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arXiv:1312.5747 · Physical Review B

Cyclotron dynamics of interacting bosons in artificial magnetic fields

Xiaopeng Li, S. Das Sarma

Published Jun 23, 2014• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.89.224302

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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 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.
The strong effective magnetic fields with flux to the order of one flux quantum per plaquette has been realized for ultracold atoms, and the quantum cyclotron orbit of a single atom in a single plaquette exposed to the magnetic field was directly revealed recently [ Phys. Rev. Lett. 107 (2011) 255301 ]. We study the quantum cyclotron orbits of a bosonic atom in a triple well with a synthetic gauge field, and find that the dynamics of the atom in real space is similar to a classical dynamic billiard. It is interesting that the billiard-like motion is a signature of the quantum evolution of the three-level system, and its behaviors are determined by the ratio of the two energy gaps of the three energy levels.
The Hall effect, which originates from the motion of charged particles in magnetic fields, has deep consequences for the description of materials, extending far beyond condensed matter. Understanding such an effect in interacting systems represents a fundamental challenge, even for small magnetic fields. In this work, we used an atomic quantum simulator in which we tracked the motion of ultracold fermions in two-leg ribbons threaded by artificial magnetic fields. Through controllable quench dynamics, we measured the Hall response for a range of synthetic tunneling and atomic interaction strengths. We unveil a universal interaction-independent behavior above an interaction threshold, in agreement with theoretical analyses. The ability to reach hard-to-compute regimes demonstrates the power of quantum simulation to describe strongly correlated topological states of matter.
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We study ultracold atom–ion collisions in the presence of an external magnetic field. At low collision energy the field can drastically modify the translational motion of the ion, which follows quantized cyclotron orbits. We present a rigorous theoretical approach for the calculation of quantum scattering amplitudes in these conditions. Collisions in different magnetic field regimes, identified by the size of the cyclotron radius with respect to the range of the interaction potential, are investigated. Our results are important in cases where use of a magnetic field to control the atom–ion collision dynamics is envisioned.
In this work we study the model of flux lattice, specifically a two-leg Bose–Hubbard ladder lattice subject to effective magnetic flux, which can be implemented using spin–orbit coupled cold atoms trapped in an optical lattice. This model has attracted much recent research interest due to that it provides a platform to study the interplay between artificial gauge fields and interactions. We consider that collective dipole oscillations are activated in this model via quenching an external harmonic trapping potential and show that this system can exhibit unique dynamical behaviors in terms that oscillation amplitude and period critically dependent on the spin–orbit coupling. A dynamical slowing down in collective dipole oscillations will take place near the transition point between the Meissner superfuild and vortex superfluid phases, which agrees quantitatively with a variational analysis. We show that such a quantum phase transition can also be probed via the damping of the collective dipole oscillation. When the quenching displacement is large, the collective center-of-mass motion behaves as damped oscillation and the damping reaches its maximum near the phase transition point. The specific dynamical phenomena are explained with eigenspectra and level populations after the quenching. In the presence of interactions, the time-dependent density–matrix renormalization group (tDMRG) method is hired to study the collective dynamics. The case with weak interactions is similar to that without interactions, except that interactions tend to enhance damping. In addition to that, Bragg reflection can be observed when the quenching displacement exceeds a critical value. The case with strong interactions is also studied, in which case the phase transition points will be dramatically changed and the system can even move into the Mott insulator phase, which will greatly affect the corresponding collective dynamics. The phenomena predicted in this work can be readily observed in current available experiments on atom flux lattices.