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arXiv:1312.7315 · Physical Review Letters

One-Dimensional Transport of Bosons between Weakly Linked Reservoirs

D. P. Simpson, Dimitri M. Gangardt, Igor V. Lerner, P. Krüger

Published Mar 12, 2014• 19 citations
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Abstract

We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference $2\mathrm{\ensuremath{\Phi}}$ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form $\ensuremath{\sim}\mathrm{sin}2\mathrm{\ensuremath{\Phi}}$. Instead, the superflow discontinuously flips direction at $2\mathrm{\ensuremath{\Phi}}=\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\pi}}$ and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena.

DOI
10.1103/physrevlett.112.100601

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We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference 2\ensuremathΦ2\mathrm{\ensuremath{\Phi}}2\ensuremathΦ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form \ensuremath∼sin2\ensuremathΦ\ensuremath{\sim}\mathrm{sin}2\mathrm{\ensuremath{\Phi}}\ensuremath∼sin2\ensuremathΦ. Instead, the superflow discontinuously flips direction at 2\ensuremathΦ=\ifmmode±\else\textpm\fi\ensuremathπ2\mathrm{\ensuremath{\Phi}}=\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\pi}}2\ensuremathΦ=\ifmmode±\else\textpm\fi\ensuremathπ and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena.
This thesis concerns the transport of ultracold bosons in a one-dimensional geometry. I consider two three-dimensional reservoirs of Bose-Einstein condensed atoms that are connected via weak tunnel junctions to each end of a one-dimensional channel. The particle current along the channel is driven only by a constant phase difference between the two reservoirs. I theoretically investigate the bosonic flow and develop a non-perturbative mean field description, showing the existence of metastable solutions for all values of tunnelling. I show there are two separate branches of the mean field solution and the lowest energy solution necessarily jumps discontinuously between these branches. I then demonstrate that such a mean field solution is robust against fluctuations for values of the Luttinger parameter pertinent to bosonic atoms and that fluctuations do not connect different branches of the mean field solution. I provide a possible experimental realisation utilising the versatility of atom chips and describe how one can experimentally observe both the phase profile in the channel and the particle flow along the channel. Finally, I explore the non-equilibrium dynamics following a quench in the tunnelling energy and demonstrate that such a quench can lead to switching between different branches of the mean field solution.
We have experimentally measured transport of superfluid, bosonic atoms in a mesoscopic system: a small channel connecting two large reservoirs. Starting far from equilibrium (superfluid in a single reservoir), we observe first resistive flow transitioning at a critical current into superflow, characterized by oscillations. We reproduce this full evolution with a simple electronic circuit model. We compare our fitted conductance to two different microscopic phenomenological models. We also show that the oscillations are consistent with LC oscillations as estimated by the kinetic inductance and effective capacitance in our system. Our experiment provides an attractive platform to begin to probe the mesoscopic transport properties of a dilute, superfluid, Bose gas.
We present an analytical derivation for the quantum decay rate of the superflow through a weak link in a one-dimensional Bose-Einstein-condensate. The effective action for the phase difference across the link reduces to that of a massive particle with damping subject to a periodic potential. We find an algebraic flow-pressure relation, characteristic for quantum nucleation of phase slips in the link and show how short-wave length fluctuations renormalizing the interaction between the Bosons remove the quantum phase transition expected in this class of systems.
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\ensuremath{\pi} (\ensuremath{\pi}$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^{3}\mathrm{He}\ensuremath{-}B$ and the internal Josephson effect in ${}^{3}\mathrm{He}\ensuremath{-}A$ are also discussed.
Coherent oscillations between two weakly coupled Bose-Einstein Condensates: Josephson effects, πππ-oscillations, and macroscopic quantum self trapping
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The Boson Josephson Junction (BJJ) dynamics is described by the two-mode non-linear Gross-Pitaevskii equation, that is solved analytically in terms of elliptic functions. The BJJ, being a neutralneutralneutral, isolated system, allows the investigations of new dynamical regimes for the phase difference across the junction and for the population imbalance, that are not accessible with Superconductor Josephson Junctions (SJJ). These include oscillations with either, or both of the following properties: 1) the time-averaged value of the phase is equal to πππ (π−phaseπ-phaseπ−phase oscillations); 2) the average population imbalance is nonzero, in states with ``macroscopic quantum self-trapping'' (MQST). The (non-sinusoidal) generalization of the SJJ `ac' and `plasma' oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and total number of condensate atoms) onto a single universal curve, for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3^33He-B and the internal Josephson effect in 3^33He-A are also discussed.
We present an experimental study on the nonequilibrium tunnel dynamics of two coupled one-dimensional Bose-Einstein quasicondensates deep in the Josephson regime. Josephson oscillations are initiated by splitting a single one-dimensional condensate and imprinting a relative phase between the superfluids. Regardless of the initial state and experimental parameters, the dynamics of the relative phase and atom number imbalance shows a relaxation to a phase-locked steady state. The latter is characterized by a high phase coherence and reduced fluctuations with respect to the initial state. We propose an empirical model based on the analogy with the anharmonic oscillator to describe the effect of various experimental parameters. A microscopic theory compatible with our observations is still missing.