D. Baillie

Ground-state phase diagram of a dipolar condensate with quantum fluctuations

We consider the ground state properties of a trapped dipolar condensate under the influence of quantum fluctuations. We show that this system can undergo a phase transition from a low density condensate state to a high density droplet state, which is stabilized by quantum fluctuations. The energetically favored state depends on the geometry of the confining potential, the number of atoms and the two-body interactions. We develop a simple variational ansatz and validate it against full numerical solutions. We produce a phase diagram for the system and present results relevant to current experiments with dysprosium and erbium condensates.

Self-bound dipolar droplet: A localized matter wave in free space

A liquid droplet is a self-bound phase of matter that holds itself together in the absence of a container. Without a container a gas will normally expand to fill space. A method is proposed to produce a self-bound dilute quantum gaseous dipolar Bose-Einstein condensate.

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.

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.

Roton spectroscopy in a harmonically trapped dipolar Bose-Einstein condensate

We study a harmonically trapped Bose-Einstein condensate with dipole-dipole interactions in a regime where a roton spectrum emerges. We show that the roton spectrum is clearly revealed in the static and dynamic structure factors which can be measured using Bragg spectroscopy. We develop and validate a theory based on the local density approximation for the dynamic structure factor.

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.

Collective Excitations of Self-Bound Droplets of a Dipolar Quantum Fluid

We calculate the collective excitations of a dipolar Bose-Einstein condensate in the regime where it self-binds into droplets stabilized by quantum fluctuations. We show that the filament-shaped droplets act as a quasi-one-dimensional waveguide along which low-angular-momentum phonons propagate. The evaporation (unbinding) threshold occurring as the atom number N is reduced to the critical value N_{c} is associated with a monopolelike excitation going soft as ε_{0}∼(N-N_{c})^{1/4}. Considering the system in the presence of a trapping potential, we quantify the crossover from a trap-bound condensate to a self-bound droplet.

Number Fluctuations of a Dipolar Condensate: Anisotropy and Slow Approach to the Thermodynamic Regime

We present a theory for the number fluctuations of a quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate measured with finite resolution cells. We show that when the dipoles are tilted to have a component parallel to the plane of the trap, the number fluctuations become anisotropic, i.e., depend on the in-plane orientation of the measurement cell. We develop analytic results for the quantum and thermal fluctuations applicable to the cell sizes accessible in experiments. We show that as cell size is increased the thermodynamic fluctuation result is approached much more slowly than in condensates with short range interactions, so experiments would not require high numerical aperture imaging to observe the predicted effect.

Finite-temperature trapped dipolar Bose gas

Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand.We develop a finite temperature Hartree theory for the trapped dipolar Bose gas. We use this theory to studythermal effects on the mechanical stability of the system and density oscillating condensate states. We presentresults for the stability phase diagram as a function of temperature and aspect ratio. In oblate traps above thecritical temperature for condensation we find that the Hartree theory predicts significant stability enhancementover the semiclassical result. Below the critical temperature we find that thermal effects are well described byaccounting for the thermal depletion of the condensate. Our results also show that density oscillating condensatestates occur over a range of interaction strengths that broadens with increasing temperature.

Calorimetry of a harmonically trapped Bose gas

We experimentally study the energy-temperature relationship of a harmonically trapped Bose-Einstein condensate by transferring a known quantity of energy to the condensate and measuring the resulting temperature change. We consider two methods of heat transfer, the first using a free expansion under gravity and the second using an optical standing wave to diffract the atoms in the potential. We investigate the effect of interactions on the thermodynamics and compare our results to various finite temperature theories.