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Physical Review Letters

Josephson-like Phase-Coherence Oscillations in Superfluid Halium

Bernard Perrin, Dominique d’Humières, C. Laroche, J-P. Hulin, Albert J. Libchaber

Published Jun 12, 1972• 7 citations
Publisher

Abstract

We report a study of the oscillations of two superfluid helium baths coupled through a small hole. At low temperature they are associated with gravitational potential energy and kinetic energy through the hole. At high temperature, an entropy term must be added and the oscillations are dispersive. From an amplitude study we show that two critical velocities appear, depending on the presence or absence of a superleak. This experiment is an analog of Josephson plasma oscillations in that the phase of the wave function oscillates with time.

DOI
10.1103/physrevlett.28.1551

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We report a study of the oscillations of two superfluid helium baths coupled through a small hole. At low temperature they are associated with gravitational potential energy and kinetic energy through the hole. At high temperature, an entropy term must be added and the oscillations are dispersive. From an amplitude study we show that two critical velocities appear, depending on the presence or absence of a superleak. This experiment is an analog of Josephson plasma oscillations in that the phase of the wave function oscillates with time.
When a chemical potential difference exists between the superfluid helium on two sides of an orifice, superfluid flow takes place at a critical velocity accompanied by the creation of quantized vortices. The frequency with which vortices are created is expected to be equal to the chemical potential difference (the analog of the ac Josephson frequency in superconducting tunneling). An experiment is described in which this frequency condition is verified by a method analogous to that used in superconductors. Experimental conditions were selected such that the gravitational head difference mgZ\mathrm{mgZ}mgZ was the dominant contribution to the chemical potential difference. ZZZ was measured by a capacitance technique. An ultrasonic transducer was used to modulate the flow through the orifice at the frequency $\ensuremath{\omega}$ so that the rate of creation of vortices was synchronized with the modulation frequency. The system was observed to exhibit dynamic stability at values of head difference $Z=\frac{n\ensuremath{\hbar}\ensuremath{\omega}}{{n}^{\ensuremath{'}}\mathrm{mg}}$ corresponding to nnn quantized vortices created every ${n}^{\ensuremath{'}}$ cycles of the modulation. The correspondence between theory and experiment is most convincing under experimental conditions such that the strength of the stability decreases rapidly with increasing values of the integer ${n}^{\ensuremath{'}}$. This was found to occur with small orifices and with moderate modulation amplitude, in agreement with the results of the analogous experiments in superconductors.
Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.
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.
Superconductivity and superfluidity of fermionic and bosonic systems are remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging. Here we report on the observation of such a mixture with dilute gases of two lithium isotopes, lithium-6 and lithium-7. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping below a certain critical velocity. Using high-precision spectroscopy of these modes, we observe coherent energy exchange and measure the coupling between the two superfluids. Our observations can be captured theoretically using a sum-rule approach that we interpret in terms of two coupled oscillators.
We analyze theoretically the transport properties of a weakly interacting ultracold Bose gas enclosed in two reservoirs connected by a constriction. We assume that the transport of the superfluid part is hydrodynamic, and we describe the ballistic transport of the normal part using the Landauer-Büttiker formalism. Modeling the coupled evolution of the phase, atom number, and temperature mismatches between the reservoirs, we predict that Helmholtz (plasma) oscillations can be observed at nonzero temperatures below Tc. We show that, because of its strong compressibility, the Bose gas is characterized by a fast thermalization compared to the damping time for plasma oscillations, accompanied by a fast transfer of the normal component. This fast thermalization also affects the gas above Tc, where we present a comparison to the ideal fermionic case. Moreover, we outline the possible realization of a superleak through the inclusion of a disordered potential.