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 ($P<P_c$) or a fully polarized normal gas ($P>P_c$), depending on the smallness of the spin polarization $P$, relative to a critical value $P_c$. 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-$T_{c}$ 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 $s$-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 $S_{\uparrow\downarrow}(q)$ falls off as $1/q$ in a universal scaling region with large momentum $\hbar q$ 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 $S_{\uparrow\downarrow}(q)$ 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