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arXiv:cond-mat/0207715 · Physical Review A

Surface modes of ultracold atomic clouds with a very large number of vortices

Miguel A. Cazalilla

Published Jun 30, 2003• 38 citations
arXivHTMLPDF

Abstract

We study the surface modes of some of the vortex liquids recently found by means of exact diagonalizations in systems of rapidly rotating bosons. In contrast to the surface modes of Bose condensates, we find that the surface waves have a frequency linear in the excitation angular momentum, $\ensuremath{\Elzxh}l>0.$ Furthermore, in analogy with the edge waves of electronic quantum Hall states, these excitations are chiral, that is, they can be excited only for values of l that increase the total angular momentum of the vortex liquid. However, differently from the quantum Hall phenomena for electrons, we also find other excitations that are approximately degenerate in the laboratory frame with the surface modes, and which decrease the total angular momentum by l quanta. The surface modes of the Laughlin as well as other scalar and vector boson states are analyzed and their observable properties characterized. We argue that measurement of the response of a vortex liquid to a weak time-dependent potential that imparts angular momentum to the system should provide valuable information for characterizing the vortex liquid. In particular, the intensity of the signal of the surface waves in the dynamic structure factor has been studied and found to depend on the type of vortex liquid. We point out that the existence of surface modes has observable consequences on the density profile of the Laughlin state. These features are due to the strongly correlated behavior of atoms in the vortex liquids. We point out that these correlations should be responsible for a remarkable stability of some vortex liquids with respect to three-body losses.

DOI
10.1103/physreva.67.063613

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We study the surface modes of some of the vortex liquids recently found by means of exact diagonalizations in systems of rapidly rotating bosons. In contrast to the surface modes of Bose condensates, we find that the surface waves have a frequency linear in the excitation angular momentum, \ensuremath\Elzxhl>0.\ensuremath{\Elzxh}l>0.\ensuremath\Elzxhl>0. Furthermore, in analogy with the edge waves of electronic quantum Hall states, these excitations are chiral, that is, they can be excited only for values of l that increase the total angular momentum of the vortex liquid. However, differently from the quantum Hall phenomena for electrons, we also find other excitations that are approximately degenerate in the laboratory frame with the surface modes, and which decrease the total angular momentum by l quanta. The surface modes of the Laughlin as well as other scalar and vector boson states are analyzed and their observable properties characterized. We argue that measurement of the response of a vortex liquid to a weak time-dependent potential that imparts angular momentum to the system should provide valuable information for characterizing the vortex liquid. In particular, the intensity of the signal of the surface waves in the dynamic structure factor has been studied and found to depend on the type of vortex liquid. We point out that the existence of surface modes has observable consequences on the density profile of the Laughlin state. These features are due to the strongly correlated behavior of atoms in the vortex liquids. We point out that these correlations should be responsible for a remarkable stability of some vortex liquids with respect to three-body losses.
We study the evolution of the excitation spectrum of a trapped rotating Bose-Einstein condensate as a function of increasing rotational frequency and discuss chiral edge states supported on the condensate surface. We describe these modes in the context of a mean-field Bogoliubov--de Gennes treatment. We find that they dominate the spectrum at fast rotation, and the dispersion relation for these excitations becomes linear in the limit of high angular momentum as in the quantum Hall effect. We also identify the edge states as primary agents in the nucleation and decay of the lattice.
In rapidly rotating condensed Bose systems we show that there is a regime of anomalous hydrodynamics which coincides with the mean field quantum Hall regime. A consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show that there are constraints which connect spatial variations of density and phase and that the vortex positions are not the simplest description of the dynamics. We demonstrate, inter alia, a simple relation between vortices and surface waves. We show that the surface waves can emulate a "normal fluid," allowing dissipation by energy and angular momentum absorbtion from vortex motion in the trap. The time scale is sensitive to the initial configuration, which can lead to long-lived vortex patches--perhaps related to those observed at JILA.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex\textit{phantom vortex}phantom vortex that, contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not\textit{not}not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortex modes which so far seem to have evaded experimental detection.
We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensates in a rotating double-well trap potential and corotating optical lattice. We show that the vortex number does not diverge when the rotational frequency $\ensuremath{\Omega}\ensuremath{\rightarrow}1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value l/l\sqrt{l}/ll​/l for l=4l=4l=4, which supports the conjecture that surface modes with angular momentum l=4l=4l=4 are excited when the rotating condensate is trapped in a double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning show very interesting features. We show the existence and pinning of hidden vortices whose phase profile is similar to that of the visible vortices.
The structure of vortices in Bose-Einstein condensed atomic gases is studied taking into account many-body correlation effects. It is shown that for excited vortices the particle density in the vortex core increases as the angular momentum of the system increases. The core density can increase by several times with only a few percent change in the angular momentum. This result provides an explanation for the observations in which the measured angular momentum is higher than the estimation based on counting the number of vortices and the visibility of the vortex cores is simultaneously reduced. The calculated density profiles for the excited vortices are in good agreement with experimental measurements of a single vortex.