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arXiv:1510.04438 · New Journal of Physics

Chaos and two-level dynamics of the atomtronic quantum interference device

Geva Arwas, Doron Cohen

Published Jan 11, 2016• 16 citations
arXivHTMLPDF

Abstract

We study the atomtronic quantum interference device employing a semiclassical perspective. We consider an M site ring that is described by the Bose–Hubbard Hamiltonian. Coherent Rabi oscillations in the flow of the current are feasible, with an enhanced frequency due to chaos-assisted tunneling. We highlight the consequences of introducing a weak-link into the circuit. In the latter context we clarify the phase–space considerations that are involved in setting up an effective 'systems plus bath' description in terms of Josephson–Caldeira–Leggett Hamiltonian.

DOI
10.1088/1367-2630/18/1/015007

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We study the atomtronic quantum interference device employing a semiclassical perspective. We consider an M site ring that is described by the Bose–Hubbard Hamiltonian. Coherent Rabi oscillations in the flow of the current are feasible, with an enhanced frequency due to chaos-assisted tunneling. We highlight the consequences of introducing a weak-link into the circuit. In the latter context we clarify the phase–space considerations that are involved in setting up an effective 'systems plus bath' description in terms of Josephson–Caldeira–Leggett Hamiltonian.
We consider a correlated Bose gas tightly confined into a ring shaped lattice, in the presence of an artificial gauge potential inducing a persistent current through it. A weak link painted on the ring acts as a source of coherent back-scattering for the propagating gas, interfering with the forward scattered current. This system defines an atomic counterpart of the rf-SQUID: the atomtronics quantum interference device. The goal of the present study is to corroborate the emergence of an effective two-level system in such a setup and to assess its quality, in terms of its inner resolution and its separation from the rest of the many-body spectrum, across the different physical regimes. In order to achieve this aim, we examine the dependence of the qubit energy gap on the bosonic density, the interaction strength, and the barrier depth, and we show how the superposition between current states appears in the momentum distribution (time-of-flight) images. A mesoscopic ring lattice with intermediate-to-strong interactions and weak barrier depth is found to be a favorable candidate for setting up, manipulating and probing a qubit in the next generation of atomic experiments.
A generalized Bose-Hubbard model in a two-mode approximation is applied to study the rotational dynamics of a direct-current atomtronic quantum interference device. Modified values of on-site interaction and pair-tunneling parameters of the Hamiltonian, derived from the small-oscillation periods of the Josephson modes, are shown to provide an excellent agreement to the Gross-Pitaevskii simulation results for the whole rotational frequency range, reaching also the critical values of imbalance and current. This amounts to a full validation of the semiclassical approximation of the modified Hamiltonian, whose quantization is employed to investigate the quantum features of the stationary states. Focusing on the frequency interval where the potential energy presents two minima, it is shown that the central frequency, at which such minima are symmetric, yields an atom number parity-protected qubit with a maximum entanglement of both persistent-current states, similar to those of superconducting circuits threaded by a half quantum of applied flux. Such a parity protection scheme survives within a small interval around the central frequency, which sets the minimum rotational frequency precision that should be required to implement the qubit. It is found that such a maximum admissible error in the frequency determination turns out to be inversely proportional to the qubit quality factor that measures the gap between the qubit energy levels and the following levels. It is shown that the chemical potential or condensate particle number could be employed as suitable control parameters to achieve the best trade-off between such qubit characteristics.
Abstract We study a quantum many-body system of attracting bosons confined in a ring-shaped potential and interrupted by a weak link. With such architecture, the system defines atomtronic quantum interference devices harnessing quantum solitonic currents. We demonstrate that the system is characterized by the specific interplay between the interaction and the strength of the weak link. In particular, we find that, depending on the operating conditions, the current can be a universal function of the relative size between the strength of the impurity and interaction. The low lying many-body states are studied through a quench dynamical protocol that is the atomtronic counterpart of Rabi interferometry. With this approach, we demonstrate how our system defines a two level system of coupled solitonic currents. The current states are addressed through the analysis of the momentum distribution.
The hallmark of superfluidity is the appearance of metastable flow-states that carry a persistent circulating current. Considering Bose-Hubbard superfluid rings, we clarify the role of “quantum chaos” in this context. We show that the standard Landau and Bogoliubov superfluidity criteria fail for such low-dimensional circuits. We also discuss the feasibility for a coherent operation of a SQUID-like setup. Finally, we address the manifestation of the strong many-body dynamical localization effect.
We study a physical system consisting of a Bose–Einstein condensate confined to a ring shaped lattice potential interrupted by three weak links. The system is assumed to be driven by an effective flux piercing the ring lattice. By employing path integral techniques, we explore the effective quantum dynamics of the system in a pure quantum phase dynamics regime. Moreover, the effects of the density's quantum fluctuations are studied through exact diagonalization analysis of the spectroscopy of the Bose–Hubbard model. We demonstrate that a clear two-level system emerges by tuning the magnetic flux at degeneracy. The lattice confinement, platform for the condensate, is realized experimentally employing a spatial light modulator.
A semiclassical theory is provided for the metastability regime diagram of atomtronic superfluid circuits. Such circuits typically exhibit high-dimensional chaos, and nonlinear resonances that couple the Bogoliubov excitations manifest. Contrary to the expectation, these resonances do not originate from the familiar Beliaev and Landau damping terms. Rather, they are described by a variant of the Cherry Hamiltonian of celestial mechanics. Consequently, we study the induced decay process and its dependence on the number of sites and condensed particles.