Alex Loshak

Quantum oscillations between two weakly coupled reservoirs of superfluid 3He

Arguments first proposed over thirty years ago, based on fundamental quantum-mechanical principles, led to the prediction that if macroscopic quantum systems are weakly coupled together, particle currents should oscillate between the two systems. The conditions for these quantum oscillations to occur are that the two systems must both have a well defined quantum phase, φ, and a different average energy per particle, μ: the term ‘weakly coupled’ means that the wavefunctions describing the systems must overlap slightly. The frequency of the resulting oscillations is then given by f = (μ2− μ1)/h, where h is Plancks constant. To date, the only observed example of this phenomenon is the oscillation of electric current between two superconductors coupled by a Josephson tunnelling weak link. Here we report the observation of oscillating mass currents between two reservoirs of superfluid 3He, the weak link being provided by an array of submicrometre apertures in a membrane separating the reservoirs. An applied pressure difference creates mass-current oscillations, which are detected as sound in a nearby microphone. The sound frequency (typically 6,000–200 Hz) is precisely proportional to the applied pressure difference, in accordance with the above equation. Thesesuperfluid quantum oscillations were first detected while monitoring an amplified microphone signal with the human ear.

Discovery of a metastable π-state in a superfluid 3He weak link

Under certain circumstances,, a superconducting Josephson junction can maintain a quantum phase difference of π between the two samples that are weakly connected to form the junction. Such systems are called ‘π-junctions’ and have formed the basis of several experiments designed to investigate the much-debated symmetry of the order parameter of high-temperature superconductors. More recently, the possibility that similar phenomena might occur in another macroscopic quantum system — a pair of weakly coupled Bose–Einstein condensates — has also been suggested. Here we report the discovery of a metastable superfluid state, in which a quantum phase difference of π is maintained across a weak link separating two reservoirs of superfluid 3He. The existence of this state, which is the superfluid analogue ofa superconducting π-junction, is likely to reflect the underlying ‘p-wave’ symmetry of the order parameter of superfluid 3He, but a precise microscopic explanation is at present unknown.

Study of an array of superfluid3He weak links

An array of 1126 identical microapertures is used as the hydrodynamic inductance in a superfluid3He Helmholtz resonator. Each aperture is 0.27 micron square, fabricated by e-beam lithography in a 0.1 micron thick SiN membrane. These dimensions are not too much larger than the superfluid coherence length and therefore, particularly at higher temperatures, an aperture might be though of as a Josephson weak link (in the sense of a Dayem bridge). The superfluid3He critical mass current, Ic, through this array has been measured over a wide range of temperatures. The results indicate that the critical current has a Ginzburg-Landau form of Ic=Ico(1-T/Tc)3/2. This temperature dependence is consistent with phase slippage (not necessarily involving vortices), at the pair breaking velocity, as the critical mechanism.

Reply: Josephson effect and a π-state in superfluid 3 He

Backhaus et al. reply — Avenel et al. have suggested a mechanism that might explain the recently discovered metastable π-state in a superfluid 3He weak-link array. We are pleased that our experiment is leading to new ideas that may extend the understanding of weak-link arrays. We agree with Avenel et al.s comment that, when the individual apertures are in a (short coherence length, low temperature) hysteretic regime, collective phenomena quite distinct from single weak-link behaviour might be observed. Nevertheless, in the temperature regime in which the coherence length is comparable to the aperture dimensions, we have shown that the collective behaviour of the array is similar to that of a single weak link,.

The intrinsic critical velocity nearT λ

We present preliminary measurements of the intrinsic critical velocity for vortex production due to flow through a submicron aperture at temperatures from 1.65K toTλ−T=3×10−3K and fluid drive pressures (Josephson frequencies) from 0.5mPa (fj=35Hz) to 250mPa (fj=17kHz). The critical velocity is probed using a constant pressure drive technique which maintains a constant phase slip nucleation rate for several minutes. The measured critical velocity qualitatively agrees with a model of thermally activated vortex half rings.