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Ultracold Bosonic Gases: Superfluidity and Quantum Interferometry

Francesco Piazza

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The aims of this dissertation are twofold. Firstly, the study of superfluidity, presented in the first part, has more a fundational character, since we investigate some well known problems, already raised in the context of superfluid helium, in order to gain a deeper understanding, by exploiting the cleannes of dilute BECs systems, as well as analyzing the new features emerging from the unique dilute BECs properties. We study the BEC flow through weak-links, first analyzing the various regimes of transport by the current-phase relation and the Josephson plasma oscillations, and then turning to the superfluid instability, determining critical velocities and examining the dissipation dynamics in different geometries and dimensionalities. Secondly, the analysis of quantum interferometry, given in the second part, has instead a more technological character, since we propose two possible implementation of interferometric protocols in double-well traps, with application to the measurement of weak-forces, and study their sensitivity in detail, especially in relation to its possible quantum enhancement.

DOI
10.15168/11572_369229

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The aims of this dissertation are twofold. Firstly, the study of superfluidity, presented in the first part, has more a fundational character, since we investigate some well known problems, already raised in the context of superfluid helium, in order to gain a deeper understanding, by exploiting the cleannes of dilute BECs systems, as well as analyzing the new features emerging from the unique dilute BECs properties. We study the BEC flow through weak-links, first analyzing the various regimes of transport by the current-phase relation and the Josephson plasma oscillations, and then turning to the superfluid instability, determining critical velocities and examining the dissipation dynamics in different geometries and dimensionalities. Secondly, the analysis of quantum interferometry, given in the second part, has instead a more technological character, since we propose two possible implementation of interferometric protocols in double-well traps, with application to the measurement of weak-forces, and study their sensitivity in detail, especially in relation to its possible quantum enhancement.
Manifestations of Quantum Physics at the thermodynamical level are found in a broadrange of physical systems. A famous example is superfluidity, discovered at the beginningof the 20th century and found in many different situations, from liquid helium to neutronstars. Dilute ultracold gases offer a unique versatility to engineer quantum many-bodysystems, which can be directly compared with theory thanks to the controllability of theirenvironment. In this thesis we present several experimental investigations led on ultracoldlithium gases. Lithium provides the possibility to study ensembles of bosons andfermions, with controllable interactions between the constituents. We present experimentaltechniques for preparation and studies of degenerate gases of lithium, with prospects forimprovement of the existing methods. We first report on an investigation of three-bodyrecombination of bosons under a resonant two-body interaction. This study, quantitativelycompared with theory constitutes a benchmark for further studies of the unitary Bose gas.Finally, we present the first experimental realization of a mixture of a Bose superfluid witha Fermi superfluid. We demon- strate that both components are in the superfluid regime,and that the counter-flow motion between them possesses the characteristics of superfluidflow, with the absence of viscosity below a critical velocity, and an onset of friction above.Using collective oscillations of the mixture, we measure the coupling between the twosuperfluids in close agreement with a theoretical model.
The experimental achievement of Bose-Einstein condensation (BEC) in 1995 has aroused a large interest among the community of the physics of ultracold atomic gases.Recently new topics have attracted the attention of this very active field of research , in particular we could mention low dimensional systems, atoms in lattices, and classical and Fermi gases.As for the case of BEC, the study of the dynamical aspects of these systems provides a very valuable information.In particular time-of-flight experiments and measurements of collective excitations have been successfully realized providing a clear signature of the BEC and the regime of interaction.Following this line, in this thesis, we want to study some dynamical aspects of these new systems nowadays avaliable due to the remarkable development of the experimental techniques.In the first chapter we present the state of the art of the field, providing the historical path and the motivation for the work developed in the next chapters.In the second chapter, we discuss some general concepts in order to introduce the formalism and notation employed throughout the thesis, as well as those topics analyzed in more detail in the further chapters.In chapter three, we explain some general techniques which are useful to deal with one dimensional systems, and analyze in detail the expansion of a one dimensional Bose gas in a guide, which differs significantly from the expansion of a BEC.In particular we are able to predict the range of parameters for which the self-similarity of the expansion is violated.Chapter four is devoted to the physics of atoms in a periodic potential.We start, as in the previous chapter, introducing some general concepts and techniques employed further.First we discuss the physics of the superfluid case in a trap, showing that under certain conditions a three dimensional gas exhibits one dimensional properties.viii In particular, static properties and the lowest collective excitations differ significantly from those of a BEC.We extend the analysis to the insulating phase showing that correlation properties depend on the on-site one-dimensional regime.These correlations can be measured in current time of flight experiments.In the fifth chapter we analyze the dynamics of classical and Fermi gases.We show in detail how expansion and collective excitations depend on the interaction regime and the trap anisotropy.In particular, the expansion can be used to distinguish between a normal Fermi gas and a superfluid one.We summarize in the last chapter the new results presented in this thesis.
Advances in trapping and cooling of ultracold gases over the last several decades have made it possible to test many formerly outstanding predictions from disparate branches of physics. This thesis touches on three historical problems that have found new life recently in the context of ultracold Bose gases of alkali atoms. The first problem revolves around an outstanding prediction from Boltzmann over a century and half old that the breathing mode of a isotropically trapped classical gas should oscillate indefinitely. I analyze recent experimental results [Nat. Phys. 11, 1009 (2015)], and attribute observed damping sources to trap imperfections. The second question is about the analogue of first and second sound modes from liquid helium in trapped dilute gases. I present the results of a joint theoretical/experimental investigation of the breathing mode of a finite temperature Bose-Einstein condensate (BEC), attributing a striking collapse revival behavior of the resultant oscillation to in-phase and out-of-phase normal modes of the thermal cloud and condensate. The third problem is that of the formation of Borromean ring-like three-body bound states, referred to as Efimov trimers, in strongly-interacting few-body systems. I extend the predicted spectrum of Efimov states into the realm of many degenerate internal levels, and investigate the difficult three-body elastic scattering problem.\nThese questions are part of the broader theme of this thesis: How can our understanding of few-body physics in the ultracold limit be translated into statements about the bulk behavior of an ultracold gas? For weakly-interacting Bose gases, this translation is well-known: the many-body properties of the gas are well-described by the tracking just the one and two particle correlations. I analyze a generalization of this procedure to higher order correlations, the general connection between few-body physics and correlations in a dilute gas, and results for the emergence of Efimov physics in the magnetic phase of the strongly-interacting Bose gas.
This chapter presents an overview of the specific experimental tools developed in the field of ultra-cold gases to achieve and probe superfluidity in vapours of bosonic atoms. First, it describes the main cooling techniques: the magneto-optical trap, which brings an atomic vapour from room temperature down to the sub-mK range, and the evaporative cooling scheme, which bridges the gap to the superfluid regime. It then proceeds to the study of interaction effects. It shows that these play a central role in the understanding of both static and dynamic properties of trapped Bose–Einstein condensates (BECs), despite the dilute character of these gases. As a consequence, gaseous BECs and superfluid helium obey the same laws of hydrodynamics and exhibit similar dynamical properties, although their densities differ by several orders of magnitude. The third section is devoted to the coherence properties of gaseous BECs. It shows that, by contrast with liquid helium, specific features of ultra-cold gases make them suitable for a direct probing of the quantum coherence associated with Bose–Einstein condensation. Finally, the possibility of tailoring trapping potentials and realizing low-dimensional systems is discussed, where one or two directions of motion are frozen.
Bose-Einstein condensation (BEC) and superfluidity are both remarkable manifestations of quantum mechanics on a macroscopic scale and have opened up the exploration of quantum phenomena in a qualitatively novel regime. The effort to realise BEC in dilute atomic gases, culminating in 1995, brought with it a powerful new set of ways to control and manipulate atoms and opened up a host of new scientific goals including quantum control, precision measurement, the study of phase transitions and the study of superfluidity – a peculiar phase of matter which is characterised by the absence of dissipation. In the 1940s, the Soviet physicist Lev Landau provided a qualitative theory for these dissipationless “super”fluids by providing an explanation of the critical velocity, below which the formation of fluid excitations is forbidden by the conservation of energy and momentum. This theory has stood the test of time and still forms the basis of our understanding today. Building on the work of Landau, we investigate the interplay between BEC and superfluidity using a novel Floquet analysis, which forms a natural way to characterise time-periodic systems. As a starting point to achieve this goal, we apply our Floquet analysis to another area of interest – the engineering of trapping potentials via the technique of time-averaging. We use Floquet theory to analyse the lowest energy state of time-periodic trapping potentials and characterise the transition from a localised state in a slowly moving trap to a delocalised trap in a rapidly oscillating time-averaged potential. We investigate how the driving parameters affect the density and phase of the Floquet ground state, and provide a quantitative measure of the degree to which they can be considered time-averaged. We investigate the conditions under which resonances occur in Floquet systems which can inform the implementation of experimental time-averaged traps since such resonances can lead to experiment-destroying, uncontrollable heating. We then investigate the breakdown of superfluidity in systems with moving obstacles using nonlinear conjugate gradient optimisation. We first perform a stability analysis, finding that superfluid Floquet states likely become unstable at the critical velocity and thus will not converge with optimisation techniques. We are unable to obtain convergence in a large region of parameter space and find that our optimisers converge best when the driving frequency is a multiple of the Bogoliubov frequency. We find that we are able to characterise the breakdown of superfluidity with two complementary measures of optimality, providing an operational definition of the critical velocity and transcritical regime which can replace the drag force in situations when it cannot be calculated.
The experimental achievement of Bose-Einstein condensation in cold alkali atomic gases in 1995 has started a period of fertile research at the intersection of atomic physics, quantum optics, and condensed matter. In this thesis, various tunneling effects in both bosonic and fermionic gases are investigated. The first part of this work deals with bosons in different Josephson-type experimental setups. After a brief general introduction we establish, in Chapter 2, a mapping between the phase and the Bogoliubov representation for the Josephson oscillations; in Chapter 3 we calculate the Josephson coupling constant for the condensate in the external Josephson effect. Chapter 4 deals with Josephson effects at the level of depletion: we describe in detail the oscillatory dynamics of the virtual quasiparticles. The next Chapter is a stability analysis for the formation of vortices in the Kibble-Zurek scenario. Finally, Chapter 6 contains a discussion on the time-evolution of the many-body states in the absence of tunneling. The second part of the thesis (Chapter 7- Chapter 9) deals with fermionic systems below the BCS critical temperature. The first two of these Chapters explore the possibility of driving transitions between hyperfine states with lasers. In Chapter 7 we show that these transitions could be used to investigate the coherence of the Cooper pairs. In Chapter 8 we imagine an internal Josephson experiment which uses a pair of lasers to drive transitions between two superfluids. Finally, in Chapter 9 we examine the properties of vortices formed in trapped Cooper-paired fermionic gases.