"Motivated by experiments on cold alkali atoms, I present a theoretical study of weakly interacting quantum degenerate particles. These experiments observe a wide range of phenomena and consequently this thesis has a broad scope, involving issues of coherence, stability, superfluidity, and kinetics. I explore six topics which exemplify the rich and exciting physics of cold alkali atoms: first, the effect of interactions on the transition temperature of a dilute Bose gas; second, the connection between broken non-gauge symmetries and the appearance of multiple condensates in a Bose gas; third, the role of thermally activated ""phase slip"" events in destroying superfluidity near the critical temperature of a Bose gas; fourth, mechanical instabilities in clouds of attractive bosons; fifth, the kinetics of a gas of partially condensed atoms; and sixth, the nonlinear optical properties of an atomic gases."
"Motivated by experiments on cold alkali atoms, I present a theoretical study of weakly interacting quantum degenerate particles. These experiments observe a wide range of phenomena and consequently this thesis has a broad scope, involving issues of coherence, stability, superfluidity, and kinetics. I explore six topics which exemplify the rich and exciting physics of cold alkali atoms: first, the effect of interactions on the transition temperature of a dilute Bose gas; second, the connection between broken non-gauge symmetries and the appearance of multiple condensates in a Bose gas; third, the role of thermally activated ""phase slip"" events in destroying superfluidity near the critical temperature of a Bose gas; fourth, mechanical instabilities in clouds of attractive bosons; fifth, the kinetics of a gas of partially condensed atoms; and sixth, the nonlinear optical properties of an atomic gases."
This doctoral dissertation is concerned with the physics of strongly interacting cold alkali atoms at low temperatures near a Feshbach resonance. In Chapter 1, we establish a connection between superfluid 4He and the BCS theory of superconductivity, and cold alkali atoms. We give the history of cold atoms, describing the significant achievements, pitfalls and challenges. In Chapter 2, we explore the thermodynamics of strongly interacting Bosonic atoms. We explore the stability of atomic Bosonic condensates near a Feshbach resonance. We show that the experimentally attained atomic condensate is a saddle point of the free energy, but the kinetics of its decay is slow. We also show that there is a second, higher density condensate branch which has an Ising-like phase transition to a molecular (paired) condensate when ramped across the Feshbach resonance. We argue that due to the high density, inelastic 3-body processes possibly render this transition unobservable. In Chapter 3, we explore the thermodynamics of Fermionic atoms near a Feshbach resonance. We determine the zero-temperature (T less than/less than T sub(F) ) pair propagator for a spinimbalanced mixture of up and down spin Fermions, and use it to show that such a mixture becomes completely polarized at mu sub(down arrow)= -0.9 mu sub(up arrow) . We also determine the Thouless criterion for superfluidity in a spin-imbalanced Fermi mixture, and construct a phase diagram of such a system at zero temperature. We then compare our results with experiments performed by two different groups. We find that interaction modifications to the minority spin self-energy inferred from our analysis is roughly double those observed in experiments. This discrepancy is consistent with the expected accuracy of the theory. In Chapter 4, we extend our analysis of the preceding chapter to calculate the surface tension of an interface between spin-polarized Fermions in the normal and superfluid phases. We show that, as expected, this surface tension decreases with increasing temperature and vanishes at a tricritical temperature, above which the transition becomes continuous. We also calculate the thickness of the interface; at T = 0, this is a few interparticle spacings, but diverges at the tricritical temperature. To compare with a set of relevant experiments, we also develop a phenomenological model for surface tension, and conclude that experimental surface tensions are an order of magnitude higher than what our microscopic calculation yields. We hypothesize possible mechanisms. In Chapter 5, we calculate the finite temperature phase diagram of a Bose-Fermi mixture produced from a spin-imbalanced two-component Fermi gas deep in the BEC phase. We show that there is a discontinuous transition between the superfluid and normal phase, with an entropy of mixing sufficient to cool the system down. We detail the construction of such a cooling scheme to cool a Fermi system below what is possible evaporatively, and find that the cooling efficiency is comparable to typical evaporative schemes. In Chapter 6, we shift our focus from thermodynamics to dynamics. We calculate shifts in the energy spectrum of a spin-balanced Fermionic superfluid of Cooper pairs due to the presence of energetically close states coupled by a Feshbach resonance. These shifts manifest themselves as clock-shifts in the radio-frequency spectrum of the superfluid. In addition to a broad asymmetric peak coming from the break-up of Cooper pairs, we find (for certain parameter ranges) a sharp, symmetric "bound-bound" spectral line coming from the conversion of Cooper pairs in one channel to pairs or molecules in another channel. Our theory shows remarkable quantitative agreement with experiments performed by an experimental group.
Since the first experimental realization of Bose-Einstein condensation in cold atomic gases in 1995 there has been a surge of activity in this field. Ingenious experiments have allowed us to probe matter close to zero temperature and reveal some of the fascinating effects quantum mechanics has bestowed on nature. It is a challenge for mathematical physicists to understand these various phenomena from first principles, that is, starting from the underlying many-body Schrödinger equation. Recent progress in this direction concerns mainly equilibrium properties of dilute, cold quantum gases. We shall explain some of the results in this article, and describe the mathematics involved in understanding these phenomena. Topics include the ground state energy and the free energy at positive temperature, the effect of interparticle interaction on the critical temperature for Bose-Einstein condensation, as well as the occurrence of superfluidity and quantized vortices in rapidly rotating gases.
Summary form only given. The dilute gas experiments on the Bose-Einstein condensation of magnetically confined alkali vapors have already generated widespread interest across a broad spectrum of traditional fields of physics. They have provided an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems with the single particle microscopic physics described in quantum optics and laser physics. The approach I discuss is based on a derivation of the quantum kinetic theory from first principles. Based on a microscopic picture of the weakly interacting bosonic gas, a generalized kinetic theory for a Markovian many-body density operator is derived. The density operator is functionally dependent on a few key variables, which must be carefully chosen. These quantities serve as master variables and determine the system's evolution on a coarse-grained time scale. The weak interactions allow a perturbative expansion of the evolution, from which kinetic equations that describe the dynamics of the expectation value of any single-time observable are obtained. The final structure of the theory has many analogies with the quantum theory of the laser, such as amplitude and phase noise for the macroscopic field, squeezing dynamics, and a nonlinear master equation describing the underlying evolution.
The most salient features of the Bose-Einstein condensation of a magnetically confined alkali vapor is the diluteness of the gas and the extremely weak effective interactions. From a theoretical point of view, the interesting aspect is the potential formulation of the many-body quantum theory for a non-uniform and potentially non-equilibrium system founded entirely on microscopic physics. The crucial postulate is the rapid attenuation of many particle quantum correlations in the dilute system which can be motivated from universal considerations. In principle, it will be possible to provide direct comparison between theory and experiment over all temperature scales with no phenomenological parameters — a challenge facing the theoretical community in the near future. The dilute gas experiments provide an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems, with the single particle microscopic physics described in quantum optics and laser physics.
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.
Bose-Einstein condensation is an exciting physical phenomenon. It was predicted in 1924 and experimentally produced in 1995 using powerful laser cooling techniques. Bose condensed gases become one of most emerging field of modern physics, embracing many area namely atomic and molecular physics, nuclear physics, astrophysics, quantum optics, and condensed matter physics. The advent of these quantum degenerate gases opens intriguing prospects for precision measurements, quantum information, and novel phases of matter. The book presents a new thorough theory treating Bose condensed gases at finite temperatures with extremely distinct background. The approach proved useful, efficient and successful as a theoretical mean to study all aspects of ultracold gases at finite temperatures. Equilibrium and dynamic properties, superfluidity and vortices, anomalous correlations, quantum mixtures and long range interactions are among the topics covered in this book. The book is written in a pedagogical style and features sufficient elementary background material. It can be therefore, accessible to all scientists from graduate students to senior researchers in cold atoms physics.