We present a theoretical treatment of coherent light scattering from an interacting 1D Bose gas at finite temperatures. We show how this can provide a nondestructive measurement of the atomic system states. The equilibrium states are determined by th
e temperature and interaction strength, and are characterized by the spatial density-density correlation function. We show how this correlation function is encoded in the angular distribution of the fluctuations of the scattered light intensity, thus providing a sensitive, quantitative probe of the density-density correlation function and therefore the quantum state of the gas.
We perform finite-temperature dynamical simulations of the arrest of a rotating Bose-Einstein condensate by a fixed trap anisotropy, using a Hamiltonian classical-field method. We consider a quasi-two-dimensional condensate containing a single vortex
in equilibrium with a rotating thermal cloud. Introducing an elliptical deformation of the trapping potential leads to the loss of angular momentum from the system. We identify the condensate and the complementary thermal component of the nonequilibrium field, and compare the evolution of their angular momenta and angular velocities. By varying the trap anisotropy we alter the relative efficiencies of the vortex-cloud and cloud-trap coupling. For strong trap anisotropies the angular momentum of the thermal cloud may be entirely depleted before the vortex begins to decay. For weak trap anisotropies, the thermal cloud exhibits a long-lived steady state in which it rotates at an intermediate angular velocity.
We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation,
when constrained to a finite conserved angular momentum. In an isotropic trapping potential the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.
We present a quantum mechanical treatment of the mechanical stirring of Bose-Einstein condensates using classical field techniques. In our approach the condensate and excited modes are described using a Hamiltonian classical field method in which the
atom number and (rotating frame) energy are strictly conserved. We simulate a T = 0 quasi-2D condensate perturbed by a rotating anisotropic trapping potential. Vacuum fluctuations in the initial state provide an irreducible mechanism for breaking the initial symmetries of the condensate and seeding the subsequent dynamical instability. Highly turbulent motion develops and we quantify the emergence of a rotating thermal component that provides the dissipation necessary for the nucleation and motional-damping of vortices in the condensate. Vortex lattice formation is not observed, rather the vortices assemble into a spatially disordered vortex liquid state. We discuss methods we have developed to identify the condensate in the presence of an irregular distribution of vortices, determine the thermodynamic parameters of the thermal component, and extract damping rates from the classical field trajectories.
