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Europhysics Letters (EPL)

Artificial gauge field induced cyclotron dynamics of ultra-cold atoms in optical lattices

Ai‐Xia Zhang, Ju-Kui Xue

Published Apr 1, 2015• 4 citations
Publisher

Abstract

We theoretically study the cyclotron dynamics of ultra-cold atoms in optical lattices exposed to an artificial magnetic field. The cyclotron orbit and its stability are discussed both analytically and numerically. We find that the cyclotron dynamics of atoms in optical lattices can be manipulated by adjusting the strength of the magnetic field. Atoms can be coherently localized in its initial position, or can be trapped in a priori prescribed orbit doing coherent cyclotron motion, or can be decoherently diffused with time. The stability of the orbit and the coherence of the system present asymmetric characters. Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in the artificial magnetic field.

DOI
10.1209/0295-5075/110/10009

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We theoretically study the cyclotron dynamics of ultra-cold atoms in optical lattices exposed to an artificial magnetic field. The cyclotron orbit and its stability are discussed both analytically and numerically. We find that the cyclotron dynamics of atoms in optical lattices can be manipulated by adjusting the strength of the magnetic field. Atoms can be coherently localized in its initial position, or can be trapped in a priori prescribed orbit doing coherent cyclotron motion, or can be decoherently diffused with time. The stability of the orbit and the coherence of the system present asymmetric characters. Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in the artificial magnetic field.
We analytically and numerically discuss the stability and dynamics of neutral atoms in a two-dimensional optical lattice subjected to an additional harmonic trap potential and artificial magnetic field. The harmonic trap potential plays a key role in modifying the equilibrium state properties of the system and stabilizing the cyclotron orbits of the condensate. Meanwhile, the presence of the harmonic trap potential and lattice potential results in rich cyclotron dynamics of the condensate. The coupling effects of lattice potential, artificial magnetic field, and harmonic trap potential lead to single periodic, multi-periodic or quasi-periodic cyclotron orbits of the condensate. So we can control the cyclotron dynamics of neutral atoms in optical lattice by manipulating the strength of harmonic confinement, artificial magnetic field, and initial conditions. Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in optical lattices exposed to the artificial gauge magnetic field and harmonic trap potential.
We study theoretically quantum dynamics of interacting bosons in artificial magnetic fields as engineered in recent ultracold atomic experiments, where quantum cyclotron orbital motion has been observed. With exact numerical simulations and perturbative analyses, we find that interactions induce damping in the cyclotron motion. The damping time is found to be dependent on interaction and tunneling strengths monotonically, while its dependence on magnetic flux is nonmonotonic. Sufficiently strong interactions would render bosons dynamically localized, inhibiting the cyclotron motion. The damping predicted by us can be construed as an interaction-induced quantum decoherence of the cyclotron motion.
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.
Abstract Topological many-body phases of matter exhibit remarkable electronic properties and ultracold atoms in optical lattices constitute promising candidates to study them in a well-controlled environment. In two-dimensional (2D) electron gases topological phases may emerge in the presence of strong magnetic fields. This situation is not directly applicable to cold atoms because they are charge neutral. Therefore, novel experimental techniques have been developed to engineer novel lattice systems, whose Hamiltonian is formally equivalent to the one of charged particles in magnetic fields. In this Tutorial, we introduce a paradigmatic topological lattice model, the Hofstadter model, and explain how it can be implemented with ultracold atoms using laser-assisted tunneling. The technique is based on imprinting phases on the tunneling matrix elements using additional laser beams. These phases are reminiscent of Aharonov–Bohm phases and can be interpreted as a magnetic flux piercing the lattice unit cell. We present experimental results on the cyclotron-like dynamics of neutral atoms in isolated four-site square plaquettes and discuss the first measurement of a 2D topological invariant, the Chern number, in artificially generated Hofstadter bands. The work presented in this Tutorial was one of the four shortlisted finalists of the 2016 DPG SAMOP dissertation prize.
This paper proposes 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-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be easily realized by the same means which are employed to create the lattice. We also address the problem of detecting this effective magnetic field. In particular, we study the center-of-mass wave packet dynamics, which is shown to exhibit certain features of cyclotron dynamics of a classical charged particle.
We investigate the cyclotron dynamics of Bose-Einstein condensate (BEC) in a quadruple-well potential with synthetic gauge fields. We use laser-assisted tunneling to generate large tunable effective magnetic fields for BEC. The mean position of BEC follows an orbit that simulated the cyclotron orbits of charged particles in a magnetic field. In the absence of atomic interaction, atom dynamics may exhibit periodic or quasi-periodic cyclotron orbits. In the presence of atomic interaction, the system may exhibit self-trapping, which depends on synthetic gauge fields and atomic interaction strength. In particular, the competition between synthetic gauge fields and atomic interaction leads to the generation of several discontinuous parameter windows for the transition to self-trapping, which is obviously different from that without synthetic gauge fields.