegenerate optical parametric oscillator in a planar
interferometer near threshold, where critical phenomena are expected. These
phenomena are associated with nonequilibrium quantum dynamics that are known to
lead to quadrature entanglement and squeezing in the oscillator field modes. We
obtain a universal form for the equation describing this system, which allows a
comparison with other phase transitions. We find that the unsqueezed
quadratures of this system correspond to a two-dimensional XY-type model with a
tricritical Lifshitz point. This leaves open the possibility of a controlled
experimental investigation into this unusual class of statistical models. We
evaluate the correlations of the unsqueezed quadrature using both an exact
numerical simulation and a Gaussian approximation, and obtain an accurate
numerical calculation of the non-Gaussian correlations.Comment: Title changed. New figures adde
Finite temperature phase diagram of a spin-polarized ultracold Fermi gas in a highly elongated harmonic trap
We investigate the finite temperature properties of an ultracold atomic Fermi
gas with spin population imbalance in a highly elongated harmonic trap.
Previous studies at zero temperature showed that the gas stays in an exotic
spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid
state at the trap center; while moving to the edge, the system changes into
either a non-polarized Bardeen-Cooper-Schriffer superfluid () or a fully
polarized normal gas (), depending on the smallness of the spin
polarization , relative to a critical value . In this work, we show how
these two phase-separation phases evolve with increasing temperature, and
thereby construct a finite temperature phase diagram. For typical interactions,
we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy
temperature, which seems to be accessible in the current experiment. The
density profile, equation of state, and specific heat of the polarized system
have been calculated and discussed in detail. Our results are useful for the
on-going experiment at Rice University on the search for FFLO states in
quasi-one-dimensional polarized Fermi gases.Comment: 9 pages and 8 figures; Published version in Phys. Rev.
Exact few-body results for strongly correlated quantum gases in two dimensions
The study of strongly correlated quantum gases in two dimensions has
important ramifications for understanding many intriguing pheomena in solid
materials, such as high- superconductivity and the fractional quantum
Hall effect. However, theoretical methods are plagued by the existence of
significant quantum fluctuations. Here, we present two- and three-body exact
solutions for both fermions and bosons trapped in a two-dimensional harmonic
potential, with an arbitrary -wave scattering length. These few-particle
solutions link in a natural way to the high-temperature properties of
many-particle systems via a quantum virial expansion. As a concrete example,
using the energy spectrum of few fermions, we calculate the second and third
virial coefficients of a strongly interacting Fermi gas in two dimensions, and
consequently investigate its high-temperature thermodynamics. Our thermodynamic
results may be useful for ongoing experiments on two-dimensional Fermi gases.
These exact results also provide an unbiased benchmark for quantum Monte Carlo
simulations of two-dimensional Fermi gases at high temperatures.Comment: 11 pages, 6 figure
Static structure factor of a strongly correlated Fermi gas at large momenta
We theoretically investigate the static structure factor of an interacting
Fermi gas near the BEC-BCS crossover at large momenta. Due to short-range
two-body interactions, we predict that the structure factor of unlike spin
correlations falls off as in a universal
scaling region with large momentum and large scattering length. The
scaling coefficient is determined by the celebrated Tan's contact parameter,
which links the short-range behavior of many-body systems to their universal
thermodynamic properties. By implementing this new Tan relation together with
the random-phase approximation and the virial expansion theory in various
limiting cases, we show how to calculate at zero
and finite temperatures for arbitrary interaction strengths, at momentum
transfer higher than the Fermi momentum. Our results provide a way to
experimentally confirm a new Tan relation and to accurately measure the value
of contact parameter.Comment: 8 pages, 3 figures; revised according to the Referee's suggestions;
publised versio
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