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Physical Review A

Chiral edge states of vortex matter

Leslie O. Baksmaty, Sungjong Woo, Michael G. Banks, Seok Jin Choi, N. P. Bigelow

Published Dec 15, 2005• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.063615

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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.
We investigate the collective excitation spectrum of a quasi-two-dimensional Bose-Einstein condensate trapped in a harmonic confinement with nonlinear rotation induced by a density-dependent gauge potential. Using a Bogoliubov--de Gennes (BdG) analysis, we show that the dipole mode frequency depends strongly on the nonlinear interaction strength, violating Kohn's theorem which is also well complemented by the analytical expression for the dipole and breathing modes obtained employing a variational analysis. We identify four different vortex displacement modes, Tkachenko, circular, quadratic, and rational, whose frequencies are rotation sensitive. An analytical Tkachenko mode frequency from a hydrodynamic approach agrees well with that computed using BdG and Fourier analysis. The excitation spectrum remains symmetric around the angular quantum number l=0l=0l=0, but energy splitting between lll and $\ensuremath{-}l$ varies with the sign and strength of the nonlinear rotation. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.
We study the vortex nucleation in a finite Bose-Einstein condensate. Using a set of non-local and chiral boundary conditions to solve the Schro¨\ddot{o}o¨dinger equation of non-interacting bosons in a rotating trap, we obtain a quantitative expression for the characteristic angular velocity for vortex nucleation in a condensate which is found to be 35% of the transverse harmonic trapping frequency.
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.
The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for metastability of an isolated vortex coincides with the largest vortex precession frequency (or anomalous mode) in the Bogoliubov excitation spectrum. The number of anomalous modes increases for an elongated condensate. The largest mode frequency exceeds the thermodynamic critical frequency and the nucleation frequency at which vortices are created dynamically. Thus, anomalous modes describe both vortex precession and the critical rotation frequency for creation of the first vortex in an elongated condensate.