Quantum turbulence in condensate collisions: an application of the classical field method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our non-perturbative method includes the effect of quantum noise, and provides for the first time a theoretical description of collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms are calculated from a single simulation, and show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms--a property which should be straightforwardly measurable.Comment: 5 pages, 3 figures: Rewritten text, replaced figure

Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques

We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented.Comment: 110 pages, 32 figures. Updated to address referee comments. To appear in Advances in Physic

Giant Vortex Lattice Deformations in Rapidly Rotating Bose-Einstein Condensates

We have performed numerical simulations of giant vortex structures in rapidly rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We reproduce the qualitative features, such as oscillation of the giant vortex core area, formation of toroidal density hole, and the precession of giant vortices, observed in the recent experiment [Engels \emph{et.al.}, Phys. Rev. Lett. {\bf 90}, 170405 (2003)]. We provide a mechanism which quantitatively explains the observed core oscillation phenomenon. We demonstrate the clear distinction between the mechanism of atom removal and a repulsive pinning potential in creating giant vortices. In addition, we have been able to simulate the transverse Tkachenko vortex lattice vibrations.Comment: 5 pages, 6 figures; revised description of core oscillation, new subfigur

Formation of fundamental structures in Bose-Einstein Condensates

The meanfield interaction in a Bose condensate provides a nonlinearity which can allow stable structures to exist in the meanfield wavefunction. We discuss a number of examples where condensates, modelled by the one dimensional Gross Pitaevskii equation, can produce gray solitons and we consider in detail the case of two identical condensates colliding in a harmonic trap. Solitons are shown to form from dark interference fringes when the soliton structure, constrained in a defined manner, has lower energy than the interference fringe and an analytic expression is given for this condition.Comment: 7 pages, 3 figures, requires ioplppt.st

Quantum turbulence and correlations in Bose-Einstein condensate collisions

We investigate numerically simulated collisions between experimentally realistic Bose-Einstein condensate wavepackets, within a regime where highly populated scattering haloes are formed. The theoretical basis for this work is the truncated Wigner method, for which we present a detailed derivation, paying particular attention to its validity regime for colliding condensates. This paper is an extension of our previous Letter [A. A. Norrie, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. Lett. 94, 040401 (2005)] and we investigate both single-trajectory solutions, which reveal the presence of quantum turbulence in the scattering halo, and ensembles of trajectories, which we use to calculate quantum-mechanical correlation functions of the field

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

Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with non-equal scattering lengths, and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified resulting in highly-directional, oppositely-propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic, and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov-de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable Helium atom laser experiment of Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show it explains the anomalous beam profiles they observed. Finally we demonstrate the paired particle beams will be EPR-entangled on formation.Comment: Corrected reference

Nonequilibrium dynamics of vortex arrest in a finite-temperature Bose-Einstein condensate

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.Comment: 10 pages, 6 figures. v2: Minor changes in response to referee's comments. To appear in PR