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arXiv:cond-mat/0610485

Vortices and phase transitions of interacting bosons in a rotating lattice ring

Qi Zhou

Published Oct 17, 2006• 0 citations
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Abstract

We investigate the ground state properties of the repulsive interacting bosons in an one dimensional rotating lattice ring, and reveal that the superfluid density of the system and the mass current it can carry in the rotating coordinate are periodic functions of the velocity of the lattice. In the weakly interacting limit, the vortices are generated at the critical velocities, and in the strongly interacting limit, the phase twist of the bosons induced by the rotating lattice manifests the superfluid density and drive the system to undergo phase transitions between the superfluid and Mott insulator.

DOI
10.48550/arxiv.cond-mat/0610485

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We investigate the ground state properties of the repulsive interacting bosons in an one dimensional rotating lattice ring, and reveal that the superfluid density of the system and the mass current it can carry in the rotating coordinate are periodic functions of the velocity of the lattice. In the weakly interacting limit, the vortices are generated at the critical velocities, and in the strongly interacting limit, the phase twist of the bosons induced by the rotating lattice manifests the superfluid density and drive the system to undergo phase transitions between the superfluid and Mott insulator.
Properties of bosonic atoms in small systems with a periodic quasi one-dimensional circular toroidal lattice potential subjected to rotation are examined by performing exact diagonalization in a truncated many body space. The expansion of the many-body Hamiltonian is considered in terms of the first band Bloch functions, and no assumption regarding restriction to nearest-neighbor hopping (tight-binding approximation) is involved. A finite size version of the zero temperature phase diagrams of Fisher et al. \cite{Fisher} is obtained and the results, in remarkable quantitative correspondence with the results available for larger systems, discussed. Ground state properties relating to superfluidity are examined in the context of two-fluid phenomenology. The basic tool, consisting of the intrinsic inertia associated with small rotation angular velocities in the lab frame, is used to obtain ground state `superfluid fractions' numerically. They are analytically associated with one-body, uniform solenoidal currents in the case of the adopted geometry. These currents are in general incoherent superpositions of contributions from each eigenstate of the associated reduced one-body densities, with the corresponding occupation numbers as weights. Full coherence occurs therefore only when only one eigenstate is occupied by all bosons. The obtained numerical values for the superfluid fractions remain small throughout the parameter region corresponding to the `Mott insulator to superfluid' transition, and saturate at unity only as the lattice is completely smoothed out.
We use second- and fourth-order correlation functions accessible in time-of-flight images to investigate the effects of rotation on one-dimensional ultracold bosons confined to a ring lattice. There exists a critical rotation frequency at which the ground state of a weakly interacting and integer-filled atomic gas is fragmented into a macroscopic superposition of two states with different circulation. The formation of such a quantum superposition (``cat'') state is accompanied by the opening of a gap in the spectrum, and by a sudden rearrangement of the momentum distribution which lowers the threshold of the Mott insulator transition. We show that both the entangled character of the ground state and the enhancement of quantum correlations can be detected in the density-density correlations of the expanding cloud. Our studies demonstrate the usefulness of these correlations for identifying physics in cold atomic systems.
Atomic clouds in a rotating optical lattice are at the intellectual intersection of several major paradigms of condensed matter physics. An optical lattice simulates the periodic potential ubiquitous in solid state physics, while rotation probes the superfluid character of these cold atomic gases by driving the formation of quantized vortices. Here we explore the theory of vortices in an optical lattice. We first provide a detailed introduction section aimed at providing the reader with the information necessary to understand and appreciate the research presented in later chapters. Next we study an infinite square lattice configuration of vortices in a rotating optical lattice near the superfluid-Mott-insulator transition. We find a series of abrupt structural phase transitions where vortices are pinned with their cores only on plaquettes or only on sites. We discuss connections between these vortex structures and the Hofstadter-butterfly spectrum of free particles on a rotating lattice. We then investigate vortex configurations within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. We find that proximity to the Mott insulating state dramatically affects the vortex structures. To illustrate we give examples in which the vortices: (i) all sit at a fixed distance from the center of the trap, forming a ring, or (ii) coalesce at the center of the trap, forming a giant vortex. We model time-of-flight expansion to demonstrate the experimental observability of our predictions. Finally for a trapped gas far from the Mott regime, the competition between vortex-vortex interactions and pinning to the optical lattice results in a complicated energy landscape, which leads to hysteretic evolution. The qualitative structure of the vortex configurations depends on the commensurability between the vortex density and the site density - with regular lattices when these are commensurate, and concentric rings when they are not. Again we model the imaging of these structures by calculating time-of-flight column densities. As in the absence of the optical lattice, the vortices are much more easily observed in a time-of-flight image than in-situ.
The vortex density of a rotating superfluid, divided by its particle mass, dictates the superfluid's angular velocity through the Feynman relation. To find how the Feynman relation applies to superfluid mixtures, we investigate a rotating two-component Bose–Einstein condensate, composed of bosons with different masses. We find that in the case of sufficiently strong interspecies attraction, the vortex lattices of the two condensates lock and rotate at the drive frequency, while the superfluids themselves rotate at two different velocities, whose ratio equals the ratio between the particle masses of the two species. In this paper, we characterize the vortex-locked state, establish its regime of stability, and find that it survives within a disk smaller than a critical radius, beyond which vortices become unbound and the two Bose-gas rings rotate together at the frequency of the external drive.
Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of $2\ensuremath{\pi}$ in the phase winding of the condensate wave function. A lattice of size $L\ifmmode\times\else\texttimes\fi{}L$ can have at most $L\ensuremath{-}1$ quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.
We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.