This work investigates the theoretical and experimental decoherence of phonons in weakly and strongly-interacting Bose-Einstein Condensates (BECs). The theoretical analysis treats phonons as open quantum systems where the environment comprises all other quasi-particle modes of the BEC. The phonons are assumed to be Gaussian states and the time in which they decohere is estimated from the evolution of their purity and nonclassical depth in the dissipative channel. The calculations are performed for various BEC systems and it is found that the excited phonon states will always decohere much more rapidly than the rate at which they relax back to equilibrium with the environment. Part II of this work considers how the decoherence of the phonons can be measured experimentally. The experiment that is currently being investigated uses a strongly-interacting [superscript]6Li BEC where the scattering length can be varied with an external magnetic field. In a strongly-interacting Bose gas the mutual interaction between the condensed and noncondensed components plays a greater role than in weakly-interacting gases and results in distinct absorption images. Understanding the effects from this mutual interaction is vital to model the in-situ absorption images of a strongly-interacting BEC in order to extract accurate information such as that which will facilitate the experimental measurement of decoherence. Three theoretical models that could be used to fit in-situ absorption images of a strongly-interacting gas are analysed. These are the bi-modal, semi-ideal and Hartree-Fock models, which will be fit against the absorption images of the [superscript]6Li BEC for various scattering lengths. The validity of these models is also investigated to determine when beyond mean-field effects may be observed in the Bose gas. Controlling decoherence is essential to the operation and physical realisation of many quantum information tasks and quantum technologies. Recently, new technologies have emerged from relativistic quantum information science that, in principle, are more precise than their non-relativistic counterparts. The practical setup of these devices utilizes phonons of BECs but the decoherence of the phonons has not been considered. In this work, one of the BEC systems used to estimate the decoherence time of the phonons has been chosen to be based on these devices. This calculation is expected to inform the practical realization of these devices and inspire future related studies. Analogue gravity investigations based on BECs also utilize phonons, for example, in the analogue of Hawking radiation. The quantum properties of these states is of particular interest in these studies and understanding how they decohere, and at what rate, could potentially inform the theory of black hole physics as well as dictate what is possible to measure experimentally.
This work investigates the theoretical and experimental decoherence of phonons in weakly and strongly-interacting Bose-Einstein Condensates (BECs). The theoretical analysis treats phonons as open quantum systems where the environment comprises all other quasi-particle modes of the BEC. The phonons are assumed to be Gaussian states and the time in which they decohere is estimated from the evolution of their purity and nonclassical depth in the dissipative channel. The calculations are performed for various BEC systems and it is found that the excited phonon states will always decohere much more rapidly than the rate at which they relax back to equilibrium with the environment. Part II of this work considers how the decoherence of the phonons can be measured experimentally. The experiment that is currently being investigated uses a strongly-interacting [superscript]6Li BEC where the scattering length can be varied with an external magnetic field. In a strongly-interacting Bose gas the mutual interaction between the condensed and noncondensed components plays a greater role than in weakly-interacting gases and results in distinct absorption images. Understanding the effects from this mutual interaction is vital to model the in-situ absorption images of a strongly-interacting BEC in order to extract accurate information such as that which will facilitate the experimental measurement of decoherence. Three theoretical models that could be used to fit in-situ absorption images of a strongly-interacting gas are analysed. These are the bi-modal, semi-ideal and Hartree-Fock models, which will be fit against the absorption images of the [superscript]6Li BEC for various scattering lengths. The validity of these models is also investigated to determine when beyond mean-field effects may be observed in the Bose gas. Controlling decoherence is essential to the operation and physical realisation of many quantum information tasks and quantum technologies. Recently, new technologies have emerged from relativistic quantum information science that, in principle, are more precise than their non-relativistic counterparts. The practical setup of these devices utilizes phonons of BECs but the decoherence of the phonons has not been considered. In this work, one of the BEC systems used to estimate the decoherence time of the phonons has been chosen to be based on these devices. This calculation is expected to inform the practical realization of these devices and inspire future related studies. Analogue gravity investigations based on BECs also utilize phonons, for example, in the analogue of Hawking radiation. The quantum properties of these states is of particular interest in these studies and understanding how they decohere, and at what rate, could potentially inform the theory of black hole physics as well as dictate what is possible to measure experimentally.
We apply modern techniques from quantum optics and quantum information science to Bose-Einstein condensates (BECs) in order to study, for the first time, the quantum decoherence of phonons of isolated BECs.In the last few years, major advances in the manipulation and control of phonons have highlighted their potential as carriers of quantum information in quantum technologies, particularly in quantum processing and quantum communication.Although most of these studies have focused on trapped ion and crystalline systems, another promising system that has remained relatively unexplored is BECs.The potential benefits in using this system have been emphasized recently with proposals of relativistic quantum devices that exploit quantum states of phonons in BECs to achieve, in principle, superior performance over standard nonrelativistic devices.Quantum decoherence is often the limiting factor in the practical realization of quantum technologies, but here we show that quantum decoherence of phonons is not expected to heavily constrain the performance of these proposed relativistic quantum devices.
We study non-equilibrium and strongly-correlated dynamics in two contexts. We begin by analysing quantum many-body systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highly-imbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a many-body quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highly-localised impurity interacting with a weakly-interacting trapped quasi low-dimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the self-trapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodically-trapped impurity through a quasi one-dimensional Bose gas. We show that placing the weakly-interacting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurity-Bose gas system exhibits phonon-induced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different strongly-correlated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a strongly-correlated system we use the powerful and near-exact time-evolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate non-equilibrium classical stochastic processes. We study its efficacy for a well-understood model of transport, the totally-asymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of sampling-based numerical methods for high variance observables we adapt and apply TEBD to simulate a path-dependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a one-dimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlo-based simulators of non-equilibrium stochastic processes.
Bose-Einstein condensation is a unique phase transition in that it is not driven by interparticle interactions, but can theoretically occur in an ideal gas, purely as a consequence of quantum statistics. This chapter addresses the question, ‘ How is this ideal Bose gas condensation modified in the presence of interactions between the particles?’ This seemingly simple question turns out to be surprisingly difficult to answer. Here we outline the theoretical background to this question and discuss some recent measurements on ultracold atomic Bose gases that have sought to provide some answers. Introduction Unlike the vast majority of phase transitions, Bose-Einstein condensation (BEC) is not driven by interparticle interactions but can theoretically occur in an ideal (noninteracting) gas, purely as a consequence of quantum statistics. However, in reality, interactions are needed for a Bose gas to remain close to thermal equilibrium. It is thus interesting to discuss if something close to ideal gas BEC can be observed in a real system and what happens in the vicinity of the BEC transition in the presence of interparticle interactions. These simple questions have not been easy to answer, either theoretically or experimentally. The theoretical foundations for studying the effect of interactions on Bose condensed systems were laid over half a century ago by Bogoliubov [1], Penrose and Onsager [2], and Belieav [3], among others. These works initially focused on zerotemperature properties and were extended to nonzero temperature in the pioneering papers of Lee, Huang, and Yang [4, 5, 6, 7]. At that time, the main experimental system was liquid He-4 in which the inter-particle interactions are strong, making connections with theory difficult. The realisation in 1995 of BEC in weakly interacting ultracold atomic gases [8, 9] thus opened up the possibility to experimentally revisit some of these long-discussed questions. This was further aided by, among other advances, the use of Feshbach resonances to tune the interaction strength in atomic gases [10, 11]. Thus, in the last twenty years the study of ultracold Bose gases has been very successful (see Chapter 3 for an insightful account of selected topics and surprising developments over this exciting period). However, the fact that, until recently, ultracold atoms were confined using harmonic potentials has hindered the study of the BEC transition itself.
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.
The analogy between the propagation of a massless scalar field in curved spacetime and the propagation of sound waves in a Bose-Einstein Condensate (BEC) gives rise to the possibility of observing the analogues of black hole radiance effects, such as Hawking Radiation and superradiance, in the laboratory. In order to provide a solid foundation for realising such analogue gravity models in an experimental setting, we have conducted a numerical investigation of phonon scattering from a BEC vortex by solving the time-dependent Gross-Pitaevskii (GP) equation, describing the dynamics of dilute gas BECs. The consideration of phonon superradiance in BECs in advance of Hawking Radiation is motivated by the fact superradiance may be easier to detect. ¶ We first present the results of one-dimensional simulations of sound waves propagating in a BEC and reflecting from a vortex-like density profile. Using these results as a guide, two-dimensional simulations of sound propagation in a BEC, and reflection from a BEC vortex, are performed. The technique of propagating the wavefunction in imaginary time was employed to find the vortex ground state. The accuracy of the simulations and the convergence of the solution to the vortex ground state was verified using a range of numerical diagnostics. Finally, preliminary simulations were performed within the superradiant frequency regime for the purposes of determining whether the amplification of incoming waves occurs given an appropriate choice of parameters. Overall, the two-dimensional modelling of reflection of cylindrical waves from a BEC vortex provides a basis for a systematic study of phonon superradiance in BECs.
In the years following the first Bose-Einstein condensation of dilute atomic gases in 1995, several experiments demonstrated many fundamental properties of two-component BEC. Subsequent to these pioneering experiments, almost a decade passed with little experimental activity, relative to investigations of single-component condensates. In somewhat of a renaissance, the initial observations of two-component BEC have been revisited in recent years, consolidating and clarifying results of the early works, and illuminating new and surprising behaviour of these rich quantum fluids. This thesis presents new experimental results on the relative phase evolution of two-component Bose-Einstein condensates (BECs). We approach our study of this system from the dual perspective of binary superfluidity and trapped atom interferometry. We observe nonequilibrium dynamics of the condensate that are deeply connected to the physics of interpenetrating superfluids. These dynamics have consequences for interferometers whose two paths are different internal spin states of the condensate atoms. Using trapped condensates for precision measurement draws upon the benefits of confined atom interferometry - long interrogation times, precise position control to measure near-field potentials - in addition to the unique coherence properties of BECs. Precision measurementwith trapped particles, however, is obstructed by the inherent inhomogeneities associated with the confinement itself. Spatial variation of the external potentials and atomic density can give rise to dephasing during the free evolution and imperfect splitting and recombination of the interferometric paths. In this thesis, we consider the dephasing of the two-componentmean field order parameter, which tends to diminish the interference signal attained with the condensate. The promise of fuhs for atom interferometry lies within using nonclassical many body states to reduce the fundamental noise limit imposed upon measuring the projection of atomic pseudospin. Before the many body quantum properties of two-component condensates can be used to their full potential, the ideal classical limit must be achieved and investigated. As in optical interferometry, the classical ideality of an interference measurement is contingent upon control of the spatialmodes - thematter wave fields, or single particle wave functions. Whilst much attention is currently focused on preparing nonclassical many body states for entanglement and squeezing of the condensate pseudospin, this thesis focuses on the ancillary yet important issue of spatial inhomogeneity of the condensate mean field. Reversal of the spatially inhomogeneous mean field evolution is demonstrated, employing the techniques of nuclear magnetic resonance. A new method is demonstrated to probe pseudospin -1/2 condensates involving microwave adiabatic passage. The technique permits simultaneous, spatially resolved absorption imaging of the spatial mode of each component. Controlled manipulation of the components into Zeeman states with different magnetic moments allows spatial separation using a Stern-Gerlach separation technique, providing a spatially resolved projection of the local condensate pseudospin from a single absorption image. We propose an interferometric technique which employs this imaging method to directly image the relative phase. The miscibility of the two components depends on the relative magnitude of the interactions between various collision partners. The boundary of this miscibility is found to be less pronounced than expected from the commonly applied results of homogeneous super-fluids.The effects of kinetic energy are shown to be significant at the threshold of miscibility, leading to a breakdown in the Thomas-Fermi approximation. Magnetic dipole transitions amongst alkali ground states are often used to prepare, manipulate, and interrogate pseudospin -1/2 condensates. We present a thorough investigation of the two-photonmagnetic dipole transitions between the |F = 1,mF = -1〉 and |F = 2,mF = +1〉 states, and the |F = 1,mF = +1〉 and |F = 2,mF = -1〉 states of 87Rb. Taking into account all 8 Zeeman levels of the electronic ground state reveals markedly different radiative shifts and effects beyond the rotating wave approximation, compared to the three-level formalism commonly used for these transitions.This has implications for Ramsey interferometry using the two-photon magnetic dipole transitions. The unchartered experimental territory offered by two-component condensates is vast, and future directions, supplementary to the work in this thesis, are elucidated.