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Physical Review Letters

Josephson effect and quantum phase slippage in superfluids

Olivier Avenel, Eric Varoquaux

Published Feb 1, 1988• 133 citations
Publisher

Abstract

We describe the operation of a hydromechanical resonator immersed in $^{4}\mathrm{He}$ and $^{3}\mathit{B}$ superfluids and opened on the main bath by two holes, a micro-orifice acting as a weak link and a long parallel channel. Transitions between adjacent quantum states differing by one hydrodynamic circulation quantum can be induced coherently, yielding a succession of steps arranged in a staircase pattern. In $^{3}\mathrm{He}$ at about 0.8 mK and 0 bar, a nearly ideal, nondissipative hydrodynamic Josephson effect can be observed.

DOI
10.1103/physrevlett.60.416

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We describe the operation of a hydromechanical resonator immersed in 4He^{4}\mathrm{He}4He and 3B^{3}\mathit{B}3B superfluids and opened on the main bath by two holes, a micro-orifice acting as a weak link and a long parallel channel. Transitions between adjacent quantum states differing by one hydrodynamic circulation quantum can be induced coherently, yielding a succession of steps arranged in a staircase pattern. In 3He^{3}\mathrm{He}3He at about 0.8 mK and 0 bar, a nearly ideal, nondissipative hydrodynamic Josephson effect can be observed.
Two chambers filled with superfluid helium to different levels were connected by a small orifice (10-15 \ensuremath{\mu}m). The flow of the liquid through the orifice was modulated by a sound field. With one experimental apparatus only a continuous flow was observed. With a modified apparatus it was possible to obtain stable states with no net flow at finite level differences between the baths. The spacing between these states is inversely proportional to the sound frequency. It depends on the total height of the liquid in one of the baths and not on the level difference between them. We conclude that the stable states of zero flow result from ultrasonic standing waves of the superfluid in one of the chambers. A phase coupling or Josephson effect can be excluded as an explanation for these states.
We study the relation between Josephson dynamics and topological excitations in a dilute Bose-Einstein condensate confined in a double-well trap. We show that the phase slips responsible for the self-trapping regime are created by vortex rings entering and annihilating inside the weak-link region or created at the center of the barrier and expanding outside the system. Large amplitude oscillations just before the onset of self-trapping are also strictly connected with the dynamics of vortex rings at the edges of the inter-well barrier. Our results extend and analyze the dynamics of the vortex-induced phase slippages suggested a few decades ago in relation to the "ac" Josephson effect of superconducting and superfluid helium systems.
Striking observations of quantised events in superfluid flow through a microscopic orifice have been made recently at Orsay, France. Sudden, stepwise reductions of the flow velocity at the critical velocity threshold, seen both in superfluid 3 He and 4 He, are interpreted as slips by 2π of the phase of the quantum mechanical wavefunction that describes the condensate of the superfluid. Moreover, in superfluid 3 He slightly below the superfluid transition, at low pressure and at a temperature of 0.9 mK, the mass flow through the orifice becomes fully dominated by quantum mechanics.
In quantum gases, weak links are typically realized with externally imposed optical potentials. We show that, in rotating binary condensates, quantized vortices in one component form hollow channels that act as self-induced weak links for the other, enabling superflow through otherwise impenetrable, phase-separated domains. This introduces a novel barrier mechanism: quantum pressure creates an effective barrier inside the vortex channel, set by the constriction width, which controls the superflow. Tuning the interspecies interaction strength drives a crossover from the hydrodynamic transport to Josephson tunneling regime. Long-range dipolar interactions further tune the weak-link properties, enabling both short links and two coupled junctions in series. Circuit models quantitatively capture the dc current-phase relations for both configurations. These results establish vortices as reconfigurable, interaction-controlled Josephson elements in superfluids.
We characterize numerically the dominant dynamical regimes in a superfluid ultracold fermionic Josephson junction. Beyond the coherent Josephson plasma regime, we discuss the onset and physical mechanism of dissipation due to the superflow exceeding a characteristic speed, and provide clear evidence distinguishing its physical mechanism across the weakly and strongly interacting limits, despite qualitative dynamics of global characteristics being only weakly sensitive to the operating dissipative mechanism. Specifically, dissipation in the strongly interacting regime occurs through the phase-slippage process, caused by the emission and propagation of quantum vortices, and sound waves-similar to the Bose-Einstein condensation limit. Instead, in the weak interaction limit, the main dissipative channel arises through the pair-breaking mechanism.