## Crystallisation of a dilute atomic dipolar condensate

Crystallisation of droplets in a dipolar condensate.
Physical Review A **92**, 061603(R) (2015)

We present a theory that explains the experimentally observed crystallization of a dilute dysprosium condensate into a lattice of droplets. The key ingredient of our theory is a conservative three-body interaction which stabilizes the droplets against collapse to high-density spikes. Our theory reproduces the experimental observations, and provides insight into the many-body properties of the droplet phase. Notably, we show that it is unlikely that a supersolid was obtained in experiments, however, our results suggest a strategy to realize this phase.

*December 2015.*

## Identifying a Superfluid Reynolds Number via Dynamical Similarity

The Strouhal frequency of vortex cluster shedding exhibits dynamical similarity, revealing a *superfluid Reynolds number*.
Physical Review Letters **114**, 155302 (2015)

The Reynolds number provides a characterisation of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, Re_s, that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at Re_s~0.7, irrespective of obstacle width.

*July 2015.*

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

Anisotropic number fluctuations are revealed in measurement cells parallel and orthogonal to the planar-projection of the dipole moment.
Physical Review Letters **113**, 265301 (2014)

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.

*December 2014.*

## Thermally activated local collapse of a flattened dipolar condensate

Density feature emerging during collapse of a flattened dipolar condensate.
Physical Review A **90**, 053605 (2014)

We consider the metastable dynamics of a flattened dipolar condensate. We develop an analytic model that quantifies the energy barrier to the system undergoing local collapse to form a density spike. We also develop a stochastic Gross-Pitaevskii equation theory for a flattened dipolar condensate, which we use to perform finite-temperature simulations verifying the local collapse scenario. We predict that local collapses play a significant role in the regime where rotons are predicted to exist and will be an important consideration for experiments looking to detect these excitations.

*November 2014.*

## Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence

Emergence of an Onsager-Kraichnan condensate with increasing point-vortex energy. Blue and red points indicate vortices that are clustered (links indicate the cluster), and green points show vortices that are paired with an anti-vortex to form a vortex dipole.
Physical Review Letters **112**, 145301 (2014)

Despite the prominence of Onsager’s point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.

*April 2014.*

## Persistent-current formation in a high-temperature Bose-Einstein condensate: An experimental test for classical-field theory

Stochastic GPE simulations of persistent current formation.
Physical Review A **88**, 063620 (2013)

Experimental stirring of a toroidally trapped Bose-Einstein condensate at high temperature generates a disordered array of quantum vortices that decays via thermal dissipation to form a macroscopic persistent current [ T. W. Neely et al., Phys. Rev. Lett. 111, 235301 (2013) ]. We perform three-dimensional numerical simulations of the experimental sequence within the stochastic projected Gross-Pitaevskii equation using ab initio determined reservoir parameters. We find that both damping and noise are essential for describing the dynamics of the high-temperature Bose field. The theory gives a quantitative account of the formation of a persistent current, with *no fitted parameters*.

*December 2013.*

## Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid

Development of Kolmogorov power-law in the incompressible kinetic energy spectrum of a forced, compressible superfluid.
Physical Review Letters **111**, 235301 (2013)

Fluids subjected to suitable forcing will exhibit turbulence, with characteristics strongly affected by the fluid’s physical properties and dimensionality. In this work, we explore two-dimensional (2D) quantum turbulence in an oblate Bose-Einstein condensate confined to an annular trapping potential. Experimentally, we find conditions for which small-scale stirring of the condensate generates disordered 2D vortex distributions that dissipatively evolve toward persistent currents, indicating energy transport from small to large length scales. Simulations of the experiment reveal spontaneous clustering of same-circulation vortices and an incompressible energy spectrum with k-5/3 dependence for low wave numbers k. This work links experimentally observed vortex dynamics with signatures of 2D turbulence in a compressible superfluid.

*December 2013.*

## Fingerprinting Rotons in a Dipolar Condensate: Super-Poissonian Peak in the Atom-Number Fluctuations

Detection regions for determining number fluctuations.
Physical Review Letters **110**, 265302 (2013)

We demonstrate that measurements of atom-number fluctuations in a trapped dipolar condensate can reveal the presence of the elusive roton excitation. The key signature is a super-Poissonian peak in the fluctuations as the size of the measurement cell is varied, with the maximum occurring when the size is comparable to the roton wavelength. The magnitude of this roton feature is enhanced with temperature. The variation in fluctuations across the condensate demonstrates that the roton excitations are effectively confined to propagate in the densest central region, realizing a density trapped roton gas. While our main results are based on full numerical solutions of the mean-field equations, we also develop and validate a simple local density theory. Finally, we consider fluctuations measured within a washer-shaped cell which filters out the contribution of modes with nonzero angular momentum and provides a signal sensitive to individual roton modes.

*Sept 2013.*

## Kibble-Zurek scaling and its breakdown for spontaneous generation of Josephson vortices in Bose-Einstein condensates

Josephson vortices appearing as topologically stable defects in a pair of tunnel-coupled annular Bose-Einstein condensates.
Physical Review Letters **110**, 215302 (2013)

Atomic Bose-Einstein condensates confined to a dual-ring trap support Josephson vortices as topo- logically stable defects in the relative phase. We propose a test of the scaling laws for defect formation by quenching a Bose gas to degeneracy in this geometry. Stochastic Gross-Pitaevskii simulations reveal a -1/4 power-law scaling of defect number with quench time for fast quenches, consistent with the Kibble- Zurek mechanism. Slow quenches show stronger quench-time dependence that is explained by the stability properties of Josephson vortices, revealing the boundary of the Kibble-Zurek regime. Interference of the two atomic fields enables clear long-time measurement of stable defects and a direct test of the Kibble-Zurek mechanism in Bose-Einstein condensation.

*May 2013.*

## Inverse Energy Cascade in Forced 2D Quantum Turbulence

Clustering of vortices in forced two-dimensional quantum turbulence. Plus (minus) vortices are shown by red (blue) dots, and the connection lines show their identification with a given cluster.
Physical Review Letters **110**, 104501 (2013)

We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the Gross-Pitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a stationary thermal cloud. The forcing injects large amounts of vortex energy into the system at the scale of a few healing lengths. A regime of forcing and damping is identified where vortex energy is efficiently transported to large length scales via an inverse energy cascade associated with the growth of clusters of same-circulation vortices, a Kolmogorov scaling law in the kinetic energy spectrum over a substantial inertial range, and spectral condensation of kinetic energy at the scale of the system size. Our results provide clear evidence that the inverse energy cascade phenomenon, previously observed in a diverse range of classical systems, can also occur in quantum fluids.

*October 2012.*

## The stochastic projected Gross-Pitaevskii equation

Energy and particle transfer mechanisms in Bose-Einstein condensate reservoir interactions.
Physical Review A **86**, 053634 (2012)

We have achieved the first full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only included growth processes, by implementing number-conserving scattering processes. We evaluate an analytic expression for the coefficient of the scattering term and compare it to that of the growth term in the experimental regime, showing the two coefficients are comparable in size. We give an overview of the numerical implementation of the deterministic and stochastic terms for the scattering process, and use simulations of a condensate excited into a large amplitude breathing mode oscillation to characterize the importance of scattering and growth processes in an experimentally accessible regime. We find that in such non-equilibrium regimes the scattering can dominate over the growth, leading to qualitatively different system dynamics. In particular, the scattering causes the system to rapidly reach thermal equilibrium without greatly depleting the condensate, suggesting that it provides a highly coherent energy transfer mechanism.

*October 2012.*

## Energy Spectra of Vortex Distributions in Two-Dimensional Quantum Turbulence

Kolmogorov constant of two-dimensional quantum turbulence.
Physical Review X **2**, 041001 (2012)

One has only to watch the chaotic eddies in a rapidly flowing stream to realize that fluid turbulence is ubiquitous in nature, yet many of the underlying mechanisms remain mysterious. In quantum fluids, such as superfluid helium at low temperature, flow occurs only in discrete units called quantized vortices, which results in strong constraints on the allowed fluid behavior. This means that a much clearer understanding of turbulence may be achievable in quantum fluids, particularly if the dynamics of vortices are further limited by reducing the dimensionality. In our paper, we report a theoretical and computational study of energy flow in a two-dimensional superfluid and derive a method for calculating the so-called Kolmogorov constant that plays a central role in turbulence.

Compressibility in a superfluid such as a Bose-Einstein condensate allows vortices to emit and absorb sound waves, and the large size of the vortex cores raises the importance of understanding their structure. Our analysis of spatial vortex configurations reveals that ideal two-dimensional turbulence, associated with the transfer of energy between length scales, occurs when vortices of the same circulation sign cluster together with intervortex distances obeying a unique power law. This characteristic clustering is scale-free, a property shared by sand piles, earthquakes, forest fires, and other naturally occurring nonlinear dynamical processes, including turbulence. The kinetic energy of the quantum fluid can move to large length scales either through the spatial expansion of clusters, or through the accumulation of more vortices in clusters.

Surprisingly, the compressible nature of the superfluid also suggests a means to calculate the Kolmogorov constant, a parameter that determines how rapidly energy is transferred between scales. Simulation of a stirred superfluid supports the concept of vortex clustering into power-law configurations and the analytically obtained value of the Kolmogorov constant, offering a new quantum window into turbulence phenomena.

*August 2012.*

## The finite temperature trapped dipolar Bose gas

Density iso-surface for system near the critical temperature showing a biconcave density oscillation.
Phys. Rev. A **86**, 033609 (2012)

We develop a finite temperature Hartree theory for the trapped dipolar Bose gas. We use this theory to study thermal effects on the mechanical stability of the system and density oscillating condensate states. We present results for the stability phase diagram as a function of temperature and aspect ratio. In oblate traps above the critical temperature for condensation we find that the Hartree theory predicts significant stability enhancement over the semiclassical result. Below the critical temperature we find that thermal effects are well described by accounting for the thermal depletion of the condensate. Our results also show that density oscillating condensate states occur over a range of interaction strengths that broadens with increasing temperature..

*July 2012.*

## Roton spectroscopy in a trapped dipolar BEC

Dynamic structure factor for a quasi-2D dipolar BEC near a roton instability. White ellipse marks the roton feature in the spectrum.
Phys. Rev. A **86**, 021604 (R) (2012)

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.

*June 2012.*

## Hot spinor gases

Shift in phase boundaries with temperature for a spin-1 condensate with ferromagnetic interactions. Other subplots indicate the transverse magnetization of the condensate and the longitudinal magnetization of the non-condensate at T=0.1T0 (about 20% of Tc).
Phys. Rev. A **85**, 053611 (2012)

We formulate a self-consistent Hartree-Fock theory for a spin-1 Bose gas at finite temperature and apply it to characterizing the phase diagram. We find that spin coherence between thermal atoms in different magnetic sub-levels develops via coherent collisions with the condensed atoms, and is a crucial factor in determining the phase diagram. We develop analytical expressions to characterize the interaction and temperature dependent shifts of the phase boundaries..

*February 2012.*

## Quantum tunneling of a vortex between two pinning potentials

Tunneling time of a vortex between two pinning potentials separated by d_0.
Phys. Rev. Lett. **108**, 015301 (2012)

A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as point-like charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.

*December 2011.*

## Suppression of Kelvon-induced decay of quantized vortices in oblate Bose-Einstein condensates

A vortex thermally excited with Kelvin waves.
Phys. Rev. A 84, 023637 (2011)

We study the Kelvin mode excitations on a vortex line in a three-dimensional trapped Bose-Einstein condensate at finite temperature. Our stochastic Gross-Pitaevskii simulations show that the activation of these modes can be suppressed by tightening the confinement along the direction of the vortex line, leading to a strong suppression in the vortex decay rate as the system enters a regime of two-dimensional vortex dynamics. As the system approaches the condensation transition temperature, we find that the vortex decay rate is strongly sensitive to dimensionality and temperature, observing a large enhancement for quasi-two-dimensional traps. Three-dimensional simulations of the recent vortex dipole decay experiment of Neely et al. [ Phys. Rev. Lett. 104 160401 (2010)] confirm two-dimensional vortex dynamics and predict a dipole lifetime consistent with experimental observations and suppression of Kelvon-induced vortex decay in highly oblate condensates.

*Aug 2011.*

## Direct simulation Monte Carlo method for cold-atom dynamics: Classical Boltzmann equation in the quantum collision regime

Schematic of ultra-cold atomic collider and comparison or experimental and theoretical results.
Phys. Rev. A 84, 023612 (2011)

We develop a direct simulation Monte Carlo method for simulating highly nonequilibrium dynamics of nondegenerate ultracold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas et al. Phys. Rev. Lett. 93, 173201 (2004)], which requires the inclusion of beyond s-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.

*Aug 2011.*

## Finite-temperature stability of a trapped dipolar Bose gas

Phys. Rev. A 83, 061602(R) (2011)

Stability phase diagram: Critical dipole strength versus temperature for various values of the contact interaction strength
We calculate the stability diagram for a trapped normal Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry, temperature, and short-range interactions on the stability. We predict a robust double instability feature in oblate trapping geometries arising from the interplay of thermal gas saturation and the anisotropy of the interaction. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate.

*Jun 2011.*

## Thermally induced coherence in a Mott insulator of bosonic atoms

Phys. Rev. A 83, 021601(R) (2011)

underlying processes behind the emergent coherence of a Mott insulator at finite temperature
Naively, one may think that increasing temperature causes quantum coherence to decrease. Using finite-temperature perturbation theory and exact calculations for the strongly correlated bosonic Mott insulating state, we show a practical counterexample that can be explored in optical lattice experiments: the short-range coherence of the Mott insulating phase can increase substantially with increasing temperature. We demonstrate that this phenomenon originates from thermally produced defects that can tunnel with ease. Since the near-zero temperature coherence properties have been measured with high precision, we expect these results to be verifiable in current experiments.

*Feb 2011.*

## Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator

Phys. Rev. A 82, 053826 (2010)

A system capable of creating 4-mode entanglement: a chi-2 crystal inside a pumped Fabry-Perot cavity, with multiple resonant nonlinear interactions.
We examine the feasibility of generating continuous-variable multipartite entanglement in an intracavity
concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci
et al. [Phys. Rev. Lett. 101, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa
correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement
present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase
diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we
investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime,
we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity.
In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster
state formation.

*Nov 2010.*

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

Phys. Rev. A 82, 013626 (2010)

Deforming a harmonic trap into a toroid to study the Kibble-Zruek mechanism
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.

*Jul 2010.*

## Observation of vortex dipoles in an oblate Bose-Einstein condensate

Physical Review Letters 104, 160401 (2010)

A collaborative team from Otago, Arizona, and Queensland have directly observed and studied vortex dipoles in a dilute gas BEC for the first time. Previous studies observed indirect evidence for the breakdown of superfluidity at a critical velocity (related to the Landau critical velocty) while dragging an obstacle through a BEC. The experimental team at Arizona was able to directly observe vortex dipole formation and dynamics above a critical sweep velocity -a velocity that agrees well with earlier theory, and numerical simulations of the experiment.

Surprisingly, for faster sweep velocities multiple dipoles form, and aggregate into giant macro-dipoles.

For an overview, see the Physics Viewpoint article featuring this work.

**(a)** *Experimental sequence:* observed after dragging an obstacle through an oblate BEC, faster than the critical velocity for superfluid flow. Images are taken back-to-back at 200ms separation (180x180microns). **(b)** *Numerical simulations:* (in situ) of the Gross-Pitaevskii equation for the experimental parameters of (a). **(c)** *Vortex-antivortex trajectories:* comparison of averaged experimental data (points with error circles), and GPE simulations.

*May 2010.*

## Vortex decay in a warm Bose-Einstein condensate

Phys. Rev. A 81, 023630 (2010)

*Top:*Vortex decay scenarios in BECs at **(a)** T=0, **(b)** T << Tc, and **(c)** near Tc. *Bottom:* separation of the system into coherent and incoherent regions in the Stochastic Projected Gross-Pitaevskii theory.
The decay of a vortex in a non-rotating Bose-Einstien condensate has been used as a sensitive test of theories of non-equilibrium dynamics at finite temperature in a recent article by honours student Sam Rooney, Ashton Bradley, and Blair Blakie. The Stochastic theory of reservoir interactions was found to provide the most complete description of vortex decay, predicting significantly shorter vortex lifetimes than theories that neglect either damping or noise.

The approach used in this work is also distinguished by having no fitting parameters, and hence may be of quantitative value for future experiments.

*Feb 2010.*

## C-field methods for Bose gases

Advances in Physics 57, 363 (2008).

Schematic of separation of the Bose gas into coherent and incoherent regions according to energy.
The truncated Wigner phase space method has been extensively developed and applied to dilute Bose gases in recent years. 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. This review starts with an overview of formalism and gives a survey of some of the recent work on modeling trapped Bose gases. Applications include zero, finite temperature, and critical regimes, low dimensional systems, and rotating systems.

*Feb 2010.*

## Spontaneous vortices in the formation of Bose-Einstein condensates

*Spontaneous vortices* forming during Bose-Einstein condensation: **(a)** Absorption images of atom density in 3 independent shots of the experiment (vortices visible as dark holes). **(b)** SPGPE simluations. **(c)** 3D isosurface of a single trajectory of the SPGPE.
Nature 455, 948-951 (2008).

Despite long standing predictions by W. H. Zurek and collaborators that vortices should occur spontaneously during the Bose-Einstein condensation transition, they have evaded experimental detection, until now.

The experimental observations of B. P. Anderson's group (Arizona) have been quantitatively explained using the Stochastic Projected Gross-Pitaevskii equation (SPGPE) of C. W. Gardiner (Otago) and M. J. Davis (Queensland).

For more about spontaneous vortices, see the Nature commentary by Professor Kris Helmerson.

This work on spontaneous vortices also featured in a radio interview of Ashton Bradley and Crispin Gardiner by Veronika Meduna on *Our Changing World:* Quantum Whirlpools.

*Feb 2010.*

## Numerical methods for the PGPE

Physical Review E 78, 026704 (2008)

In-trap position and momentum densities for thermal fields (top), and ground states.

The secrets of our long-developed numerical methods for simulating the projected Gross-Pitaevskii equation in a harmonic trap are revealed in this work. Evidence for thermalization in the trapped system is also presented.

*Feb 2010.*

## Theory of correlations between bosons released from an optical lattice

Physical Review A 78, 013627 (2008)

Second order correlation function for bosons in a 1D super-lattice

Ms. Emese Toth, in collaboration with Dr. A.-M. Rey (ITAMP/JILA), has developed a comprehensive theory for correlations between bosons released from an optical lattice.

*Feb 2010.*

## Tests for superfluidity of trapped quasi2D Bose gases

Physical Review A 77, 023618 (2008)

Density and phase images of quasi-2D Bose gas near the BKT transition.

In collaboration with Drs. Tapio Simula and Matthew Davis, we have published the results of a study examining signatures for the onset of superfluidity in a quasi-2D Bose gas, expected to happen at the Berezinskii-Kosterlitz-Thouless transition. Our results show that scissor mode oscillations can be used to reveal the reduction in rotational inertia arising from the appearance of a superfluid component.

*Feb 2010.*

## Theory for finite-T correlations in a trapped interacting Bose gas

Physical Review A 77, 023602 (2008)

One-body density matrix for a Bose gas slightly below the critical temperature.

Ms Alice Bezett has completed a formalism for calculating position and momentum space correlation functions appropriate to real experimental parameter regimes. Based on a classical field method, this formalism is valid in the critical region and should be applicable to current and future experiments.

*Feb 2010.*

## Theory-experiment study of lattice dynamical instabilities

Physical Review A 77, 012712 (2008)

Time-of-flight experimental images of condensate after dynamics at Brillouin zone edge

In collaboration with the experimental group of Prof. Andrew Wilson and the theory group of Dr. Matthew Davis we have completed a detailed study of condensate instabilities when prepared near the Brillouin zone boundary using an optical lattice. Large scale quantum simulations with the truncated Wigner method reveal the important role played by vacuum and thermal fluctuations.

*Feb 2010.*

## Theory of Fermi gas loading in optical lattice

Physical Review A 75, 063609 (2007)

Isentropic curves of degeneracy temperature versus lattice depth.

A quantitative theory has been developed for the thermal properties of a degenerate Fermi gas loaded from a harmonic trap into a combined harmonic optical lattice potential. Our results show that this commonly used experimental procedure typically causes a factor of 2 degradation in the degeneracy temperature. We show how the use of excited bands can overcome this limitation.

*Feb 2010.*

## Revealing the Bose Glass Phase

Physical Review A 76, 011602(R) (2007)

Phase diagram showing superfluid, bose glass and Mott insulator phases in a strongly disordered lattice.

In collaboration with Dr Buonsante and colleagues in Torino a meanfield decoupling approach is used to model the properties of a Bose gas in a deep optical lattice with disorder. We characterize the phase diagram of this system at zero and finite temperatures and elucidate the regimes where the Bose Glass phase appears. This work appears in Physical Review A

*Feb 2010.*

## Spectroscopy of Mott Insulator States

New Journal of Physics 8, 157 (2006

The emergence of a defect state in the response spectrum.

In this work I propose using a novel Raman spectroscopy scheme for probing the Mott-insulating state of a Bose gas in a deep optical lattice. By developing a new linear response analysis that retains correlations between the system and excited particles, I demonstrate that the excitation defects give rise to excitonic-like states in the spectrum of this system. This work appears in New Journal of Physics. Note: recent results by Wolfgang Ketterle's group reported in Science appear to be in good agreement with our theory.

*Feb 2010.*

## Georgia Tech Experiment Verifies Vortex Bragg Scattering Theory

Physical Review A 73, 041605(R) (2006)

Bragg scattered output of a vortex lattice in a BEC.

In a 2001 Physical Review Letter with Prof. Rob Ballagh, we proposed the idea that Bragg Scattering could be used as a spatially sensitive mechanism for detecting vortices in Bose Einstein condensates. Recent experiments by Chandra Raman's group at Georgia Tech have confirmed these results. More can be seen at the Raman Group homepage.

*Feb 2010.*

## Thermal Vortex-Pair Creation in 2D Bose-Einstein Condensates

Physical Review Letters, 73, 023604 (2006)

The influence of thermally activated vortices on an interference experiment.

Work done in collaboration with Dr Tapio Simula used classical field techniques to explore the superfluid phase diagram of a trapped 2D Bose gas. These theoretical results are in good agreement with recent experiments by the ENS group of Jean Dalibard. This work appears in Physical Review Letters and additional results and movies from this work are available here.

*Feb 2010.*