**Engineering time-averaged optical potentials for Bose-Einstein condensates** **-- PhD, T. A. Bell (2020)**

Bose-Einstein condensates are superfluids which when engineered under suitable laboratory conditions support dissipationless flows and facilitate the development of quantum enhanced applications. Realising those suitable conditions requires experimental technologies which enable the complete dynamical control of the superfluid density and velocity profiles. This thesis conceives and demonstrates several dynamical controls using optical potentials formed using commercially available spatial-light-modulator technologies, and constitutes important progress toward many future experiments and the realisation of practical applications.

Experimental systems and control sequences are designed using complimentary acousto-optic deflection and digital micromirror spatial light modulator technologies, rather than magnetic field based approaches, given their inherently favourable spatial and temporal resolutions. An experimental apparatus which includes a time-averaged acousto-optic controlled potential is constructed to generate toroidal potentials suitable for developing inertial rotation sensors. Density and phase manipulation strategies are developed using that apparatus which prepare condensates with arbitrarily controllable wavefunctions. Complementary digital micromirror based adaptations are subsequently developed during this project.

Corrugations across the condensate density distributions are reduced using an iteratively corrected spatial light modulator configuration. Rigorous and generalised scan requirements are established for engineering time-averaged potentials; numerical methods are conceived which facilitate the simulation of these systems. The combination of the feedforward density control and time-averaging phase control enable the deterministic preparation of persistent currents around multiply connected condensates. These capabilities enable experiments into many-body groundstates, superfluid turbulence, atomtronics and metrology.

Spatial light modulator trapping sequences geared toward the study of Onsager vortices, vortex dipole optics, inertial rotation sensing and wake turbulence are specifically developed. Several upgraded experimental systems are finally designed using knowledge gained during this thesis, which enable these various applications in future. This thesis therefore constitutes significant progress toward several important experimental investigations using dynamically controllable optical trapping technologies.

**Engineering time-averaged optical potentials for Bose-Einstein condensates -- Honours, C. Manning (2020)**

Superfluidity has been exhibited in numerous systems including Bose-Einstein condensates (BECs) and liquid helium. Superfluids have many characterising features with a particularly striking one being the superfluid fountain effect. This effect is characterised by the flow of a superfluid from one cooler reservoir to another hotter one. Since the superfluid fountain effect has yet to be observed in BECs, the aim of this project is to experimentally look for the superfluid fountain effect in a BEC confined within a ‘dumbbell’ configuration. This thesis focuses on the technical and analytical steps needed to look for the fountain effect in a BEC, including determining an appropriate heating method for the BEC and accurate measurement technique of its temperature. Heating techniques of ‘bubbling’ and ‘shaking’ were tested and found to be appropriate ways to have control over partially heating the BEC or turning it entirely into a thermal cloud. Another intermediate test was to measure the superfluid transport in the newly implemented optical ‘box’ potential that provides optimal isolation of the two dumbbell reservoirs. Despite promising preliminary results, the search for the superfluid fountain effect was eventually halted by the experiment’s vacuum system failing after a number of other delays throughout the year. This thesis however makes progress towards looking for the superfluid fountain effect in a BEC to fill a gap in the demonstrations of a BEC as a superfluid and provides more knowledge as to how BECs transport when out of thermal equilibrium.

**Engineering time-averaged optical potentials for Bose-Einstein condensates -- Honours, K. Goddard Lee (2019)**

The recent development of configurable optical trapping techniques for dilute atomic Bose- Einstein condensates, a macroscopically occupied quantum state and hence a superfluid, allow highly controllable experiments. The UQ BEC lab is capable of creating highly oblate BECs, ideal for experiments on two dimensional vortex dynamics. In this thesis, we present two experimental studies of the dynamics of these point vortices. In 1949 Lars Onsager predicated that point vortices in a bounded fluid must cluster at high energies, at a negative thermodynamic temperature. This was a very influential theory, explaining the stability of large two dimensional vortices, such as the Great Red Spot on Jupiter. The first section of this thesis investigates a system of same-signed vortices, known as the chiral system. This is predicted to have on-axis vortex equilibrium states at low energy, with a symmetry breaking transition to off-axis vortex clusters at high energies. We present the first observations of these equilibrium states, as well as the relaxation of a non-equilibrium state into an off- axis cluster. The data is very well described by our numerical calculations. These results answer some previously open theoretical questions such the relaxation time of vortices into equilibrium. The second experiment involves the dynamics of bound vortex-antivortex pairs, known as dipoles, the two dimensional equivalent of a smoke ring. As the dipoles carry linear momentum and energy, they obey a relation similar to Snell’s law in optics. Preliminary data shows qualitative agreement between the trajectories of the dipoles and simulations. Overall these results demonstrate the versatility of the apparatus, for investigating vortex dynamics, suggesting several future areas of experimental interest.

**Transport and Turbulence in Quasi-Uniform and Versatile Bose-Einstein Condensates -- PhD, G. Gauthier (2019)**

Turbulence, motion characterized by chaotic changes in pressure and flow velocity, is a challenging problem in physics. However, its underlying properties are found to be universal and do not depend on the host fluid. Meanwhile, transport phenomena, irreversible exchange processes due to the statistical continuous random motion of particles, although being complicated from a microscopic point of view, can often be modelled quite simply by tracking macroscopic quantities of interest in the system. In this thesis, using atomic Bose-Einstein condensates, we study both these phenomena inside a quantum fluid using a highly configurable BEC platform developed to provide arbitrary dynamic control over the 2D superfluid system. Furthermore, the experiments are modelled using the Gross-Pitaevskii equation, the

point vortex model and the hydrodynamic equations.

After theoretical background and introduction to the apparatus, the technique of direct imaging of a digital micromirror device is described, which achieves the highly versatile and dynamic 2D potentials that facilitate the experimental studies described. Superfluid transport through a mesoscopic channel of tuneable length and width is next described. By investigating low amplitude oscillations and their dependence on the system parameters, a resistor, capacitor, and inductor model is used to model the transport. Surprisingly, the “contact inductance” of the channel at the reservoirs is a dominant effect

for a significant portion of the parameter range. The resistive transport for high initial bias is also studied, showing an Ohmic resistive relationship over the broad parameter range. Next, the transport between two reservoirs initially prepared at different temperatures, but with similar particle number, was explored.

Our 2D superfluid system, with hard-wall confinement, provides an ideal experimental system for the study of 2D quantum turbulence. The system is utilized to demonstrate the first experimental realization of large Onsager vortex clusters in the negative absolute temperature regime, through the injection of high energy clusters into the 2D superfluid. The clusters are found to be surprisingly stable for long time periods. The vortex cluster energy loss rate is studied while changing the system parameters, suggesting thermal damping is the dominant loss mechanism. The techniques and results presented in this thesis open up new avenues for the study of quantum fluids, be it by providing a concise atomtronic model for predicting superfluid transport or expanding the accessible parameters space available to fundamental studies of turbulence. The realization of negative temperature vortex distributions, long ago predicted by Onsager, open up the experimental study of the full phase-diagram of 2D vortex matter. The refinement of optical trapping techniques for BECs presents new and promising directions for future BEC experiments in configured potentials.

**Creation and Applications of Large Toroidal Time-Averaged Optical Potentials for BECs -- MPhil, J. A. P. Glidden (2017)**

This thesis reports the final stages of construction and performance of a high atom number rubidium-87 Bose-Einstein condensate (BEC) apparatus, and the generation of timeaveraged optical potentials geared towards interferometric applications. A detailed description of the hybrid trap used in our experiment is given, which comprises magnetic confinement from a quadrupole field, and optical trapping from a focussed 1064 nm laser beam. We present the typical temperatures of atom clouds at all stages of cooling, from the 3D magneto-optical trap, through to the onset of condensation in the hybrid trap. Our trap typically realises nearly-pure BECs of 1.5–2.0 × 106 atoms, at temperatures of (217 ± 6) nK, over duty cycles of 16–25 s. The implementation of a time-averaged optical potential is also discussed, as a means of generating versatile, planar potentials for BECs. In this work, we focus on the generation of large, ring-shaped potentials, which have trapping frequencies in the ranges 2π × (110–140, 35–55)Hz vertically and radially, respectively. The details of a feedforward algorithm are presented, which allows for the realisation of smooth ring structures up to 150 µm in radius, which enclose areas ten times larger than optical ring traps created previously. These larger rings are promising candidates for interferometric measurements of the rotation-induced Sagnac phase, with the device sensitivity proportional to the enclosed area. We typically retain 2.5–3.0 × 106 atoms in these large traps, after evaporatively cooling to temperatures of (44 ± 9) nK. The measured lifetimes in the trap are on the order of 16 s. These ring condensates are expected to be fully phase coherent, despite their reduced dimensionality, as a result of high atom numbers, weak confinement, and low temperatures. We present preliminary data demonstrating these coherence properties, and outlay future plans for a comprehensive study of this coherence, probing both fully coherent rings, and those expected to fall within the phase-fluctuating regime. The control afforded using our time-averaged optical potentials is demonstrated through the generation of acoustic waves propagating around the ring condensates. The dispersion is linear for low driving frequencies, and allows for a determination of the speed of iv sound, and the chemical potential, found here to be cs = 1.34 mm. s−1 , and µ = kB ×18 nK respectively.

**Design, construction, and performance towards a versatile 87Rb and 41K BEC apparatus**** -- ****MPhil, N. McKay Parry (2016)**

The possibility to mould and control pure quantum systems has been offered by the experimental observation of Bose-Einstein condensation, a unique phase of matter when macroscopic quantities of a gas occupy the lowest quantum state. Techniques for creating these degenerate gases vary from laboratory to laboratory; each offers an unique test bed for studying quantum physics on a macroscopic scale. This thesis reports on the experimental design, construction and performance of an apparatus to create two-component 87Rb and 41K condensates for studies of non-equilibrium dynamics.

**Design, construction & characterisation of a versatile high atom number BEC apparatus****-- ****Honours, T. A. Bell (2014)**

Bose Einstein Condensates represent a valuable experimental medium for the study and application of fundamental atomic science. Within tailored trapping potentials, many exotic quantum phenomena may be probed or exploited, including Feshbach resonances, atomic clock measurements, Bragg spectroscopy, and superfluidity. While experimental condensates were first produced within magnetic traps, optical potentials are advantageous for interferometry, since they permit spin entangled sensitivity enhancement. Exploit- ing the strengths of each distinct approach, hybrid methods were proposed for the rapid production of large condensates within optical potentials. Following the work of, the present thesis aims to experimentally develop an optimised hybrid apparatus for the rapid production of condensates within optical potentials. Although condensates have not yet been produced, many preliminary trapping configurations have been demonstrated, representing substantial progress for the year available. We have successfully generated large Magneto- Optical Traps with 3 × 10^{9} atoms, and Compressed Magneto-Optical Traps of 1.2 × 10^{9 }at temperatures of 32μK. Long lived Magnetic Traps with up to 3 × 10^{8} atoms have been ad- ditionally formed. Transfer into the magnetic potential is however not yet optimised, with larger numbers expected once magnetic bias fields are employed to spatially overlap trap centres. Implementing a period of optical pumping should also increase loading into the magnetic potential. To form condensates it remains to firstly compress and evaporatively cool within the magnetic potential. An Optical Dipole Trap must then be overlapped and evaporative cooling continued to degeneracy.

**All-optical 87Rb Bose-Einstein condensate apparatus: construction and operation**** ****-- PhD, I. L. H. Humbert (2012)**

A new apparatus was built by the author and we report on the experimental details of the trapping of 87Rb atoms from a hot vapour and cooling them in a magneto-optical trap, and further evaporation to quantum degeneracy in a crossed optical dipole trap operating at a wavelength of λ = 1064nm, with accurate control of the power in both beams via a feedback loop. The evaporation of neutral atoms of 87Rb in far red detuned optical dipole traps using linearly polarised laser light is spin independent, and mixed spinor condensates of the F=1 manifold can be formed. As an empirical technique we found by applying a magnetic gradient field during the final evaporation that we can selectively populate mF spin states or prepare mixtures. This intriguing mechanism was found earlier as well by M. S. Chang, but is yet not fully understood and subject of our future research. We can now routinely prepare an almost pure condensate containing up to 7000 atoms in the condensed phase purely in the mF = 0 spin state.

**Bose-Einstein Condensates in Non-Harmonic Optical Potentials**** ****-- ****PhD, Sebastian Schnelle (2011)**

This thesis presents work on Bose-Einstein condensates in non-harmonic optical potentials. First, a new trap design developed at the University of Queensland is presented that allows the creation of nearly arbitrary two-dimensional potential landscapes by spatially scanning a far red-detuned laser beam using a two-dimensional acousto-optic modulator. In conjunction with a feed-forward technique this trap is capable of producing optical traps which have the necessary stability to be used in ultra-cold atom research. Different geometries are presented. In particular toroidal trap geometries are discussed which are interesting because they offer the possibility for a multiply connected Bose-Einstein condensate. The trap also offers the possibility of dynamic potentials which have been employed to measure the critical velocity of superfluidity in Bose-Einstein condensates. Secondly, measurements on condensation dynamics are presented which use an optical dim- ple potential superimposed upon a harmonic magnetic trap. In the experiments the dimple potential is ramped on slowly or turned on suddenly for a range of dimple depths and widths and the condensate fraction and temperature are measured as a function of hold times. Lastly, progress on experiments to measure the critical velocity of superfluidity in Bose- Einstein condensates is reported.