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arXiv:cond-mat/0412015 · Physical Review A

Effective magnetic fields in degenerate atomic gases induced by light beams with orbital angular momenta

Gediminas Juzeliūnas, Patrik Öhberg, Julius Ruseckas, Alexander Klein

Published May 23, 2005• 99 citations
arXivHTMLPDF

Abstract

We investigate the influence of two resonant laser beams on the mechanical properties of degenerate atomic gases. The control and probe beams of light are considered to have orbital angular momenta (OAM) and act on the three-level atoms in the electromagnetically induced transparency configuration. The theory is based on the explicit analysis of the quantum dynamics of cold atoms coupled with two laser beams. Using the adiabatic approximation, we obtain an effective equation of motion for the atoms driven to the dark state. The equation contains a vector-potential-type interaction as well as an effective trapping potential. The effective magnetic field is shown to be oriented along the propagation direction of the control and probe beams containing OAM. Its spatial profile can be controlled by choosing proper laser beams. We demonstrate how to generate a constant effective magnetic field, as well as a field exhibiting a radial distance dependence. The resulting effective magnetic field can be concentrated within a region where the effective trapping potential holds the atoms. The estimated magnetic length can be considerably smaller than the size of the atomic cloud.

DOI
10.1103/physreva.71.053614

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We investigate the influence of two resonant laser beams on the mechanical properties of degenerate atomic gases. The control and probe beams of light are considered to have orbital angular momenta (OAM) and act on the three-level atoms in the electromagnetically induced transparency configuration. The theory is based on the explicit analysis of the quantum dynamics of cold atoms coupled with two laser beams. Using the adiabatic approximation, we obtain an effective equation of motion for the atoms driven to the dark state. The equation contains a vector-potential-type interaction as well as an effective trapping potential. The effective magnetic field is shown to be oriented along the propagation direction of the control and probe beams containing OAM. Its spatial profile can be controlled by choosing proper laser beams. We demonstrate how to generate a constant effective magnetic field, as well as a field exhibiting a radial distance dependence. The resulting effective magnetic field can be concentrated within a region where the effective trapping potential holds the atoms. The estimated magnetic length can be considerably smaller than the size of the atomic cloud.
We study the influence of two resonant laser beams (to be referred to as the control and probe beams) on the centre-of-mass motion of ultra-cold atoms characterized by three energy levels of the Λ-type. The laser beams being in the electromagnetically induced transparency (EIT) configuration drive the atoms to their dark states. We impose the adiabatic approximation and obtain an effective equation of motion for the dark state atoms. The equation contains a vector potential type interaction as well as an effective trapping potential. We concentrate on the situation where the control and probe beams are co-propagating and have orbital angular momenta (OAM). The effective magnetic field is then oriented along the propagation direction of the control and probe beams. Its spatial profile can be shaped by choosing proper laser beams. We analyse several situations where the effective magnetic field exhibits a radial dependence. In particular, we study effective magnetic fields induced by Bessel beams, and demonstrate how to generate a constant effective magnetic field for a ring geometry of the atomic trap. We also discuss a possibility of creating an effective field of a magnetic monopole.
We consider the influence of the control and probe beams in the electromagnetically induced transparency configuration on the mechanical motion of ultracold atomic gases (atomic Bose-Einstein condensates or degenerate Fermi gases). We carry out a microscopic analysis of the interplay between radiation and matter and show that the two beams of light can provide an effective magnetic field acting on electrically neutral atoms in the case where the probe beam has an orbital angular momentum. As an example, we demonstrate how a Meissner-like effect can be created in an atomic Bose-Einstein condensate.
The adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields creating a dark state can give rise to effective gauge potentials. We show that these potentials lead to effective magnetic fields if the light fields possess a relative orbital angular momentum. This allows to study quantum-Hall like effects in ultra-cold atomic gases in various geometries. If the atom-light interaction creates several degenerate adiabatic eigenstates, the associated gauge potentials are non-Abelian. 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.
We propose a scheme to create an effective magnetic field for ultracold atoms in a planar geometry. The setup allows the experimental study of classical and quantum Hall effects in close analogy to solid-state systems including the possibility of finite currents. The present scheme is an extention of the proposal in Phys. Rev. Lett. 93, 033602 (2004), where the effective magnetic field is now induced for three-level $\ensuremath{\Lambda}$-type atoms by two counterpropagating laser beams with shifted spatial profiles. Under conditions of electromagnetically induced transparency the atom-light interaction has a space-dependent dark state, and the adiabatic center-of-mass motion of atoms in this state experiences effective vector and scalar potentials. The associated magnetic field is oriented perpendicular to the propagation direction of the laser beams. The field strength achievable is one flux quantum over an area given by the transverse beam separation and the laser wavelength. For a sufficiently dilute gas the field is strong enough to reach the lowest Landau level regime.
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.
Polariton formalism is applied for studying the propagation of a probe field of light in a cloud of cold atoms influenced by two control laser beams of larger intensity. The laser beams couple resonantly three hyperfine atomic ground states to a common excited state, thus forming a tripod configuration of the atomic energy levels involved. The first control beam can have an optical vortex, with the intensity of the beam going to zero at the vortex core. The second control beam without a vortex ensures the lossless (adiabatic) propagation of the probe beam at a vortex core of the first control laser. We investigate the storage of the probe pulse into atomic coherences by switching off the control beams and its subsequent retrieval by switching the control beams on. The optical vortex is transferred from the control to the probe fields during the storage or retrieval of the probe field. We analyze the conditions needed for the vortex to be transferred efficiently to the regenerated probe beam and discuss the possibilities of experimental implementation of the proposed scheme using atoms such as rubidium or sodium.