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Engineering time-averaged optical potentials for Bose-Einstein condensates

Thomas A. Bell

Published Mar 27, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.14264/uql.2020.493

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arXiv:1605.04928•Optica•Oct 10, 2016•211 citations
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.
This thesis focusses on the use of a Digital Micromirror Device (DMD) to produce spatially and temporally varying optical potentials for the manipulation of ultracold atoms. I discuss the apparatus used to generate ultracold atomic samples as well as that used to manipulate them, including a comparison of the various light sources used with the DMD. Here I demonstrate the advantages in image quality that can be achieved using a superluminescent diode. I also report on work which uses the capability to produce spatially and temporally controlled potentials to engineer a synthetic dimension of harmonic oscillator sites, forming a lattice consisting of 10s of lattice sites on which Bloch Oscillations are demonstrated. Finally I describe simulations which demonstrate the clustering behaviour of quantised vortices in a Bose-Einstein condensate when arranged in linear structures, as could be done by the method of phase imprinting using a DMD. I demonstrate the use of a cluster detection algorithm which is novel in the field of quantised vortices, and show that in many cases, vortex clusters can be modelled by methods similar to those used for single vortices.
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 dimple 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. The measurements taken are compared to equilibrium thermodynamics and quantum kinetic theory and for the first time a quantitative model is presented that allows correct prediction of condensate fractions and temperatures in good agreement with the measurements. Also presented are first results in condensate rethermalization experiments where a dimple potential is suddenly switched off and the condensate left to rethermalize in a much wider magnetic potential. The measurements show a sudden breakdown in condensate fraction followed by a subsequent recovery. So far no theory exists to properly interpret the results as quantum kinetic theory cannot be applied to the problem. Lastly, progress on experiments to measure the critical velocity of superfluidity in Bose-Einstein condensates is reported. Calculations have been carried out that show the creation of solitons and vortices as mechanisms to dissipate energy leading to a breakdown of superfluid behaviour at velocities lower than that predicted by Landau’s theory of superfluidity, the first theory to describe superfluidity. Progress on an experiment is presented that uses the scanning beam trap developed as part of this project to create a line potential with a moving barrier to measure the critical velocity and show solitons and vortices as the mechanisms for energy dissipation as seen in the calculations.
Since the first Bose-Einstein Condensate (BEC) was demonstrated in a dilute atomic gas [1], rotating BECs have been of interest to researchers due to their quantized circulation. We propose a new method of creating controlled vortices in a BEC. Atoms are held in the focus of a scanning beam that rapidly scans to produce a time-averaged potential [2]. We have made theoretical calculations to measure the heating caused by a scanning beam trap and to find the regime where a scanning beam produces a time-averaged potential. The scanning beam splits the BEC into four parts then imprints a relative phase on each part such that, when the parts recombine, a vortex forms. We have simulated such a system using the Gross-Pitaevskii equation and have demonstrated the laser scanning pattern using a two-dimensional acousto-optic modulator (AOM). The optics for the scanning beam trap have been designed and the experimental trap dimensions are used in our simulations. To carry out the experimental part of this project, we are currently building and testing an all-optical BEC apparatus: we have made a magneto-optical trap (MOT) which cools the 87Rb atomsto 30uK. We are currently setting up an optical dipole trap to perform the final stages of cooling.
The development of novel trapping potentials for degenerate quantum gases has been an important factor driving experimental progress in the field. The introduction of spatial light modulators (SLMs) into quantum gas laboratories means that a range of configurable geometries are now possible. Here we demonstrate the production of arbitrary and dynamic high-resolution traps for Bose-Einstein condensates (BECs) using a (1200 x 1920) pixel digital-micromirror device (DMD) and commercially available microscope objectives. Direct imaging of the DMD provides significant advantages over phase-based SLMs, while still providing high resolution projected patterns. We find that atoms confined in a hybrid optical/magnetic or all-optical potential can be patterned using repulsive blue- detuned (532 nm) light with 630(10) nm full-width at half-maximum (FWHM) resolution, while imaging at 780 nm similarly achieves 960(80) nm resolution FWHM, within 5% and 8% of the diffraction limit respectively. This performance is > 7 times improved over previously reported DMD trapping. The result is near arbitrary control of the atomic distribution over the spatial extent of the BEC trapping volume. Furthermore, we produce time-averaged potentials with the DMD, demonstrating the ability to produce multiple grayscale levels with minimal heating of the atomic cloud. These techniques, along with the high level of dynamic control afforded by DMDs, will enable the realization and control of diverse optical potentials for superfluid dynamics and atomtronics applications with quantum gases.
Abstract : The Bose-Einstein condensation (BEC) laboratory at the University of Arizona has built a program of research that focuses on two areas of BEC physics. First, we developed techniques necessary to experimentally investigate dynamic quasi-condensed states. With our system, we have instituted new directions of experimental BEC physics: studying spontaneous formation of topological defects during the BEC phase transition, and studying transitions to superfluid turbulent states. As phase transitions and turbulence occur throughout natural phenomena, this work is further relevant to a wide range of subjects in physics. Our first published results have been enabled using the support of ARO award DAAD19-03-1-0368; our research in these areas is also ongoing. Our second main efforts have revolved around refining capabilities for studying and manipulating vortices and ultra-cold gases in disc-shaped and annular potentials using optical potentials, with a particular eye towards quantum engineering of vortex and persistent current states. These efforts involve often separate areas of investigation: manipulating condensates with laser light, two-dimensional physics, fluid dynamics and turbulence, phase-transition dynamics, and vortices and persistent currents. Our efforts are collaborative, with theoretical work at multiple universities and experimental work in Arizona progressing in tandem.
Programable spatial light modulators (SLMs) have significantly advanced the configurable optical trapping of particles. Typically, these devices are utilized in the Fourier plane of an optical system, but direct imaging of an amplitude pattern can potentially result in increased simplicity and computational speed. Here we demonstrate high-resolution direct imaging of a digital micromirror device (DMD) at high numerical apertures (NA), which we apply to the optical trapping of a Bose-Einstein condensate (BEC). We utilise a (1200 x 1920) pixel DMD and commercially available 0.45 NA microscope objectives, finding that atoms confined in a hybrid optical/magnetic or all-optical potential can be patterned using repulsive blue-detuned (532 nm) light with 630(10) nm full-width at half-maximum (FWHM) resolution, within 5% of the diffraction limit. The result is near arbitrary control of the density the BEC without the need for expensive custom optics. We also introduce the technique of time-averaged DMD potentials, demonstrating the ability to produce multiple grayscale levels with minimal heating of the atomic cloud, by utilising the high switching speed (20 kHz maximum) of the DMD. These techniques will enable the realization and control of diverse optical potentials for superfluid dynamics and atomtronics applications with quantum gases. The performance of this system in a direct imaging configuration has wider application for optical trapping at non-trivial NAs.