Abstract
We show that the orbital Josephson effect appears in a wide range of driven atomic Bose–Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: the Gross–Pitaevskii equation, exact diagonalization of the few-mode problem and the multi-configurational time-dependent Hartree for bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that the few-mode approximation represents the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the (t,t′)-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.
Highlights
We show that the orbital Josephson effect appears in a wide range of driven atomic Bose–Einstein condensed systems, including quantum ratchets, double wells and box potentials
Previous work on the orbital Josephson effect (OJE) [17] has focused on the quantum ratchet on a ring potential because the OJE was originally identified in that context
Starting with two very simple illustrative examples, a double well [5] and a box potential [19], we show that the OJE is a general concept that can be studied in a variety of existing experimental BEC systems
Summary
We present a recipe for the realization of an orbital Josephson junction. Our goal is to develop an effectively time-independent description that involves only two single-particle states We do this by using an extended version of the (t, t )-formalism to describe the dynamics of the field operators ψ (r, t) in second quantization [17]. We assume the static single-particle part H0(r) to be the predominant term in the equation of motion (2) This condition is met for systems with weak particle interactions λ, and a weak overall amplitude of the driving potential V (r, t). This assumption implies that the low-energy eigenstates of the undriven (t < 0) system are condensates, with a negligible amount of depletion [37] and with the condensate orbitals given by eigenstates of H0(r). Suggesting one ought to use a transformed representation of equation (3) that involves creation and annihilation operators with respect to the unperturbed Floquet states (eigenmodes of H0)
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