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Condensate Mixtures and Tunneling

Eddy Timmermans

Published Sep 14, 1998• 0 citations
OpenAlex

Abstract

The experimental study of condensate mixtures is a particularly exciting application of the recently developed atomic-trap Bose-Einstein condensate (BEC) technology: such multiple condensates represent the first laboratory systems of distinguishable boson superfluid mixtures. In addition, as the authors point out in this paper, the possibility of inter-condensate tunneling greatly enhances the richness of the condensate mixture physics. Not only does tunneling give rise to the oscillating particle currents between condensates of different chemical potentials, such as those studied extensively in the condensed matter Josephson junction experiments, it also affects the near-equilibrium dynamics and stability of the condensate mixtures. In particular, the stabilizing influence of tunneling with respect to spatial separation (phase separation) could be of considerable practical importance to the atomic trap systems. Furthermore, the creation of mixtures of atomic and molecular condensates could introduce a novel type of tunneling process, involving the conversion of a pair of atomic condensate bosons into a single molecular condensate boson. The static description of condensate mixtures with such type of pair tunneling suggests the possibility of observing dilute condensates with the liquid-like property of a self-determined density.

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Communications in Theoretical Physics•Apr 15, 2004•1 citation
The experimental study of condensate mixtures is a particularly exciting application of the recently developed atomic-trap Bose-Einstein condensate (BEC) technology: such multiple condensates represent the first laboratory systems of distinguishable boson superfluid mixtures. In addition, as the authors point out in this paper, the possibility of inter-condensate tunneling greatly enhances the richness of the condensate mixture physics. Not only does tunneling give rise to the oscillating particle currents between condensates of different chemical potentials, such as those studied extensively in the condensed matter Josephson junction experiments, it also affects the near-equilibrium dynamics and stability of the condensate mixtures. In particular, the stabilizing influence of tunneling with respect to spatial separation (phase separation) could be of considerable practical importance to the atomic trap systems. Furthermore, the creation of mixtures of atomic and molecular condensates could introduce a novel type of tunneling process, involving the conversion of a pair of atomic condensate bosons into a single molecular condensate boson. The static description of condensate mixtures with such type of pair tunneling suggests the possibility of observing dilute condensates with the liquid-like property of a self-determined density.
We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid 4He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of 4He superfluid component below λ-point, in particular—the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid 4He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject.
Superfluidity has become a topic of active interest in the field of atom trap Bose-Einstein condensates (BECs). We motivate this line of research by placing the BEC developments against the general backdrop of the theory of superfluidity and by highlighting the advantages offered by the atom trap technology. We review the standard description of the BEC dynamics, as well as basic concepts of superfluidity and we present theoretical arguments for expecting the BECs to exhibit superfluid behaviour. In atom traps, as in condensed and nuclear matter, superfluidity can manifest itself in a manifold of guises. Moreover, some of its manifestations can even be undesirable, as we illustrate by the poignant example of sympathetic cooling with condensates. We also review recent experimental evidence for superfluid BEC behaviour and we suggest further experiments to probe superfluidity in atom traps. The low densities of the BECs allow optical imaging and imply that the relevant physics occurs on time and length scales that are much slower and larger than in the traditional 4He superfluid. Consequently, BEC experiments can study known superfluid phenomena and structures in a different and, perhaps, more detailed manner. In addition, the flexibility offered by existing techniques in atomic, molecular and optical physics is unprecedented in the field of low-temperature physics and suggests the prospect of creating superfluids of fundamentally novel structures. Finally, it is conceivable that new applications of superfluidity may arise from these studies.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.
Recently, effects of Feshbach resonances in atom-atom interactions were observed by varying the external magnetic field of an atomic Bose-Einstein condensate (BEC). We point out that the quasi-bound molecules created in the intermediate state of the resonance can form a second, molecular condensate. The many-body state of the system is then a hybrid atomic/molecular condensate with inter-condensate tunneling of atom pairs. A sudden variation of the magnetic field results in oscillations of the number of atoms and molecules in their respective condensates, providing a signature of this novel type of quantum tunneling.
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.
Tunneling dynamics of multi-atomic molecules between atomic and multi-atomic molecular Bose–Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose–Einstein condensates depends on not only the inter-atomic-molecular nonlinear interactions and the initial number of atoms in these condensates, but also the tunneling coupling between the atomic condensate and the multi-atomic molecular condensate. It is discovered that besides oscillating tunneling current between the atomic condensate and the multi-atomic molecular condensate, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling. Moreover, the conception of the molecular Bose–Einstein condensate, which is different from the conventional single-atomic Bose–Einstein condensate, is specially emphasized in this paper.