arXiv subjects

P. B. Blakie

Publications and source records attributed to P. B. Blakie.

At least 91 records · Page 5Linked to original sources

arXiv2010

Geometric scale invariance as a route to macroscopic degeneracy: loading a toroidal trap with a Bose or Fermi gas

An easily scalable toroidal geometry presents an opportunity for creating large scale persistent currents in Bose-Einstein condensates, for studies of the Kibble-Zurek mechanism, and for investigations of toroidally trapped degenerate Fermi gases. We consider in detail the process of isentropic loading of a Bose or Fermi gas from a harmonic trap into the scale invariant toroidal regime that exhibits a high degree of system invariance when increasing the radius of the toroid. The heating involved in loading a Bose gas is evaluated analytically and numerically, both above and below the critical temperature. Our numerical calculations treat interactions within the Hartree-Fock-Bogoliubov-Popov theory. Minimal change in degeneracy is observed over a wide range of initial temperatures, and a regime of cooling is identified. The scale invariant property is further investigated analytically by studying the density of states of the system, revealing the robust nature of scale invariance in this trap, for both bosons and fermions. We give analytical results for a Thomas-Fermi treatment. We calculate the heating due to loading a spin-polarized Fermi gas and compare with analytical results for high and low temperature regimes. The Fermi gas is subjected to irreducible heating during loading, caused by the loss of one degree of freedom for thermalization.

cond-mat.quant-gas↗

arXiv2009

Decay of a quantum vortex: test of non-equilibrium theories for warm Bose-Einstein condensates

The decay of a vortex from a non-rotating high temperature Bose-Einstein condensate (BEC) is modeled using the stochastic projected Gross-Pitaevskii equation (SPGPE). In order to exploit the tunability of temperature in SPGPE theory while maintaining the total atom number constant, we develop a simple and accurate Hartree-Fock method to estimate the SPGPE parameters for systems close to thermal equilibrium. We then calculate the lifetime of a vortex using three classical field theories that describe vortex decay in different levels of approximation. The SPGPE theory is shown to give the most complete description of the decay process, predicting significantly shorter vortex lifetimes than the alternative theories. Using the SPGPE theory to simulate vortex decay for a trapped gas of $5\times 10^5$ $^{87}$Rb atoms, we calculate a vortex lifetime $\bar{t}$ that decreases linearly with temperature, falling in the range 20{\rm s}$ >\bar{t} >$1.5{\rm s} corresponding to the temperature range $0.78T_c\leq T\leq0.93T_c$. The vortex lifetimes calculated provide a lower bound for the lifetime of a persistent current with unit winding number in our chosen trap geometry, in the limit of vanishing vortex pinning potential.

cond-mat.quant-gas↗

arXiv2009

Quantitative test of mean-field description of a trapped two-dimensional Bose gas

We investigate the accuracy of two mean-field theories of the trapped two-dimensional Bose gas at predicting transition region properties by comparison to non-perturbative classical field calculations. To make these comparisons we examine the density profiles and the predictions for the Berezinskii-Kosterlitz-Thouless superfluid transition temperature over a parameter range in which the degree of thermal activation in the tightly trapped direction varies considerably. These results present an important test of these mean-field theories, and provide a characterization of their typical accuracy.

cond-mat.quant-gas↗

arXiv2009

Transition region properties of a trapped quasi-two-dimensional degenerate Bose gas

The c-field simulation technique is used to study a trapped quasi-two dimensional Bose gas. We calculate the central curvature of the system density and fluctuations of the condensate mode in the degenerate regime. These results provide new understanding of the system behavior in the region of the superfluid transition.

cond-mat.quant-gas↗

arXiv2009

Critical temperature of a Bose gas in an optical lattice

We present theory for the critical temperature of a Bose gas in a combined harmonic lattice potential based on a mean-field description of the system. We develop practical expressions for the ideal-gas critical temperature, and corrections due to interactions, the finite-size effect, and the occupation of excited bands. We compare our expressions to numerical calculations and find excellent agreement over a wide parameter regime.

cond-mat.quant-gas↗

arXiv2009

Finite temperature theory of superfluid bosons in optical lattices

A practical finite temperature theory is developed for the superfluid regime of a weakly interacting Bose gas in an optical lattice with additional harmonic confinement. We derive an extended Bose-Hubbard model that is valid for shallow lattices and when excited bands are occupied. Using the Hartree-Fock-Bogoliubov-Popov mean-field approach, and applying local density and coarse-grained envelope approximations, we arrive at a theory that can be numerically implemented accurately and efficiently. We present results for a three-dimensional system, characterizing the importance of the features of the extended Bose-Hubbard model and compare against other theoretical results and show an improved agreement with experimental data.

cond-mat.quant-gas↗

arXiv2009

Statistical mechanics of a Feshbach coupled Bose-Fermi gas in an optical lattice

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. The phase diagram of the resulting atom-molecule mixture in chemical and thermal equilibrium is determined numerically in the absence of interactions under the constraint of particle conservation. In the limiting cases of vanishing or large lattice depth we derive simple analytical results for important thermodynamic quantities. One such quantity is the dissociation energy, defined as the detuning of the molecular energy spectrum with respect to the atomic one for which half of the atoms have been converted into dimers. Importantly we find that the dissociation energy has a non-monotonic dependence on lattice depth.

cond-mat.other↗

arXiv2009

Adiabatic cooling of a tunable Bose-Fermi mixture in an optical lattice

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. Thus by adjusting the magnetic field the portion of fermionic and bosonic particles in the system can be continuously varied. We analyze the statistical mechanics of this system and consider the interplay of the lattice physics with the atom-molecule conversion. We study the entropic behavior of the system and characterize the temperature changes that occur during adiabatic ramps across the Feshbach resonance. We show that an appropriate choice of filling fraction can be used to reduce the system temperature during such ramps.

cond-mat.other↗

arXiv2009

Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low energy c-field region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the dipolar PGPE. We introduce a set of auxiliary oscillator states to perform a Fourier transform necessary to evaluate the dipolar interaction in reciprocal space. We extensively characterize the accuracy of our approach, and derive Ehrenfest equations for the evolution of the angular momentum.

cond-mat.quant-gas↗

arXiv2009

Analysis of the Holzmann-Chevallier-Krauth theory for the trapped quasi-two-dimensional Bose gas

We provide an in depth analysis of the theory proposed by Holzmann, Chevallier and Krauth (HCK) [Europhys. Lett., {\bf 82}, 30001 (2008)] for predicting the temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition to a superfluid state occurs in the harmonically trapped quasi-two-dimensional (2D) Bose gas. Their theory is based on a meanfield model of the system density and we show that the HCK predictions change appreciably when an improved meanfield theory and identification of the transition point is used. In this analysis we develop a consistent theory that provides a lower bound for the BKT transition temperature in the trapped quasi-2D Bose gas.

cond-mat.other↗

arXiv2008

Critical properties of a trapped interacting Bose gas

We develop a practical theoretical formalism for studying the critical properties of a trapped Bose-Einstein condensate using the projected Gross-Pitaevskii equation. We show that this approach allows us investigate the behavior of the correlation length, condensate mode and its number fluctuations about the critical point. Motivated by recent experiments [Science {\bf 315}, 1556 (2007)] we calculate the critical exponent for the correlation length, observe clear finite-size effects, and develop characteristic length scales to characterize the finite-size influences. We extend the Binder cumulant to the trapped system and discuss an experimental method for measuring number fluctuations.

cond-mat.stat-mech↗

arXiv2008

PGPE theory of finite temperature collective modes for a trapped Bose gas

We develop formalism based on the projected Gross Pitaevskii equation to simulate the finite temperature collective mode experiments of Jin et al. [PRL 78, 764 (1997)]. We examine the $m=0$ and $m=2$ quadrupolar modes on the temperature range $0.51T_c-0.83T_c$ and calculate the frequencies of, and phase between, the condensate and noncondensate modes, and the condensate mode damping rate. This study is the first quantitative comparison of the projected Gross-Pitaevskii equation to experimental results in a dynamical regime.

cond-mat.other↗

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2008

Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates

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.

cond-mat.other↗

arXiv2008

Numerical method for evolving the Projected Gross-Pitaevskii equation

In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and non-equilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.

physics.comp-ph↗

arXiv2008

Theory of correlations between ultra-cold bosons released from an optical lattice

In this paper we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We consider the system evolution during expansion and give criteria for a far field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including Bogoliubov, meanfield decoupling, and particle-hole perturbative solution about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on the system correlations. Comparison with the directly calculated correlation functions is used to justify a Gaussian form of our theory from which we develop a general three-dimensional formalism for inhomogeneous lattice systems suitable for numerical calculations of realistic experimental regimes.

cond-mat.other↗

arXiv2007

Superfluidity of an interacting trapped quasi-2D Bose gas

We investigate the harmonically trapped interacting Bose gas in a quasi-2D geometry using the classical field method. The system exhibits quasi-long-range order and non-classical rotational inertia at temperatures below the Berezinskii-Kosterlitz-Thouless cross-over to the superfluid state. In particular, we compute the scissors-mode oscillation frequencies and find that the irrotational mode changes its frequency as the temperature is sweeped across the cross-over thus providing microscopic evidence for the emergence of superfluidity.

cond-mat.other↗

arXiv2007

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.

cond-mat.other↗