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arXiv:1601.05431 · New Journal of Physics

Realizing and optimizing an atomtronic SQUID

Amy C. Mathey, Ludwig Mathey

Published May 27, 2016• 34 citations
arXivHTMLPDF

Abstract

We demonstrate how a toroidal Bose–Einstein condensate with a movable barrier can be used to realize an atomtronic SQUID. The magnitude of the barrier height, which creates the analogue of an SNS junction, is of crucial importance, as well as its ramp-up and -down protocol. For too low of a barrier, the relaxation of the system is dynamically suppressed, due to the small rate of phase slips at the barrier. For a higher barrier, the phase coherence across the barrier is suppressed due to thermal fluctuations, which are included in our Truncated Wigner approach. Furthermore, we show that the ramp-up protocol of the barrier can be improved by ramping up its height first, and its velocity after that. This protocol can be further improved by optimizing the ramp-up and ramp-down time scales, which is of direct practical relevance for on-going experimental realizations.

DOI
10.1088/1367-2630/18/5/055016

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We demonstrate how a toroidal Bose–Einstein condensate with a movable barrier can be used to realize an atomtronic SQUID. The magnitude of the barrier height, which creates the analogue of an SNS junction, is of crucial importance, as well as its ramp-up and -down protocol. For too low of a barrier, the relaxation of the system is dynamically suppressed, due to the small rate of phase slips at the barrier. For a higher barrier, the phase coherence across the barrier is suppressed due to thermal fluctuations, which are included in our Truncated Wigner approach. Furthermore, we show that the ramp-up protocol of the barrier can be improved by ramping up its height first, and its velocity after that. This protocol can be further improved by optimizing the ramp-up and ramp-down time scales, which is of direct practical relevance for on-going experimental realizations.
We investigate the dynamics of an atomtronic superconducting quantum interference device (SQUID) created by two mobile barriers, moving at two different, constant velocities in a quasi-one-dimensional toroidal condensate. We implement a multiband truncated Wigner approximation numerically to demonstrate the functionality of a SQUID reflected in the oscillatory voltage-flux dependence. The relative velocity of the two barriers results in a chemical potential imbalance analogous to a voltage in an electronic system. The average velocity of the two barriers corresponds to a rotation of the condensate, analogous to a magnetic flux. We demonstrate that the voltage equivalent shows characteristic flux-dependent oscillations. We point out the parameter regime of barrier heights and relaxation times for the phase slip dynamics, resulting in a realistic protocol for atomtronic SQUID operation.
We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.
We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.
Atomtronic devices are matter-wave circuits designed to emulate the functional behavior of their electronic counterparts. Motivated by superconducting quantum interference devices (SQUIDs), atomic quantum interference devices (AQUIDs) have been developed using Bose-Einstein condensates (BECs) confined in toroidal geometries. Here, we propose and numerically investigate an alternative implementation of an AQUID based on a BEC confined in a rotating-box potential. A ringlike topology is established by introducing a central depletion region via a repulsive potential barrier. We observe the hallmark AQUID feature—quantized phase winding that increases in discrete steps with angular velocity. Centrifugal effects induced by rotation degrade phase coherence and impair AQUID performance, which we mitigate by applying a counteracting harmonic confinement. Phase slips are found to be mediated by a vortex propagating from the central depletion zone to the edge of the condensate. To characterize the voltage response, we induce a bias current by translating the box along its long axis while keeping the central barrier fixed. This generates a density imbalance between the two reservoirs, exhibiting a periodic dependence on angular velocity—analogous to the voltage-flux relation in electronic SQUIDs. Our results demonstrate that rotating-box geometries provide a viable and flexible platform for realizing AQUIDs with controllable dynamics and well-defined response characteristics.
We propose to design atomtronic circuits with Bose-Einstein condensates (BECs) in circuit-like traps that are controlled via mobile barriers. Using classical-field simulations, we demonstrate a universal set of logical gates and show how to assemble them into circuits. We first demonstrate an gate based on a T-shaped BEC, utilizing a combination of mobile and static barriers. The mobile barriers provide the logical input of the gate, while the static barrier functions as a Josephson junction that generates the output of the gate via a density imbalance across the barrier. Next, we show how to combine three gates into a circuit, with a design composed of two T shapes and an H shape. Furthermore, we demonstrate how to use Josephson oscillations to create a gate and combine it with an gate, thereby showcasing a universal set of gates and their assembly into circuits.
We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID).We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment.The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here.Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.