Controlling quantum fluids at their fundamental length scale will yield superlative quantum simulators, precision sensors, and spintronic devices. This scale is typically below the optical diffraction limit, precluding precise wave-function engineering using optical potentials alone. We present a protocol to rapidly control the phase and density of a quantum fluid down to the healing length scale using strong time-dependent coupling between internal states of the fluid in a magnetic field gradient. We demonstrate this protocol by simulating the creation of a single stationary soliton and double soliton states in a Bose-Einstein condensate with control over the individual soliton positions and trajectories, using experimentally feasible parameters. Such states are yet to be realized experimentally, and are a path towards engineering soliton gases and exotic topological excitations.
Controlling quantum fluids at their fundamental length scale will yield superlative quantum simulators, precision sensors, and spintronic devices. This scale is typically below the optical diffraction limit, precluding precise wave-function engineering using optical potentials alone. We present a protocol to rapidly control the phase and density of a quantum fluid down to the healing length scale using strong time-dependent coupling between internal states of the fluid in a magnetic field gradient. We demonstrate this protocol by simulating the creation of a single stationary soliton and double soliton states in a Bose-Einstein condensate with control over the individual soliton positions and trajectories, using experimentally feasible parameters. Such states are yet to be realized experimentally, and are a path towards engineering soliton gases and exotic topological excitations.
To engineer the wavefunction of a Bose–Einstein condensate is to exert control over both the density and phase of the Bose–Einstein condensate order parameter. Having the ability to engineer the condensate order parameter down to the smallest length scale relevant to condensate dynamics—the healing length scale—would enable the study of new combinations of topological defects and may pave the way to using Bose–Einstein condensates as versatile, precise quantum simulators. In this thesis, we present a new wavefunction engineering technique which reaches the sub-optical healing length scale. Influenced by magnetic resonance imaging, we name this technique magnetic resonance control. This technique uses time-varying coupling between internal spin states of a spinor Bose–Einstein condensate within a magnetic field gradient to address spatial regions of the condensate, enabling control over both the phase and the density of the condensate order parameter down to the healing length scale. Techniques already exist to engineer condensate wavefunctions, but not with such a fine degree of control. These techniques primarily rely on either the intensity variation of a laser beam, which limits the resolution to the diffraction limit (larger than the typically sub-optical healing length scale), or the adiabatic inversion of a magnetic trapping potential, which can not be easily changed to produce a variety of structures in the condensate wavefunction. To develop our magnetic resonance control technique, we simulate a spinor condensate in one dimension with time-dependent coupling between spin states and time-dependent external magnetic field gradients using the Gross–Pitaevskii equation. We show that magnetic resonance control can engineer a single black soliton using experimentally feasible parameters. A black soliton is an ideal target state to select for this demonstration because engineering such a state requires control over both the phase and density of the condensate with healing-length resolution. We demonstrate that magnetic resonance control can be extended to engineer more complicated target states by simulating the creation of multiple solitons in a condensate, with control over the initial positions and trajectories of the solitons. When magnetic resonance control is applied to Bose–Einstein condensates in the laboratory, it will be necessary to have an imaging system capable of resolving the fine structures created. As an alternative to high-cost, custom-manufactured lenses, and in-vacuum optical systems, I have designed and bench-tested an objective lens with a high numerical aperture (0.36) and a long working distance (35 mm) consisting of standard catalogue lenses. Using 780 nm light, suitable for imaging rubidium condensates, this objective can achieve a resolution of 1.3 μm across a diffraction-limited field of view of 360 μm through a 5 mm thick glass window of a science cell. By changing the spacing between the lens elements, this objective lens can compensate for the aberrations produced by a glass window up to 15 mm thick, and by changing the aperture size the objective becomes suitable for diffraction-limited monochromatic imaging on the D2 line of all the alkalis. Before performing proof-of-principle magnetic resonance control experiments on real Bose–Einstein condensates, we needed to construct an experimental apparatus capable of producing spinor Bose–Einstein condensates. In this thesis I summarise my main contributions to this group endeavour, including: constructing the ultra-high vacuum system; supervising the bakeout of our vacuum system; designing and aligning the optical systems to produce laser beams of different, tunable frequencies to trap, cool, and image rubidium gas; trapping a cloud of rubidium atoms in a magneto-optical trap; constructing laser beam shutters, photodetectors, and photodetector signal filters; and designing and constructing our side imaging and top imaging systems. Using our spinor Bose–Einstein condensate apparatus, I performed the first proof-of-principle magnetic resonance control experiments. With a pair of condensates side-by-side, separated by 200 μm, we can use magnetic resonance control to invert the spin of one condensate only, while leaving the other condensate unaffected. We anticipate magnetic resonance control being used in the laboratory to engineer the first black soliton in a Bose–Einstein condensate. Looking beyond solitons, magnetic resonance control could have applications to the field of magnon spintronics, and extending the technique to higher dimensions could enable the study of exotic topological defects such as spin knots in a quantum fluid.
Bose-Einstein condensates (BECs), a quantum state of matter formed when bosonic atoms are cooled close to absolute zero, have become the premier platform for investigating fundamental physics with atomic vapours. Experiments on Bose-Einstein condensates now achieve exquisite control over many aspects of the system, including interactions, trapping potential, and dynamics. This has precipitated a new wave of research into many-body quantum phenomena and, in particular, solitons. These structures are fundamental excitations of an interacting non-linear medium, of interest to a multitude of scientific disciplines from non-linear optics to financial markets. The highly controllable environment of BECs form an attractive playground for the study of solitons allowing the non-linearity to be dynamically tuned, facilitating deeper investigations into these structures. Consistently generating and analysing solitons in BEC experiments continues to be problematic. In particular, the non-linear dynamics of BECs, though required for the generation of solitons, produce particularly challenging control and optimization problems. These control problems must be solved before further investigations into the fundamental physics of soliton dynamics can be answered. This thesis makes three important advances in the control and measurement of BECs that will lead to better generation and observation of solitons. (1) a theoretical model for a control scheme capable of highly precise wavefunction engineering, (2) the experimental implementation of a machine learning algorithm for online optimisation, and (3) a continuous non-destructive imaging system capable of directly observing soliton dynamics in real-time. Together, these advances provide a suite of tools for manipulating and exploiting solitons in Bose-Einstein condensates. A novel technique was developed theoretically, offering control of the macroscopic wavefunction of a Bose-Einstein condensate with unprecedented spatial resolution and speed. The ability to control the atomic wavefunction at the fundamental length scale is key to the advancement of many quantum technologies such as quantum simulators. The magnetic resonance control scheme is demonstrated through simulation of a 87Rb condensate with the exemplar model generating a single dark soliton with corresponding π phase kink. The soliton represents a structure at the fundamental length scale of the system, and demonstrates the potential of the scheme for precision state engineering. The scheme is extended to generate higher-order soliton modes which are yet to be experimentally realised. A machine learning algorithm based on Gaussian processes was developed and implemented on the evaporative cooling stage of the production of a 87Rb Bose-Einstein condensate, successfully demonstrating fast optimisation to condensation. The Gaussian process develops a statistical model based on the data that enables the characterisation of the relationship between the experimental controls and resultant quality of the BEC. This relationship is often obfuscated through technical details of the apparatus, frustrating the use of theoretical models to design optimal evaporation ramps. These models often only consider ergodic dynamics with two-body s-wave interactions and no other loss rates with better ramps likely exploiting more complex interactions. The internal model generated from the Gaussian process utilised uncertainty in measured data, making the optimisation more robust to experimental noise than alternate methods. The algorithm is shown to produce high quality Bose-Einstein condensates in 10 times fewer experimental iterations than previously used online optimisation techniques. By exploiting information on the sensitivity of each control, the model can be used to aid experimental design. The convergence of the optimisation is further improved by eliminating a superfluous parameter identified by the model. The general usefulness of machine learning compared with bespoke optimisation algorithms has seen machine learning approach ubiquity. Finally, an experimentally straightforward technique for continuous non-destructive imaging of matter-wave solitons was developed and implemented, facilitating measurements of stochastic phenomena. The technique is readily practicable on any ultracold atom experiment with an existing absorption imaging system, simply requiring the probe laser be far-detuned from resonance. With a signal-to-noise of ∼ 33 at 1.25 GHz detuning, the technique is capable of producing 100 images with no observable heating or atom loss. Coupled with a fast optical phase locked loop, the technique can be used in conjunction with absorption imaging to generate a series of non-destructive images followed by a final high signal-to-noise absorption image solely through moving the laser on resonance for the final image. The high performance and utility of this imaging setup make it a powerful tool for ultra-cold atom experiments.
Abstract While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose–Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton state can be obtained by selectively driving the impurity atoms. This allows to fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.
While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.
We present experiments investigating different aspects concerning the coherent manipulation of a Bose-Einstein condensate wavefunction with far blue detuned dipole potentials. In a first set of experiments we study a waveguide for matter waves as an important atom optical element allowing to hold and guide the atoms for long observation times. We present a flexible realization of this waveguide based on a tube shaped Laguerre Gaussian laser beam and investigate the dynamics of a Bose condensed ensemble transferred into this guide. In a second set of experiments we study the dynamics of dark solitons created by the manipulation of the phase of the condensate wave function by temporally applied dipole potentials. This method of phase imprinting represents a powerful tool for the design of matter waves and the controlled creation of various excitations. The dynamics of dark solitons in matter waves is investigated in detail by experimentally and numerically studying the temporal evolution of the condensate density as well as by mapping the velocity field of the excited condensate wavefunction. In these measurements we directly detect the flux of the wave function associated with the dark soliton using spatially resolved Bragg scattering. Experiments investigating the creation and interaction of several dark solitons conclude this chapter.
Single topological defects and related structures have been experimentally created inside clouds of Bose-Einstein condensates. However, a practical protocol for creating multiple defects inside a single cloud—a prerequisite for studying defect interactions—has been lacking. Here we propose, and theoretically analyze, a practical protocol for the creation of configurations of topological monopoles, quantum knots, and skyrmions in Bose-Einstein condensates by employing fictitious magnetic fields induced by the interaction of the atomic cloud with coherent light fields. It is observed that a single coherent field is not enough for this purpose, but instead we find incoherent superpositions of several coherent fields that introduce topological point charges. We numerically estimate the experimentally achievable strengths and gradients of the induced fictitious magnetic fields and find them to be adjustable at will to several orders of magnitude greater than those of the physical magnetic fields employed in previous experimental studies. This property together with ultrafast control of the optical fields paves the way for advanced engineering of topological defects in quantum gases. Published by the American Physical Society 2024