Cyclotron dynamics of cold atoms in 2D optical lattices

Abstract

We propose a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assistent tunneling and involves a low-frequency periodic driving of the optical lattice. We also address the problem of detecting this effective magnetic field. In particular, we discuss interference patterns of the atomic wave function and study the center of mass wave-packet dynamics, which shows some features of cyclotron dynamics of a classical charged particle. Introduction. – A major motivation of current research with cold atoms in optical lattices is the prospect of simulating the solid state physics. However, to have a full access to phenomena of the solid state physics this system (which can be considered as an artificial crystal) should be accomplished by artificial electric and magnetic fields. In present days experiments the former case of external electric field is routinely mimicked by accelerating the optical lattice [1–3], or by using the gravitational force [4–6] or a combination of gravitational and levitational forces [7]. The case of magnetic field is more difficult for laboratory realization because it requires a setup, where atomic wave function acquires a finite phase when the atom tunnels along a closed path on the lattice. This setup was suggested in the seminal paper [8], where the authors use two independent 2D optical lattices for two different internal atomic states, which are coupled by additional Raman lasers. The Rabi transition between internal states induces hopping of the atom between nearest lattice sites, where the required phase accumulation is achieved by using a special geometry for the Raman beams. This idea was developed further in Ref. [9, 10]. It was shown that one can also introduce an exotic (unphysical) field and non-Abelian gauge potentials by using the Raman-laser technique. For atoms in a harmonic trap (no lattice) the Raman scheme with 3 spin states of the F = 1 electronic ground state of Rb atom was realized in the recent experiment [11]. In this setup the magnitude of the effective magnetic field is defined by the gradient of the real magnetic field which splits the F = 1 level into Zeeman sublevels. In the paper the authors put forward a conjecture that this scheme should work in the presence of an optical lattice as well. We note that the cited experiment also illuminated a drawback of the Raman-laser based techniques. Namely, the spontaneous emission from the Raman beams removes atom from the trap, causing the population to decay within approx. 2 seconds.