Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study

Within the classical field model, we find that the phase of a Bose-Einstein condensate undergoes a true diffusive motion in the microcanonical ensemble, the variance of the condensate phase change between time zero and time $t$ growing linearly in $t$. The phase diffusion coefficient obeys a simple scaling law in the double thermodynamic and Bogoliubov limit. We construct an approximate calculation of the diffusion coefficient, in fair agreement with the numerical results over the considered temperature range, and we extend this approximate calculation to the quantum field.Comment: 9 pages, 6 figure

Splitting and merging an elongated Bose-Einstein condensate at finite temperature

We analyze coherence effects during the splitting of a quasi one-dimensional condensate into two spatially separated ones and their subsequent merging into a single condensate. Our analysis takes into account finite-temperature effects, where phase fluctuations play an important role. We show that, at zero-temperature, the two split condensates can be merged into a single one with a negligible phase difference. By increasing temperature to a finite value below the critical point for condensation ($T_c$), i.e., $0 \le T/T_c < 1$, a considerable enhancement of phase and density fluctuations appears during the process of splitting and merging. Our results show that if the process of splitting and merging is sufficiently adiabatic, the whole process is quite insensitive to phase fluctuations and even at high temperatures, a single condensate can be produced.Comment: 8 pages, 6 figure

Two point correlations of a trapped interacting Bose gas at finite temperature

We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of s-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of $0.6T_c$ to $1.0T_c$. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.Comment: 9 pages, 4 figure

Full counting statistics of heteronuclear molecules from Feshbach-assisted photo association

We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation [Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities with sum frequency generation and using quantum optics methods we consider the cases where the molecules are formed from atoms out of two Bose-Einstein condensates, out of a Bose-Einstein condensate and a gas of degenerate fermions, and out of two degenerate Fermi gases with and without superfluidity. Bosons are treated in a single mode approximation and fermions in a degenerate model. In these approximations we can numerically solve the master equations describing the system's dynamics and thus we find the full counting statistics of the molecular modes. The full quantum dynamics calculations are complemented by mean field calculations and short time perturbative expansions. While the molecule production rates are very similar in all three cases at this level of approximation, differences show up in the counting statistics of the molecular fields. The intermediate field of closed-channel molecules is for short times second-order coherent if the molecules are formed from two Bose-Einstein condensates or a Bose-Fermi mixture. They show counting statistics similar to a thermal field if formed from two normal Fermi gases. The coherence properties of molecule formation in two superfluid Fermi gases are intermediate between the two previous cases. In all cases the final field of deeply-bound molecules is found to be twice as noisy as that of the intermediate state. This is a consequence of its coupling to the lossy optical cavity in our model, which acts as an input port for quantum noise, much like the situation in an optical beam splitter.Comment: replacement of earlier manuscript cond-mat/0508080 ''Feshbach-assisted photoassociation of ultracold heteronuclear molecules'' with minor revision

Dipolar Relaxation in an ultra-cold Gas of magnetically trapped chromium atoms

We have investigated both theoretically and experimentally dipolar relaxation in a gas of magnetically trapped chromium atoms. We have found that the large magnetic moment of 6 $\mu_B$ results in an event rate coefficient for dipolar relaxation processes of up to $3.2\cdot10^{-11}$ cm$^{3}$s$^{-1}$ at a magnetic field of 44 G. We present a theoretical model based on pure dipolar coupling, which predicts dipolar relaxation rates in agreement with our experimental observations. This very general approach can be applied to a large variety of dipolar gases.Comment: 9 pages, 9 figure

Anisotropic pseudo-potential for polarized dilute quantum gases

Anisotropic pseudopotential relevant to collisions of two particles polarized by external field is rigorously derived and its properties are investigated. Such low-energy pseudopotential may be useful in describing collective properties of dilute quantum gases, such as molecules polarized by electric field or metastable $^3P_2$ atoms polarized by magnetic field. The pseudopotential is expressed in terms of reactance (K--) matrix and derivatives of Dirac delta-function. In most applications it may be represented as a sum of traditional spherically-symmetric contact term and anisotropic part. The former contribution may be parameterized by a generalized scattering length. The anisotropic part of pseudopotential may be characterized by off-diagonal scattering length for dipolar interactions and off-diagonal scattering volume for quadrupolar interactions. Two-body matrix element of the pseudopotential in a basis of plane waves is also derived.Comment: 1 Fig, submitted to Phys. Rev.

Conventional character of the BCS-BEC cross-over in ultra-cold gases of 40K

We use the standard fermionic and boson-fermion Hamiltonians to study the BCS-BEC cross-over near the 202 G resonance in a two-component mixture of fermionic 40K atoms employed in the experiment of C.A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004). Our mean-field analysis of many-body equilibrium quantities shows virtually no differences between the predictions of the two approaches, provided they are both implemented in a manner that properly includes the effect of the highest excited bound state of the background scattering potential, rather than just the magnetic-field dependence of the scattering length. Consequently, we rule out the macroscopic occupation of the molecular field as a mechanism behind the fermionic pair condensation and show that the BCS-BEC cross-over in ultra-cold 40K gases can be analysed and understood on the same basis as in the conventional systems of solid state physics.Comment: 16 pages, 10 eps figures; final versio

Hydrodynamic excitations of trapped dipolar fermions

A single-component Fermi gas of polarized dipolar particles in a harmonic trap can undergo a mechanical collapse due to the attractive part of the dipole-dipole interaction. This phenomenon can be conveniently manipulated by the shape of the external trapping potential. We investigate the signatures of the instability by studying the spectrum of low-lying collective excitations of the system in the hydrodynamic regime. To this end, we employ a time-dependent variational method as well as exact numerical solutions of the hydrodynamic equations of the system.Comment: 4 pages, 2 eps figures, final versio

Classical field techniques for condensates in one-dimensional rings at finite temperatures

For a condensate in a one-dimensional ring geometry, we compare the thermodynamic properties of three conceptually different classical field techniques: stochastic dynamics, microcanonical molecular dynamics, and the classical field method. Starting from non-equilibrium initial conditions, all three methods approach steady states whose distribution and correlation functions are in excellent agreement with an exact evaluation of the partition function in the high-temperature limit. Our study helps to establish these various classical field techniques as powerful non-perturbative tools for systems at finite temperatures.Comment: 7 pages, 7 figures; minor changes, one reference adde

Collapsing Bose-Einstein condensates beyond the Gross-Pitaevskii approximation

We analyse quantum field models of the bosenova experiment, in which $^{85}$Rb Bose-Einstein condensates were made to collapse by switching their atomic interactions from repulsive to attractive. Specifically, we couple the lowest order quantum field correlation functions to the Gross-Pitaevskii function, and solve the resulting dynamical system numerically. Comparing the computed collapse times with the experimental measurements, we find that the calculated times are much larger than the measured values. The addition of quantum field corrections does not noticeably improve the agreement compared to a pure Gross-Pitaevskii theory.Comment: 8 pages, 4 figure