The measurement of the optical phase of far-detuned laser light by phase modulation spectroscopy is promising as a non-destructive probe of the dynamics of Bose-Einstein condensates. We have developed the experimental technique on a room-temperature Cs vapour cell, and a Cs magneto-optical trap (MOT). We measure column densities with an accuracy better than 7%. A numerical model, including Doppler broadening and transitions between all relevant hyperfine levels, accurately describes the data from the Cs cell. The same model without Doppler broadening gives quantitative agreement with measurements from the Cs MOT. We show that the conditions needed for non-destructive measurements of BEC dynamics are achievable with conventional equipment and a simple, robust experimental setup.
The measurement of the optical phase of far-detuned laser light by phase modulation spectroscopy is promising as a non-destructive probe of the dynamics of Bose-Einstein condensates. We have developed the experimental technique on a room-temperature Cs vapour cell, and a Cs magneto-optical trap (MOT). We measure column densities with an accuracy better than 7%. A numerical model, including Doppler broadening and transitions between all relevant hyperfine levels, accurately describes the data from the Cs cell. The same model without Doppler broadening gives quantitative agreement with measurements from the Cs MOT. We show that the conditions needed for non-destructive measurements of BEC dynamics are achievable with conventional equipment and a simple, robust experimental setup.
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.
Lasers are increasingly being used to impart mechanical forces on materialparticles ranging from atoms to biological cells. I present here experimentsinvolving such forces, concentrating on the formation and excitation of Bose-Einstein condensates (BEC) in ultra-cold rubidium 87 vapours. Also reportedare experiments in laser locking using hyperfine spectroscopy of 87Rb andexperiments in the optical manipulation of particles much larger than atoms.The cooling and imaging techniques used in BEC experiments dependcrucially on lasers with frequencies stabilised relative to the hyperfine structureof atoms. This structure is typically probed using saturated absorptionspectroscopy or polarisation spectroscopy, but the reliability of both is compromisedby the narrowness of the spectral lines involved. An extension ofpolarisation spectroscopy is presented which overcomes this by measuringa combination of Stokes parameters, the ratio of which provides a usefulfeedback signal over many times the line-width.Particles up to the size of biological cells can also be trapped and relocatedusing tightly focused laser beams called optical tweezers. Slight displacementsof particles within tweezer traps are used here to measure opticalforces applied by a tapered optical fiber lens that delivers light to a trappedpolystyrene bead. The optical force on the bead was mapped as it was movedrelative to the taper, showing that the taper provides a long and well colli-mated force-field that might be used as an optical “conveyor belt”.A BEC is a macroscopic collection of particles which collectively displayquantum coherence. Condensates are created by trapping and cooling particlesto temperatures below the critical temperature Tc for Bose condensation.These experiments produce BECs of 87Rb atoms with an atom chip apparatusthat confines atoms to a cigar shaped region using a nearly harmonicmagnetic potential. One axis of this trap is much weaker than the others andis bisected by a Gaussian sheet of laser light, to which atoms are attracted.The beam thus provides a narrow potential well (dimple) of variable depthsuperimposed on the magnetic trap.This trap was used to form condensates by mechanical compression (whichraises Tc) rather than cooling. Thermodynamic properties of vapours wereobserved before and after the dimple potential was turned on and comparedto detailed theoretical calculations based on semi-classical Hartree-Fock (mean-field) theory, which is often presumed to be accurate for Bosegases. Good agreement was found when the dimple was switched on slowlyin a reversible process. Rapid turn-on however produced much less heating(and hence higher final condensate fractions) than predicted.The dynamics of condensation formation were studied by measuring theproperties of vapours at various times after suddenly switching on the dimple.This contrasts with experiments in which high energy atoms are rapidly removedfrom a cloud. Condensates form in such systems after a very differentkind of rethermilsation process.The dimple is also used to create overdensities which propagate throughthe BEC after the optical potential is suddenly turned off. Analytical calculationsof classical hydrodynamics and numerical simulations of the condensatebased on the Gross-Pitaevskii wave equation both show that the leading edgeof such pulses should form shock waves in finite time. The regime in whichthis occurs is experimentally accessible and data are shown which are compatiblewith theoretical predictions. However the existence of shock waves isnot demonstrated because the available imaging resolution is insufficient. Aproposal is made to repeat this experiment using much larger condensates,which calculations show should make shock waves apparent.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.
Research on degenerate quantum gases of dilute atomic gases has become a well established field in modern physics and revealed many astonishing phenomena. The first experiments on Bose and Fermi gases at low temperatures aimed to prove the predictions of quantum mechanics on a macroscopic scale. Since then we make use of Bose and Fermi gases and mixtures of any combination to model other many body systems. A property of Bose Einstein condensates is superfluidity which we want to investigate further in toroidal potentials with a new apparatus which can produce an all-optical BEC. This means trapping thermal atoms in an optical dipole trap and cooling the sample by evaporation into the quantum degenerate regime. This new technique was first successfully demonstrated by M.D. Barrett et al. in 2001 and promises to be faster and simpler than the well established and common way of evaporation in magnetic traps. 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 l = 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. This thesis contains the theoretical framework of Bose-Einstein condensation with in mean-field theory, the concepts of cooling of atoms in magneto-optical traps, the trapping and evaporation in optical dipole traps and the experimental realisation. In the future this experiment will be extended by a fast scanning dipole trap to apply arbitrary time averaged potentials of more complex geometries, such as toroidal traps to study the effects of superfluidity in a periodic potential. The production of toroidal traps and cold atoms in such a trap are outlined in this thesis.
We present an experimental study to characterize a sodium vapor-cell magneto-optical trap (VCMOT) in terms of the number and density of trapped atoms, loading rate and load-ing time. We have investigated how these quantities change with the vapor temperature, magnetic- eld gradient and laser intensity. The results obtained are explained with a sim-ple model that employs the Doppler theory. Good agreement is obtained for most of the experimental data. Investigations on the size of the cloud as a function of the trap external parameters are also carried out. The information MOT in order to obtain the maximum presented here is useful in optimizing the number and density of trapped atoms, normally required for experiments of atomic collisions and Bose-Einstein condensation. I.