Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction

K. Xhani, E. Neri, L. Galantucci, F. Scazza, A. Burchianti, K.-L. Lee, C. F. Barenghi, A. Trombettoni, M. Inguscio, M. Zaccanti, G. Roati, and N. P. Proukakis

Phys. Rev. Lett. 124, 045301 – Published 31 January 2020

Abstract

We study the onset of dissipation in an atomic Josephson junction between Fermi superfluids in the molecular Bose-Einstein condensation limit of strong attraction. Our simulations identify the critical population imbalance and the maximum Josephson current delimiting dissipationless and dissipative transport, in quantitative agreement with recent experiments. We unambiguously link dissipation to vortex ring nucleation and dynamics, demonstrating that quantum phase slips are responsible for the observed resistive current. Our work directly connects microscopic features with macroscopic dissipative transport, providing a comprehensive description of vortex ring dynamics in three-dimensional inhomogeneous constricted superfluids at zero and finite temperatures.

Received 20 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.045301

Physics Subject Headings (PhySH)

Phase slips Quantum transport Vortices in superfluids

Bose-Einstein condensates Josephson junctions Superfluids Ultracold gases

Schroedinger equation

Atomic, Molecular & Optical

Authors & Affiliations

K. Xhani ^1,2, E. Neri ³, L. Galantucci ¹, F. Scazza ^2,4, A. Burchianti ^2,4, K.-L. Lee¹, C. F. Barenghi ¹, A. Trombettoni ⁵, M. Inguscio^2,4,6, M. Zaccanti ^2,3,4, G. Roati ^2,4, and N. P. Proukakis ¹

¹Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
²European Laboratory for Non-Linear Spectroscopy (LENS), Università di Firenze, 50019 Sesto Fiorentino, Italy
³Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
⁴Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy
⁵CNR-IOM DEMOCRITOS Simulation Center and SISSA, Via Bonomea 265, I-34136 Trieste, Italy
⁶Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy

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Vol. 124, Iss. 4 — 31 January 2020

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Images

Figure 1
Phase diagram of a thin Josephson junction: (a) Critical population imbalance $z_{cr}$ as a function of $V_{0} / μ (T)$ , via numerical simulations at $T = 0$ (blue symbols) and $T \approx 0.3 T_{c}$ (red circles), and experimental data (black triangles). Grey shaded area accounts for the experimental range of particle number. Vertical error bars are set by the discreteness of the numerically probed $z_{0}$ values (simulations) and the standard deviations over at least four measurements (experiments); horizontal experimental error bars are set by the combined uncertainties in measuring barrier width, particle number, and laser power. Insets: Comparison of numerical (blue and red lines) and experimental population imbalance evolution in Josephson (left) and dissipative (right) regimes. (b) Maximum superfluid current, ${| I |}_{\max}$ , based on the numerical time derivative of population imbalance (down triangles), and on the numerical and experimental estimate ${| I |}_{\max} ≃ z_{cr} ω_{J} N_{BEC} / 2$ . Green shaded area: Predicted maximum supercurrent (including second-order harmonics in the current-phase relation), accounting for the uncertainty in $V_{0} / μ$ [36].
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Figure 2
Vortex ring generation and early-stage dynamics. (a) Density-weighted $x$ component of superfluid velocity at the barrier (dashed line denotes mean speed of sound $⟨ c ⟩ = \sqrt{μ / 2 M}$ ). (b) Mean radius and (c) position of the first few generated vortex rings (units of $l_{x} = \sqrt{ℏ / M ω_{x}}$ ). (d) Temporal evolution of the incompressible ( $E_{k}^{i}$ ) and compressible ( $E_{k}^{c}$ ) kinetic energy of the BEC. Vertical shaded blue areas denote the maxima of superfluid velocity when VRs are generated, while grey areas indicate the times when the VRs enter the Thomas-Fermi surface. Shown are both $T = 0$ (blue symbols) and $T \approx 0.4 T_{c}$ (red symbols) for $z_{0} = 0.25$ , $V_{0} / μ ≃ 0.8$ and $N_{BEC} ≃ 6 \times 10^{4}$ . (e) BEC density isosurface at 19.5 ms, when the third and fourth VRs are visible.
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Figure 3
Role of initial population imbalance $z_{0}$ (for fixed $V_{0} / μ ≃ 0.8$ for which $z_{c r} ≃ 0.11$ ) on: (a) velocity $v_{VR}$ (left axis, red and black circles) and incompressible kinetic energy $E_{k, VR}^{i}$ (right axis, grey squares) of first nucleated VRs. Pink triangles indicate the VR energy calculated with the analytical formula for homogeneous unbounded BECs [36]; (b) total number $N_{VR}$ of VRs penetrating the bulk (left axis, circles) and vortex induced dissipations $ε_{i}$ and $ε_{c}$ (right axis, green and yellow squares). Blue line connects $N_{VR}$ estimates from the time-averaged phase-slippage rate $Δ μ (t) / h$ [60]. Inset: Lifetimes, $τ$ , of first nucleated VRs. Each subplot shows $T = 0$ (black symbols) and $T \approx 0.4 T_{c}$ (red symbols) results.
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Figure 4
Vortex ring evolution under different conditions: (a) Evolution of the semiaxes and mean radius of the fourth VR ( $z_{0} = 0.25$ , $V_{0} / μ ≃ 0.8$ ), with barrier kept on (blue line) or removed during [13,53] ms (orange line). Shadowed areas mark limiting values of the two semiaxes. Dashed blue and orange lines on top: Transverse TF radius at the instantaneous VR location. (b) Dynamical 2D VR profiles with barrier on (blue) and removed (orange) plotted alongside the corresponding transverse TF surface (dash-dotted lines). Displayed profiles correspond to evolution times marked by vertical solid lines in (a), with the VR surviving only until $t ≃ 23 ms$ with barrier on. (c) Typical evolution of a 2D VR profile in the case of barrier removal at $T \approx 0.4 T_{c}$ . The VR moves off axis, generating a single vortex handle at the boundary.
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