arXiv subjects

S. A. Morgan

Publications and source records attributed to S. A. Morgan.

15 recordsLinked to original sources

arXiv2007

A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas

We describe a number conserving approach to the dynamics of Bose-Einstein condensed dliute atomic gases. This builds upon the works of Gardiner [C. W. Gardiner, Phys. Rev. A 56, 1414 (1997)], and Castin and Dum [Y. Castin and R. Dum, Phys. Rev. A 57, 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of non-condensate to condensate particle numbers, rather than inverse powers of the total number of particles. This requires the number of condensate particles to be a majority, but not necessarily almost equal to the total number of particles in the system. We argue that a second-order treatment of the relevant dynamical equations of motion is the minimum order necessary to provide consistent coupled condensate and non-condensate number dynamics for a finite total number of particles, and show that such a second-order treatment is provided by a suitably generalized Gross-Pitaevskii equation, coupled to the Castin-Dum number-conserving formulation of the Bogoliubov-de Gennes equations. The necessary equations of motion can be generated from an approximate third-order Hamiltonian, which effectively reduces to second order in the steady state. Such a treatment as described here is suitable for dynamics occurring at finite temperature, where there is a significant non-condensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant non-condensate fraction, even if the non-condensate fraction is initially negligible.

cond-mat.other↗

arXiv2005

Novel Dynamical Resonances in Finite-Temperature Bose-Einstein Condensates

We describe a variety of intriguing mode-coupling effects which can occur in a confined Bose-Einstein condensed system at finite temperature. These arise from strong interactions between a condensate fluctuation and resonances of the thermal cloud yielding strongly non-linear behaviour. We show how these processes can be affected by altering the aspect ratio of the trap, thereby changing the relevant mode-matching conditions. We illustrate how direct driving of the thermal cloud can lead to significant shifts in the excitation spectrum for a number of modes and provide further experimental scenarios in which the dramatic behaviour observed for the $m=0$ mode at JILA (Jin {\it et al.} 1997) can be repeated. Our theoretical description is based on a successful second-order finite-temperature quantum field theory which includes the full coupled dynamics of the condensate and thermal cloud and all relevant finite-size effects.

cond-mat.stat-mech↗

arXiv2005

Quantitative test of thermal field theory for Bose-Einstein condensates II

We have recently derived a gapless theory of the linear response of a Bose-condensed gas to external perturbations at finite temperature and used it to explain quantitatively the measurements of condensate excitations and decay rates made at JILA [D. S. Jin et.al., Phys. Rev. Lett. 78, 764 (1997)]. The theory describes the dynamic coupling between the condensate and non-condensate via a full quasiparticle description of the time-dependent normal and anomalous averages and includes all Beliaev and Landau processes. In this paper we provide a full discussion of the numerical calculations and a detailed analysis of the theoretical results in the context of the JILA experiment. We provide unambiguous proof that the dipole modes are obtained accurately within our calculations and present quantitative results for the relative phase of the oscillations of the condensed and uncondensed atom clouds. One of the main difficulties in the implementation of the theory is obtaining results which are not sensitive to basis cutoff effects and we have therefore developed a novel asymmetric summation method which solves this problem and dramatically improves the numerical convergence. This new technique should make the implementation of the theory and its possible future extensions feasible for a wide range of condensate populations and trap geometries.

cond-mat.other↗

arXiv2003

Finite temperature theory of the trapped two dimensional Bose gas

We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the two-dimensional trapped Bose gas and indicate how semiclassical approximations to this and other formalisms have lead to confusion. We numerically obtain results for the fully quantum mechanical HFB theory within the Popov approximation and show that the presence of the trap stabilizes the condensate against long wavelength fluctuations. These results are used to show where phase fluctuations lead to the formation of a quasicondensate.

cond-mat.stat-mech↗

arXiv2003

Microcanonical temperature for a classical field: application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a UV cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behaviour of the specific heat.

cond-mat.stat-mech↗

arXiv2003

The response of Bose-Einstein condensates to external perturbations at finite temperature

We present a theory of the linear response of a Bose-condensed gas to external perturbations at finite temperature. The theory developed here is the basis of a recent quantitative explanation of the measurements of condensate excitations and decay rates made at JILA [D. S. Jin et al., Phys. Rev. Lett. 78, 764 (1997)]. The formalism is based on a dynamic, number-conserving, mean-field scheme and is valid in the collisionless limit of well-defined quasiparticles. The theory is gapless, consistent with the generalized Kohn theorem for the dipole modes, and includes the time-dependent normal and anomalous averages, Beliaev and Landau processes, and all relevant finite size effects. The important physical process where the thermal cloud is driven directly by the external perturbation is explicitly included. This is required for consistency with the dipole modes and is also needed to explain the JILA observations.

cond-mat↗

arXiv2003

Quantitative test of thermal field theory for Bose-Einstein condensates

We present numerical results from a full second order quantum field theory of Bose-Einstein condensates applied to the 1997 JILA experiment [D. S. Jin et al., Phys. Rev. Lett. Vol. 78, 764 (1997)]. Good agreement is found for the energies and decay rates for both the lowest-energy m = 2 and m = 0 modes. The anomalous behaviour of the m = 0 mode is due to experimental perturbation of the non-condensate. The theory includes the coupled dynamics of the condensate and thermal cloud, the anomalous pair average and all relevant finite size effects.

cond-mat↗

arXiv2003

The Gross-Pitaevskii equation and higher order theories in one-dimensional Bose gases

We investigate the properties of the one-dimensional Bose gas at zero temperature, for which exact results exist for some model systems. We treat the interactions between particles in the gas with an approximate form of the many-body T-matrix, and find a form of Gross-Pitaevskii equation valid in 1D. The results presented agree with the exact models in both the weakly and strongly interacting limits, and interpolate smoothly between them. We also investigate the use of mean-field treatments of trapped BECs to describe the 1D system in the strongly interacting limit. We find that the use of the many-body T-matrix to describe interactions leads to qualitative agreement with the exact models for some physical quantities. We indicate how the standard mean-field treatments need to be modified to extend and improve the agreement.

cond-mat↗

arXiv2002

Solutions of the Gross-Pitaevskii equation in two dimensions

In two dimensions the Gross-Pitaevskii equation for a cold, dilute gas of bosons has an energy dependent coupling parameter describing particle interactions. We present numerical solutions of this equation for bosons in harmonic traps and show that the results can be quite sensitive to the precise form of the coupling parameter that is used.

cond-mat↗

arXiv2002

Energy dependent scattering and the Gross-Pitaevskii Equation in two dimensional Bose-Einstein condensates

We consider many-body effects on particle scattering in one, two and three dimensional Bose gases. We show that at zero temperature these effects can be modelled by the simpler two-body T-matrix evaluated off the energy shell. This is important in 1D and 2D because the two-body T-matrix vanishes at zero energy and so mean-field effects on particle energies must be taken into account to obtain a self-consistent treatment of low energy collisions. Using the off-shell two-body T-matrix we obtain the energy and density dependence of the effective interaction in 1D and 2D and the appropriate Gross-Pitaevskii equations for these dimensions. We present numerical solutions of the Gross-Pitaevskii equation for a 2D condensate of hard-sphere bosons in a trap. We find that the interaction strength is much greater in 2D than for a 3D gas with the same hard-sphere radius. The Thomas-Fermi regime is therefore approached at lower condensate populations and the energy required to create vortices is lowered compared to the 3D case.

cond-mat↗

arXiv2002

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation derived earlier [Davis, et al., J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. We find that this equation will evolve randomised initial wave functions to equilibrium, and compare our numerical data to the predictions of a gapless, second-order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)]. We find that we can determine the temperature of the equilibrium state when this theory is valid. Outside the range of perturbation theory we describe how to measure the temperature of our simulations. We also determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. As the Gross-Pitaevskii equation is non-perturbative, we expect that it can describe the correct thermal behaviour of a Bose gas as long as all relevant modes are highly occupied.

cond-mat↗

arXiv2001

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomised initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B {\bf 33}, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is non-perturbative, we expect that it can describe the correct thermal behaviour of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

cond-mat↗

arXiv2001

Calculation of mode coupling for quadrupole excitations in a Bose-Einstein condensate

In this paper we give a theoretical description of resonant coupling between two collective excitations of a Bose condensed gas (BEC) on, or close, to a second harmonic resonance. Using analytic expressions for the quasi-particle wavefunctions we show that the coupling between quadrupole modes is strong, leading to a coupling time of a few milliseconds (for a TOP trap with radial frequency 100 Hz and 10^4 atoms). Using the hydrodynamic approximation, we derive analytic expression for the coupling matrix element. These can be used with an effective Hamiltonian (that we also derive) to describe the dynamics of the coupling process and the associated squeezing effects.

cond-mat.soft↗

arXiv1999

A Gapless Theory of Bose-Einstein Condensation in Dilute Gases at Finite Temperature

In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with higher order cubic and quartic terms. The quadratic part is diagonalized exactly by transforming to a quasiparticle basis, while the non-quadratic terms are dealt with using first and second order perturbation theory. The conventional treatment of these terms, based on factorization approximations, is shown to be inconsistent. Infra-red divergences can appear in individual terms of the perturbation expansion, but we show analytically that the total contribution beyond quadratic order is finite. The resulting excitation spectrum is gapless and the energy shifts are small for a dilute gas away from the critical region, justifying the use of perturbation theory. Ultra-violet divergences can appear if a contact potential is used to describe particle interactions. We show that the use of this potential as an approximation to the two-body T-matrix leads naturally to a high-energy renormalization. The theory developed in this paper is therefore well-defined at both low and high energy and provides a systematic description of Bose-Einstein condensation in dilute gases. It can therefore be used to calculate the energies and decay rates of the excitations of the system at temperatures approaching the phase transition.

cond-mat.stat-mech↗

arXiv1998

Phenomenological damping in trapped atomic Bose-Einstein condensates

The method of phenomenological damping developed by Pitaevskii for superfluidity near the $λ$ point is simulated numerically for the case of a dilute, alkali, inhomogeneous Bose-condensed gas near absolute zero. We study several features of this method in describing the damping of excitations in a Bose-Einstein condensate. In addition, we show that the method may be employed to obtain numerically accurate ground states for a variety of trap potentials.

quant-ph↗