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arXiv:cond-mat/0207677 · Physical Review A

Superfluidity and mean-field energy loops: Hysteretic behavior in Bose-Einstein condensates

Erich J. Mueller

Published Dec 16, 2002• 130 citations
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Abstract

We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallow-tail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current-carrying states due to quantum fluctuations.

DOI
10.1103/physreva.66.063603

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We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallow-tail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current-carrying states due to quantum fluctuations.
We investigate the hysteresis characteristics in a system of dipolar Bose gases loaded into a triangular lattice. We perform a large-size cluster mean-field analysis for the corresponding dipolar Bose-Hubbard model in the hard-core boson limit and show that in varying the chemical potential the system can exhibit a hysteretic behavior without forming the standard "hysteresis-loop" structure. In this anomalous hysteresis, the quantum melting transition from the supersolid (or solid) to superfluid state can occur, but the reverse process (quantum solidification) is impossible.
We study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a ``disorder'' potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the system's eigenstates. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level.
The Bloch states of Bose-Einstein condensates (BECs) in pure nonlinear lattices (NLs) are dynamically unstable so that they cannot show superfluidity. We overcome this problem by finding that the two-component BECs in NLs can be stabilized by coherent linear coupling. Furthermore, in the limit of strong coherent coupling, the lowest Bloch band in the whole Brillouin zone can be dynamically stable. We also find a hysteretic behavior with looplike structure in the Bloch band resembling the so-called ``swallowtail'' loop. The dynamical stabilization and the looplike band structure can be realized in experiments by current technology. Our results are obtained from a discrete model, and major results are also confirmed by a continuum model.
We review our studies on Bose and Fermi superfluids of cold atomic gases in optical lattices at zero temperature. Especially, we focus on superfluid Fermi gases along the crossover between the Bardeen-Cooper-Schrieffer (BCS) and the Bose-Einstein condensate (BEC) states, which enable us to study the Bose and the Fermi superfluids in a unified point of view. We discuss basic static and long-wavelength properties (such as the equation of state, incompressibility, and effective mass), energetic stability, and energy band structures of the superfluid Fermi gases in an optical lattice periodic along one spatial direction. The periodic potential causes pairs of atoms to be strongly bound, and this can affect the static and long-wavelength properties and the stability of the superflow. Regarding the band structure, a peculiar loop structure called “swallowtail” can appear in superfluid Fermi gases and in the Bose case, but the mechanism of emergence in the Fermi case is very different from that in bosonic case. Other quantum phases that the cold atomic gases in optical lattices can show are also briefly discussed based on their roles as quantum simulators of Hubbard models.
Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling can exhibit hysteresis loops of atomic currents. Cold atoms in ring-shape potentials are thus promising for demonstrating rate-dependent hysteresis and its associated phenomena.