S. A. Morgan

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 randomized 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 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

PHENOMENOLOGICAL DAMPING IN TRAPPED ATOMIC BOSE-EINSTEIN CONDENSATES

The method of phenomenological damping developed by Pitaevskii for superfluidity near the

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

\lambda

Simulations of thermal Bose fields in the classical limit

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.

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

We consider many-body effects on particle scattering in one-, two-, and three-dimensional (3D) Bose gases. We show that at T=0 these effects can be modeled 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. Our results provide an alternative derivation of those of Kolomeisky and co-workers. 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.

Interactions and entanglements in BECs

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Interactions in trapped Bose-Einstein condensates

In this paper, we give a theoretical description of resonant coupling between two collective excitations of a Bose-condensed gas on, or close to, a second-harmonic resonance. Using analytic expressions for the quasiparticle wave functions, 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 an 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.

NONLINEAR MIXING OF QUASIPARTICLES IN AN INHOMOGENEOUS BOSE CONDENSATE

In this article we discuss aspects of correlations and entanglements in condensed gases. This requires us to look at the quantum fluctuations in the field that describes the condensates. We discuss ways in which these effects can be observed in experiments and used in precision measurements

Comparison of gapless mean-field theories for trapped Bose-Einstein condensates

This lecture describes recent work in our group on gapless mean-field theories for trapped Bose-Einstein condensates. We discuss the physical basis for these theories and compare them to the better known approaches. The proposed theories are based on suitable inclusion of the anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the widely used HFB-Popov approach for which it is constant. The predictions of these theories differ from the corresponding HFB-Popov ones by at most a few per cent for the lower-temperature gases studied in the laboratory at present. For systems that may well be studied in the next few years the effects can be much more profound.