arXiv subjects

Matthew J. Davis

Publications and source records attributed to Matthew J. Davis.

69 records · Page 4Linked to original sources

arXiv2010

Vortex pairing in two-dimensional Bose gases

Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. While this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.

cond-mat.quant-gas↗

arXiv2009

Drag force on an impurity below the superfluid critical velocity in a quasi-one-dimensional Bose-Einstein condensate

The existence of frictionless flow below a critical velocity for obstacles moving in a superfluid is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytical solutions to the Bogoliubov-de Gennes equations for a gray soliton. Our results raise questions regarding the quantum dynamics in the formation of persistent currents in superfluids.

cond-mat.quant-gas↗

arXiv2009

Quantum-limited metrology and Bose-Einstein condensates

We discuss a quantum-metrology protocol designed to estimate a physical parameter in a Bose-Einstein condensate of N atoms, and we show that the measurement uncertainty can decrease faster than 1/N. The 1/N scaling is usually thought to be the best possible in any measurement scheme. From the perspective of quantum information theory, we outline the main idea that leads to a measurement uncertainty that scales better than 1/N. We examine in detail some potential problems and challenges that arise in implementing such a measurement protocol using a Bose-Einstein condensate. We discuss how some of these issues can be dealt with by using lower-dimensional condensates trapped in nonharmonic potentials.

quant-ph↗

arXiv2009

Atomic entanglement generation and detection via degenerate four-wave-mixing of a Bose-Einstein condensate in an optical lattice

The unequivocal detection of entanglement between two distinct matter-wave pulses is a significant challenge that has yet to be experimentally demonstrated. We describe a realistic scheme to generate and detect continuous variable entanglement between two atomic matter-wave pulses produced via degenerate four-wave-mixing from an initially trapped Bose-Einstein condensate loaded into a one-dimensional optical lattice. We perform a comprehensive numerical investigation for fixed condensate parameters to determine the maximum violation of separability and Einstein-Podolsky-Rosen inequalities for field quadrature entanglement, and describe and simulate an experimental scheme for measuring the necessary quadratures.

cond-mat.other↗

arXiv2008

Quantum Metrology: Dynamics vs. Entanglement

A parameter whose coupling to a quantum probe of $n$ constituents includes all two-body interactions between the constituents can be measured with an uncertainty that scales as $1/n^{3/2}$, even when the constituents are initially unentangled. We devise a protocol that achieves the $1/n^{3/2}$ scaling without generating any entanglement among the constituents, and we suggest that the protocol might be implemented in a two-component Bose-Einstein condensate.

quant-ph↗

arXiv2007

Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz

The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss the novel features of the solutions, and how they deviate from the well-known string solutions [H. B. Thacker, Rev. Mod. Phys.\ \textbf{53}, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive 1D Bose gas on a ring.

cond-mat.other↗

arXiv2007

Dynamical instabilities of Bose-Einstein condensates at the band-edge in one-dimensional optical lattices

We report on experiments that demonstrate dynamical instability in a Bose-Einstein condensate at the band-edge of a one-dimensional optical lattice. The instability manifests as rapid depletion of the condensate and conversion to a thermal cloud. We consider the collisional processes that can occur in such a system, and perform numerical modeling of the experiments using both a mean-field and beyond mean-field approach. We compare our numerical results to the experimental data, and find that the Gross-Pitaevskii equation is not able to describe this experiment. Our beyond mean-field approach, known as the truncated Wigner method, allows us to make quantitative predictions for the processes of parametric growth and thermalization that are observed in the laboratory, and we find good agreement with the experimental results.

cond-mat.other↗

arXiv2007

Calculation of the microcanonical temperature for the classical Bose field

The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated by a time average over a sufficiently long period of dynamical evolution. In this paper we describe in detail how to calculate the temperature and chemical potential from the dynamics of a microcanonical classical field, using the particular example of the classical modes of a Bose-condensed gas. The accurate determination of these thermodynamics quantities is essential in measuring the shift of the critical temperature of a Bose gas due to non-perturbative many-body effects.

cond-mat.other↗

arXiv2007

Critical temperature of a trapped Bose gas: comparison of theory and experiment

We apply the Projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature $T_c$ of a harmonically confined Bose gas as reported in Gerbier \emph{et al.} [Phys. Rev. Lett. \textbf{92}, 030405 (2004)]. The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.

cond-mat.other↗

arXiv2007

Classical Region of a Trapped Bose Gas

The classical region of a Bose gas consists of all single-particle modes that have a high average occupation and are well-described by a classical field. Highly-occupied modes only occur in massive Bose gases at ultra-cold temperatures, in contrast to the photon case where there are highly-occupied modes at all temperatures. For the Bose gas the number of these modes is dependent on the temperature, the total number of particles and their interaction strength. In this paper we characterize the classical region of a harmonically trapped Bose gas over a wide parameter regime. We use a Hartree-Fock approach to account for the effects of interactions, which we observe to significantly change the classical region as compared to the idealized case. We compare our results to full classical field calculations and show that the Hartree-Fock approach provides a qualitatively accurate description of classical region for the interacting gas.

cond-mat.other↗

arXiv2006

Quantum effects in the dynamical localization of Bose-Einstein condensates in optical lattices

We study quantum effects in the dynamics of a Bose-Einstein condensate loaded onto the edge of a Brillouin zone of a one-dimensional periodic potential created by an optical lattice. We show that quantum fluctuations trigger the dynamical instability of the Bloch states of the condensate and can lead to the generation of arrays of matter-wave gap solitons. Our approach also allows us to study the instability-induced anomalous heating of the condensate at the edge of the Brillouin zone and growth of the uncondensed atomic fraction. We demonstrate that there are regimes in which the heating effects do not suppress the formation of the localised states. We show that a phase imprinting technique can ensure the formation of gap soliton trains after short evolution times and at fixed positions.

cond-mat.other↗

arXiv2006

Population and Phase Coherence during the Growth of an Elongated Bose-Einstein Condensate

We study the growth of an elongated phase-fluctuating condensate from a non-equilibrium thermal cloud obtained by shock-cooling. We compare the growth of the condensate with numerical simulations, revealing a time delay and a reduction in the growth rate which we attribute to phase fluctuations. We measure the phase coherence using momentum Bragg spectroscopy, and thereby observe the evolution of the phase coherence as a function of time. Combining the phase coherence results with the numerical simulations, we suggest a simple model for the reduction of the growth rate based on the reduction of bosonic stimulation due to phase fluctuations and obtain improved agreement between theory and experiment.

cond-mat.other↗

arXiv2005

Monte Carlo techniques for real-time quantum dynamics

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the "weight", and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The method is applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.

quant-ph↗

arXiv2004

The time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultra-cold atomic Bose-Einstein condensates (BEC) to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to $6.022\times10^{23}$ (Avogadro's number) of particles. This system is realisable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

quant-ph↗

arXiv2004

The Projected Gross-Pitaevskii Equation for harmonically confined Bose gases

We extend the Projected Gross Pitaevskii equation formalism of Davis et al. [Phys. Rev. Lett. \bf{87}, 160402 (2001)] to the experimentally relevant case of harmonic potentials. We outline a robust and accurate numerical scheme that can efficiently simulate this system. We apply this method to investigate the equilibrium properties of a harmonically trapped three-dimensional Bose gas at finite temperature, and consider the dependence of condensate fraction, position and momentum distributions, and density fluctuations on temperature. We apply the scheme to simulate an evaporative cooling process in which the preferential removal of high energy particles leads to the growth of a Bose-Einstein condensate. We show that a condensate fraction can be inferred during the dynamics even in this non-equilibrium situation.

cond-mat.other↗