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arXiv:1805.00696 · Low Temperature Physics

Analogues of Josephson junctions and black hole event horizons in atomic Bose-Einstein condensates

A. I. Yakimenko, Oles Matsyshyn, Artem Oliinyk, Volodymyr Biloshytskyi, Oksana Chelpanova, S. I. Vilchinskiĭ

Published Oct 1, 2018• 1 citation
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Abstract

We study dynamical processes in coherently coupled atomic Bose-Einstein condensates. Josephson effects in ring-shaped and dumbbell geometries are theoretically investigated. Conditions for observation of the Josephson effect are revealed. We found that multicharged persistent current in toroidal condensate can be robust even for supersonic atomic flow. In numerical simulations the acoustic analogues of event horizon in quantized superflow were observed. These theoretical finding open perspectives for investigation of Bose Josephson junctions and quantum aspects of acoustic analogue of Hawking radiation in existing experimental setups.

DOI
10.1063/1.5055844

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We study dynamical processes in coherently coupled atomic Bose-Einstein condensates. Josephson effects in ring-shaped and dumbbell geometries are theoretically investigated. Conditions for observation of the Josephson effect are revealed. We found that multicharged persistent current in toroidal condensate can be robust even for supersonic atomic flow. In numerical simulations the acoustic analogues of event horizon in quantized superflow were observed. These theoretical finding open perspectives for investigation of Bose Josephson junctions and quantum aspects of acoustic analogue of Hawking radiation in existing experimental setups.
Abstract Considerable progress in experimental studies of atomic gases in a toroidal geometry opens up novel prospects for the investigation of fundamental properties of superfluid states and creation of new configurations for atomtronic circuits. In particular, a setting with Bose–Einstein condensates loaded in a dual-ring trap suggests a possibility to consider the dynamics of tunneling between condensates with different angular momenta. Accordingly, we address the tunneling in a pair of coaxial three-dimensional (3D) ring-shaped condensates separated by a horizontal potential barrier. A truncated (finite-mode) Galerkin model and direct simulations of the underlying 3D Gross–Pitaevskii equation are used for the analysis of tunneling superflows driven by an initial imbalance in atomic populations of the rings. The superflows through the corresponding Bose–Josephson junction are strongly affected by persistent currents in the parallel rings. Josephson oscillations of the population imbalance and angular momenta in the rings are obtained for co-rotating states and non-rotating ones. On the other hand, the azimuthal structure of the tunneling flow demonstrates formation of Josephson vortices (fluxons) with zero net current through the junction for hybrid states , built of counter-rotating persistent currents in the coupled rings.
We theoretically propose a finite-size quasi-one-dimensional Bose-Einstein condensate with coherent source and drain placed at its two ends, which can in principle sustain a stationary sonic black hole with a single event horizon. Our analysis is focused on the condensate persistence against quantum fluctuations. We show that similar to black hole-white hole pairs, dynamical instabilities occur. Investigating in detail the instabilities' dependence on the system parameters, we also identify windows of formally infinite black hole lifetimes. By using quantum depletion of the condensate as a diagnostic tool, we validate the usage of Bogoliubov theory to describe the analog Hawking process, and establish novel signatures of Hawking radiation in the depleted cloud, both inside and outside the event horizon.
Coupled coaxially stacked toroidal condensates with persistent currents suggest an appealing physical platform for investigation of various phenomena related to interacting superflows from Josephson effects in the regime of weak interactions to the quantum Kelvin-Helmholtz instability for merging rings. We suggest experimentally accessible methods to prepare states with different topological charges in two coupled coaxial ring-shaped atomic Bose-Einstein condensates. Our results open up the way to direct observation of rotational Josephson vortices in atomic Bose-Einstein condensates.
Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the "surface gravity") is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose–Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a view to finding which experimental settings could magnify this effect and provide an observable signal. We discuss constraints and problems for our model and identify the issues that should be addressed in the near future in order to set up an experiment. In particular we identify an experimentally plausible configuration with a Hawking temperature of order 70 n K; to be contrasted with a condensation temperature of the order of 90 n K.