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arXiv:0712.1677 · Physical Review A

Quasirelativistic behavior of cold atoms in light fields

Gediminas Juzeliūnas, Julius Ruseckas, Markus Lindberg, Luis Santos, Patrik Öhberg

Published Jan 29, 2008• 110 citations
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Abstract

We study the influence of three laser beams on the center-of-mass motion of cold atoms with internal energy levels in a tripod configuration. We show that, as for electrons in graphene, the atomic motion can be equivalent to the dynamics of ultrarelativistic two-component Dirac fermions. We propose and analyze an experimental setup for observing such a quasirelativistic motion of ultracold atoms. We demonstrate that the atoms can experience negative refraction and focusing by Veselago-type lenses. We also show how the chiral nature of the atomic motion manifests itself as an oscillation of the atomic internal state population, which depends strongly on the direction of the center-of-mass motion. For certain directions an atom remains in its initial state, whereas for other directions the populations undergo oscillations between a pair of internal states.

DOI
10.1103/physreva.77.011802

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We study the possibility for generating a new type of spin-orbit coupling for the center-of-mass motion of cold atoms, using laser beams that resonantly couple NNN atomic internal ground states to an extra state. After a general analysis of the scheme, we concentrate on the tetrapod setup (N=4N=4N=4) where the atomic state can be described by a three-component spinor, evolving under the action of a Rashba-Dresselhaus-type spin-orbit coupling for a spin 1 particle. We illustrate a consequence of this coupling by studying the negative refraction of atoms at a potential step and show that the amplitude of the refracted beam is significantly increased in comparison to the known case of spin 1/21/21/2 Rashba-Dresselhaus coupling. Finally, we explore a possible implementation of this tetrapod setup, using stimulated Raman couplings between Zeeman sublevels of the ground state of alkali-metal atoms.
We propose an experimental setup for the observation of quasirelativistic massless fermions. It is based on a T3{\mathcal{T}}_{3}T3​ optical lattice, realized by three pairs of counterpropagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the T3{\mathcal{T}}_{3}T3​ Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudospin S=1S=1S=1. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.
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 present a calculation of one-dimensional sub-Doppler cooling of neutral atoms, in which the atomic center-of-mass motion is quantized. The cooling field consists of a pair of counterpropagating, linearly polarized laser beams, with their polarizaton vectors at an angle \ensuremath{\theta} with respect to each other. The steady-state atomic density matrix is analyzed as a function of \ensuremath{\theta}. It is shown that, depending on the internal atomic level scheme, the equilibrium population of the quantized ground state of atomic center-of-mass motion can either increase or decrease significantly when \ensuremath{\theta} is reduced from \ensuremath{\pi}/2. These effects are interpreted based on the spatial localization of atoms in the light-induced potential wells.
A group-theoretical approach is applied to study the behavior of lossless two-level atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is described quantum mechanically in terms of the SU (2) group parameters. The evolution operator is found in an explicit way after solving a single ODE for one of the group parameters. The translational motion in a standing wave is governed by the classical Hamilton equations which are coupled to the SU (2) group equations. It is shown that the full set of equations may be chaotic in some ranges of the control parameters and initial conditions. It means physically that there are regimes of motion with chaotic center-of-mass motion and irregular internal dynamics. It is established that the chaotic regime is specified by the character of oscillations of the group parameter characterizing the mean interaction energy between the atom and the laser field. It is shown that the effect of chaotic walking can be observed in a real experiment with cold atoms crossing a standing-wave laser field.
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.