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Towards interferometry with bright solitary waves in a ring

M. M. H. Yu

Published Jan 1, 2016• 1 citation
OpenAlex

Abstract

This thesis presents the work towards the realisation of an interferometer using bright solitary waves in a ring. The splitting of a bright solitary wave, which is created from a 85Rb Bose-Einstein condensate in an optical waveguide, is realised through scattering from a narrow potential well formed from a tightly focussed red detuned laser beam. We observe reflection of up to 25% of the atoms, along with the trapping of atoms at the position of the potential. Such a reflected fraction is much larger than the theoretical predictions for a single, narrow Gaussian potential. A more detailed model, which accounts for the diffraction pattern of the laser beam, suggests that the presence of these small subsidiary intensity maxima is the cause of the enhancement in quantum reflection. An upgrade of the apparatus sees a new set of magnetic coils, a compact coil mount, and a crossed optical dipole trap with independently controllable beams implemented. This enables the control of magnetic curvature and dipole trap position, and maximises the optical access to the science cell. To generate a ring trap for the interferometry scheme, a spatial light modulator (SLM) is incorporated into the experiment. Through underfilling the SLM panel with the laser beam, and the use of the analytical first phase guess prior to the error minimising Mixed Region Amplitude Freedom (MRAF) algorithm, we are able to generate speckle-free, high quality holograms of arbitrary shapes. Furthermore, we demonstrate atom trapping in a ring potential, which is formed at the intersection of the SLM beam and a red detuned horizontal light sheet.

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This thesis presents the work towards the realisation of an interferometer using bright solitary waves in a ring. The splitting of a bright solitary wave, which is created from a 85Rb Bose-Einstein condensate in an optical waveguide, is realised through scattering from a narrow potential well formed from a tightly focussed red detuned laser beam. We observe reflection of up to 25% of the atoms, along with the trapping of atoms at the position of the potential. Such a reflected fraction is much larger than the theoretical predictions for a single, narrow Gaussian potential. A more detailed model, which accounts for the diffraction pattern of the laser beam, suggests that the presence of these small subsidiary intensity maxima is the cause of the enhancement in quantum reflection. An upgrade of the apparatus sees a new set of magnetic coils, a compact coil mount, and a crossed optical dipole trap with independently controllable beams implemented. This enables the control of magnetic curvature and dipole trap position, and maximises the optical access to the science cell. To generate a ring trap for the interferometry scheme, a spatial light modulator (SLM) is incorporated into the experiment. Through underfilling the SLM panel with the laser beam, and the use of the analytical first phase guess prior to the error minimising Mixed Region Amplitude Freedom (MRAF) algorithm, we are able to generate speckle-free, high quality holograms of arbitrary shapes. Furthermore, we demonstrate atom trapping in a ring potential, which is formed at the intersection of the SLM beam and a red detuned horizontal light sheet.
This thesis presents the development of an experimental apparatus to produce Bose-Einstein condensates (BECs) with tunable interparticle interactions. The ability to precisely control the strength of these interactions, and even to switch them from repulsive to attractive, allows one to probe novel regimes of condensate physics, from the collapse of attractively interacting BECs and the formation of solitary matter-waves to the observation of beyond mean-field effects in strongly repulsive condensates. The construction and characterisation of both a single and crossed beam optical dipole trap is presented. In the single beam case we develop a technique allowing the guided transport of atoms along the beam and up to a room-temperature surface; a technique which can be used to evaporatively cool the trapped atomic cloud. We produce Bose-Einstein condensates of 87Rb in the F=1, mF=-1 state in this trap, comparing the effect of beam waist on the evaporation trajectory. In the crossed beam trap Bose-Einstein condensation of 87Rb is realised in three distinct trapping configurations, along with a 1D optical lattice formed by changing the polarisation of the beams. A method of direct cooling of 85Rb atoms in the crossed trap is developed using a magnetic Feshbach resonance to precisely tune both the elastic and inelastic scattering properties of the atoms. The resonance used for this work occurs at 155G in collisions between atoms in the F=2, mF=-2 state of 85Rb. Bose-Einstein condensates of up to 40,000 85Rb atoms are formed in this trap and we demonstrate the presence of tunable interatomic interactions, exploring the collapse phenomenon associated with attractive condensates. By loading the 85Rb condensate into a quasi-1D waveguide we show that stable attractive condensates can be created, taking the form of bright solitary matter-waves. We observe a solitary wave of ~2,000 atoms which propagates, without dispersion, along the waveguide over a distance of ~1.1mm. The particle-like nature of the solitary wave is demonstrated by classical reflection of the wavepacket from a repulsive Gaussian barrier.
We report the observation of quantum reflection from a narrow attractive potential using bright solitary matter waves formed from a 85Rb^{85}\mathrm{Rb}85Rb Bose-Einstein condensate. We create the attractive potential using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the confinement of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a simple Gaussian potential well. A more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.
Interferometry with atoms is a young discipline of physics. The ¯rst interfer- ometers were realised in the early 1990s, using light pulses as beamsplitters in momentum space. Recent developments in atom optics have led to new proposals for interferometers, where the splitting takes place spatially. Mag- netic and optical traps are both suited for this kind of interferometer if a well de¯ned and highly controllable trap is realised. In this thesis results from two experiments that in principle allow the creation of such traps are presented. After reviewing the principles and techniques of atom optics necessary for the understanding of this thesis, a theoretical discussion about the spatial single atom interferometer in a double well potential follows. It is shown that within reasonable limits the system can be reduced to two levels and solved by the Bloch equations. Using the realistic case of a not perfectly symmetric double well potential allows an understanding of the physics behind such an interferometer: how phase is accumulated and how localisation of the atoms leads to the loss of the interferometric signal. Then two experiments are presented. One experiment was newly built up as part of this thesis: it uses a novel hybrid atom chip' with a combination of a magneto-optical ¯lm and current-carrying structures to produce the magnetic trapping potentials. This experiment allowed 5¢108 87Rb atoms to be captured in a magneto-optical trap, where the atom-chip's surface acts as a mirror. The atoms were then transferred into a purely magnetic trap which was created by current carrying structures on the chip. From there on, RF radiation enforced evaporative cooling, so that a quantum degenerate Bose-Einstein condensate of up to 105 atoms was created. It was also shown that the magneto-optical ¯lm is able to hold and trap the atoms. In the second experiment atoms are trapped in the spatially varying inten- sity of light of 1.03 ¹m wavelength. This experiment used an existing set-up as a basis and was modi¯ed and improved for this new project. This experiment starts with 109 87Rb atoms in a 6-beam magneto-optical trap. After examining and optimising the loading process, 1:5 ¢ 105 atoms could be loaded directly from the Magneto-optical trap into the optical dipole potential of two crossed laser beams at 1.03 ¹m. Evaporative cooling was demonstrated though the phase transition to quantum degeneracy was not reached.
This thesis describes the formation of a 85Rb Bose-Einstein condensate and the subsequent creation of a bright solitary matter-wave in a quasi-one-dimensional optical waveguide, with experiments investigating the dynamics of a solitary wave in comparison with a repulsive Bose-Einstein condensate. In the final chapters of this thesis, progress towards the interaction of a solitary wave with a narrow barrier and an attractive atom-surface potential is presented. Beyond the above, a review of recent soliton and solitary wave theory is presented from the perspective of an experimentalist, culminating in the numerical analysis of a variety of key areas, namely, quantum reflection, solitary wave size and solitary wave profile. The modelling and experimental results relating to the merging of ultracold gases of 85Rb and 87Rb, in order to create isotopic mixtures, is also described within this thesis. Such a scheme could be used as an initial step in the process of forming molecules or undertaking sympathetic cooling. Finally, the creation of a complex LabVIEW based experimental control system is also described within.
Bright solitons in atomic Bose-Einstein condensates are a strong candidate for high precision matter-wave interferometry, as their inherent stability against dispersion supports long interrogation times. One analog to a beam splitter for these solitons is a narrow potential barrier. A very narrow barrier is desirable for interferometric purposes, but the width in a typical realisation, using a blue-detuned optical dipole potential, is limited by the wavelength of the laser light. We investigate a soliton interferometry scheme using the geometric scalar potential experienced by atoms in a spatially dependent dark state to overcome this limit. We propose a possible implementation and numerically probe the effects of deviations from the ideal.
Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.