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Physical Review A

AtomicZitterbewegungin Abelian vector gauge potentials

Jian-Jun Song, Bradley A. Foreman

Published Oct 19, 2009• 8 citations
Publisher

Abstract

We propose a scheme to realize Zitterbewegung (ZB) with cold atoms in an Abelian vector potential. Two dark states can be created by interacting alkali-metal atoms with three coaxial Gaussian beams. Atoms moving in the subspace spanned by the two dark states feel a vector gauge potential that is nonvanishing only along the laser axis. We show that cold atoms in this Abelian vector potential undergo ZB with a large amplitude detectable in experiment.

DOI
10.1103/physreva.80.045602

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We propose a scheme to realize Zitterbewegung (ZB) with cold atoms in an Abelian vector potential. Two dark states can be created by interacting alkali-metal atoms with three coaxial Gaussian beams. Atoms moving in the subspace spanned by the two dark states feel a vector gauge potential that is nonvanishing only along the laser axis. We show that cold atoms in this Abelian vector potential undergo ZB with a large amplitude detectable in experiment.
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We propose an optical lattice scheme which would permit the experimental observation of Zitterbewegung (ZB) with ultracold, neutral atoms. A four-level tripod variant of the setup for stimulated Raman adiabatic passage (STIRAP) has previously been proposed for generating non-Abelian gauge fields. Dirac-like Hamiltonians, which exhibit ZB, are simple examples of such non-Abelian gauge fields; we show how a variety of them can arise, and how ZB can be observed, in a tripod system. We predict that the ZB should occur at experimentally accessible frequencies and amplitudes.
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
We propose a scheme to generate an Abelian gauge field in an atomic gas using two crossed laser beams. If the internal atomic state follows adiabatically the eigenstates of the atom-laser interaction, Berry's phase gives rise to a vector potential that can nucleate vortices in a Bose gas. The present scheme operates even for a large detuning with respect to the atomic resonance, making it applicable to alkali-metal atoms without significant heating due to spontaneous emission. We test the validity of the adiabatic approximation by integrating the set of coupled Gross-Pitaevskii equations associated with the various internal atomic states, and we show that the steady state of the interacting gas indeed exhibits a vortex lattice, as expected from the adiabatic gauge field.
We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.