Disruption of reflecting Bose-Einstein condensates due to inter-atomic interactions and quantum noise

We perform fully three-dimensional simulations, using the truncated Wigner method, to investigate the reflection of Bose-Einstein condensates from abrupt potential barriers. We show that the inter-atomic interactions can disrupt the internal structure of a cigar-shaped cloud with a high atom density at low approach velocities, damping the center-of-mass motion and generating vortices. Furthermore, by incorporating quantum noise we show that scattering halos form at high approach velocities, causing an associated condensate depletion. We compare our results to recent experimental observations.Comment: 5 figure

Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behaviour of a simple homogeneous Bose gas.Comment: Replaced paper same as original; correction to author list on cond-mat mad

Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen

We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9kHz) of transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic "foot" extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.Comment: 16 page J Phys B format plus 6 postscript figure

Derivation of quantum work equalities using quantum Feynman-Kac formula

On the basis of a quantum mechanical analogue of the famous Feynman-Kac formula and the Kolmogorov picture, we present a novel method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with previous methods in the literature, our method shows higher similarity in form to that deriving the classical fluctuation relations, which would give important insight when exploring new quantum fluctuation relations.Comment: 5 page

Thermal effects on chaotic directed transport

We study a chaotic ratchet system under the influence of a thermal environment. By direct integration of the Lindblad equation we are able to analyze its behavior for a wide range of couplings with the environment, and for different finite temperatures. We observe that the enhancement of the classical and quantum currents due to temperature depend strongly on the specific properties of the system. This makes difficult to extract universal behaviors. We have also found that there is an analogy between the effects of the classical thermal noise and those of the finite $\hbar$ size. These results open many possibilities for their testing and implementation in kicked BECs and cold atoms experiments.Comment: 5 pages, 4 figure

Memory-Controlled Diffusion

Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and non-local spatial-temporal memory effects. The realization of the memory kernels are restricted due the conservation of the basic quantity $p$. A general criteria is given for the existence of stationary solutions. In case the memory kernel depends on $p$ polynomially the transport is prevented. Owing to the delay effects a finite amount of particles remains localized and the further transport is terminated. For diffusion with non-linear memory effects we find an exact solution in the long-time limit. Although the mean square displacement shows diffusive behavior, higher order cumulants exhibits differences to diffusion and they depend on the memory strength

A quantum interface between light and nuclear spins in quantum dots

The coherent coupling of flying photonic qubits to stationary matter-based qubits is an essential building block for quantum communication networks. We show how such a quantum interface can be realized between a traveling-wave optical field and the polarized nuclear spins in a singly charged quantum dot strongly coupled to a high-finesse optical cavity. By adiabatically eliminating the electron a direct effective coupling is achieved. Depending on the laser field applied, interactions that enable either write-in or read-out are obtained.Comment: 10 pages, 5 figures, final versio

Monte Carlo simulations of bosonic reaction-diffusion systems

An efficient Monte Carlo simulation method for bosonic reaction-diffusion systems which are mainly used in the renormalization group (RG) study is proposed. Using this method, one dimensional bosonic single species annihilation model is studied and, in turn, the results are compared with RG calculations. The numerical data are consistent with RG predictions. As a second application, a bosonic variant of the pair contact process with diffusion (PCPD) is simulated and shown to share the critical behavior with the PCPD. The invariance under the Galilean transformation of this boson model is also checked and discussion about the invariance in conjunction with other models are in order.Comment: Publishe

Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation

We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a {\em rotating} dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched through the critical point for condensation, as in the experiment of Haljan et al. [Phys. Rev. Lett., 87, 21043 (2001)]. In contrast to stirring a vortex-free condensate, where topological constraints require that vortices enter from the edge of the condensate, we find that phase defects in the initial non-condensed cloud are trapped en masse in the emerging condensate. Bose-stimulated condensate growth proceeds into a disordered vortex configuration. At sufficiently low temperature the vortices then order into a regular Abrikosov lattice in thermal equilibrium with the rotating cloud. We calculate the effect of thermal fluctuations on vortex ordering in the final gas at different temperatures, and find that the BEC transition is accompanied by lattice melting associated with diminishing long range correlations between vortices across the system.Comment: 15 pages, 12 figure