A vortex in a superfluid gas inside an optical lattice can behave as a massive particle moving in a periodic potential and exhibiting quantum properties. In this paper we discuss these properties and show that the excitation of vortex dynamics in a two-dimensional lattice can lead to striking measurable changes in its dynamic response. It would be possible by means of Bragg spectroscopy to carry out the first direct measurement of the effective vortex mass. In addition, the experiments proposed here provide an alternative way to study the pinning to the underlying lattice and the dissipative damping.
A vortex in a superfluid gas inside an optical lattice can behave as a massive particle moving in a periodic potential and exhibiting quantum properties. In this paper we discuss these properties and show that the excitation of vortex dynamics in a two-dimensional lattice can lead to striking measurable changes in its dynamic response. It would be possible by means of Bragg spectroscopy to carry out the first direct measurement of the effective vortex mass. In addition, the experiments proposed here provide an alternative way to study the pinning to the underlying lattice and the dissipative damping.
Abstract In Josephson junction arrays, vortices form stable topological excitations. A key step towards the understanding of their properties was the observation made by Eckern and Schmid that in low‐capacitance junction arrays a vortex behaves as a massive particle moving in a periodic potential and subject to dissipation. The mass is low and quantum effects become observable. The present contribution provides a review of these properties together with a discussion of similar scenarios realized in optical lattices.
Superfluids with strong spatial modulation can be experimentally produced in the area of cold atoms under the influence of optical lattices. Here we address 87Rb bosons at T=0 K in a flat geometry under the influence of a periodic potential with the Gross-Pitaevskii theory. The statics and dynamics of vortex excitations are studied in the case of one-dimensional (1D) and of two-dimensional (2D) optical lattices, as function of the intensity of the optical lattice. We compute how the vortex energy depends on the position of its core and the energy barrier that a vortex has to surmount in order to move in the superfluid. The dynamics of a vortex dipole, a pair of vortices of opposite chirality, differ profoundly from the case of a uniform superfluid. In the 1D case, when parallel ridges of density are present, the dynamics depends on the positions of the two vortices. If they are in the same channel between two ridges, then the two vortices approach each other until they annihilate each other in a short time. If the two vortices are in distinct channels, the dipole undergoes a rigid translation but with a velocity depending on the intensity of the optical lattice and this translation velocity can even change sign with respect to the case of the uniform superfluid. Superimposed on this translation an oscillatory motion is also present. A superposition of translation along a channel and an oscillation is also found with a single vortex when the system is bounded inside a circular trap. These oscillatory motions can be both longitudinal, i.e., along the channel, as well as transverse. In all cases the transverse motions are one sided, in the sense that the vortex core never crosses the equilibrium position nearest the starting position. In the case of the 2D lattices we study (square, triangular, and honeycomb), the two vortices of a dipole move mainly by jumps between equilibrium positions and approach each other until annihilation. This behavior has some similarity with what has been found for a vortex dipole in the supersolid state of dipolar bosons. We show that a rapid ramp down of the optical potential improves the visibility of the density holes at the vortex core.
Quantized vortices stunningly illustrate the coherent nature of a superfluid Bose condensate of alkali atoms. Introducing an optical lattice depletes this coherence. Consequently, novel vortex physics may emerge in an experiment on a harmonically trapped gas in the presence of a rotating optical lattice. The most dramatic effects would occur in proximity to the Mott state, an interaction dominated insulator with a fixed integer number of particles per site. We model such a rotating gas, showing that the lattice-induced spatial profile of the superfluid density drives a gross rearrangement of vortices. For example, instead of the uniform vortex lattices commonly seen in experiments, we find parameters for which the vortices all sit at a fixed distance from the center of the trap, forming a ring. Similarly, they can coalesce at the center, forming a giant vortex. We find that the properties of this system are hysteretic, even far from the Mott state. We explain this hysteresis in terms of vortex pinning, commensurability between vortex density and pinning site density, and energy barriers against changing the number of vortices. Finally, we model time-of-flight expansion, demonstrating the experimental observability of our predictions.
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.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
We derive an effective action for the vortex-position degree of freedom in a superfluid by integrating out condensate phase- and density-fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius R, or the typical distance between vortices, is very much larger than the coherence length $\ensuremath{\xi}$. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid, we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy J and the on-site interaction energy U. We comment on the possibility of realizing vortex-Landau-level physics.