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We describe the operation of a hydromechanical resonator immersed in 4 He and 3 He-Z? 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 He at about 0.8 mK and 0 bar, a nearly ideal, nondissipative hydrodynamic Josephson effect can be observed.PACS 67.50.Fi, 74.50.+r Josephson suggested in 1962 that supercurrents would develop between two superconductors weakly connected via a tunnel junction. At zero applied voltage, a quantum-mechanical phase difference 8 would generate a dc current, given, in the case of ideal superconductive tunneling, by /=y c sin^0,J c being the critical current in the weak link. Also, an electrochemical potential difference across the tunnel junction, 8/u, would lead to the appearance of an ac current the frequency and magnitude of which are governed by Eq. (1) withThese suggestions were quickly confirmed by experiments which showed furthermore that suitable weak links are not limited to pure tunnel junctions but can be made in a large variety of ways-point contacts, microbridges, etc.-with geometrical dimensions which may be comparable in size to, or larger than, the superconductive coherence length £. 2 In these latter cases, the current-phase relation is not purely sinusoidal, not even necessarily single valued, but it does retain a periodicity of 27T in the phase. Such a J-8 relation can be described in a phenomenological way 2,3 with the help of a nonideality parameter a by J w =J c sin£, <$ = £+a sinfFor a^O, the ideal case of Eq. (l) is recovered. For a> 1, the J-8 characteristics are indistinguishable from parallel slanting straight segments. Equation (3) provides an interpolation scheme between these two limits and describes in a convenient, if not necessarily very accurate, way both the hysteretic case (a > 1), where the J-8(f> curve folds back on itself and where dissipation occurs, and the purely dispersive case (a < 1). The discovery of this new class of effects in superconductors led Richards and Anderson, 4 on the basis of the deep-rooted analogy between superconductivity and superfluidity, 5,6 to get started a long-lasting search for the corresponding phenomena in superfluid 4 He and, later, in superfluid 3 He-Z? in which the theoretical picture 7,8 for Josephson-type effects is more satisfactory than in 4 He. Anderson introduced the unifying concept of phase slippage^ to account for the motion of the phase resulting from Eq. (2) both for mere ideal fluid acceleration and when vortices move across the potential flow lines. This concept also applies to the ideal case discussed by Josephson and to phase slips produced by depairing effects. 2 The features common to these different cases, included in (3), are the requirement of phase coherence throughout the superfluid and the periodicity by 2n of the basi...

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Flow measurements in ultrapure 4 He through a micron-size orifice at millikelvin temperatures show, for the first time, the transition from thermal to quantum nucleation of nanometer-size vortices below a crossover temperature of 0.147 K. These observations establish the close relationship between this type of critical flow and negative-ion motion in superfluid 4 He and strongly suggest that the underlying mechanism, the nucleation of vortex half rings, is identical. PACS numbers: 67.40.Hf, 67.40.Vs There is continuing interest in the problem of critical velocities in superfluid 4 He and the nucleation of quantized vortices [1-5]. From a number of independent studies, it has become apparent that the critical velocity iV through apertures less than about one micron in size increases in a near-linear fashion as the temperature is reduced below 1 K, following a relation of the form v c -v c0 (\-T/To) with T 0^2 A5 K. Slightly different temperature dependences have been reported recently [6-8], indicating possible variations with the nature of the substrate and the measuring technique. This temperature variation of v c in a range where the internal variables of the superfluid such as the superfluid density p s or the vortex core radius ao are independent of temperature is a distinctive feature which we have attributed [1,9] to the nucleation of vortices by thermal activation. The rate of such processes is expressed by the Kramers formula: r c , = -exp^ E a (u s ) k B T (la)The problem here, tackled first in the vicinity of the lambda point by Iordanskii and by Langer and Fisher (ILF) [10], is to determine the activation energy E a in terms of the superfluid velocity at the nucleation site u s , and the attempt frequency wjln.As the energies involved are small, the nucleated vortices are of very small size, of the order of a few nm. It can then be expected that, below some crossover temperature T q , thermal nucleation will give way to quantum tunneling, in which case the rate becomes temperature independent and is given by [11] 1/2 r -^o iq 2K 864;r Eg hcoo exp 36 E a 5 hcoo , +^5 |(3)_ In (OQT (lb) (oo being related, within small corrections in the case of low-damping systems (G)OT<&\), to the thermal attempt frequency [11]. The crossover temperature T q between the thermal and the quantum regimes is quite generally related to the attempt frequency G> 0 [1 ll' ksT a =ho)o/2n.The existence of such thermal and quantum nucleation phenomena has been established both theoretically [12] and experimentally [13] for negative ions moving at high speed (~55 m/s) through superfluid 4 He. We report here the first observation of the saturation of the critical velocity v c as T is lowered below 150 mK in ultrapure 4 He at zero pressure. We interpret this effect as evidence for vortex nucleation by quantum tunneling, bringing significant and novel information on this problem, in particular on coo which is otherwise an elusive quantity to determine.These new experimental results were obtained using the same double-hole hydromechani...

We present here an experimental study of Wigner islands formed by electrons floating over helium. Electrons are trapped electrostatically in a mesoscopic structure covered with a helium film, behaving as a quantum dot in the near-classical limit. By removing electrons one by one, we are able to find the addition spectrum, i.e., the energy required to add (or extract) one electron from the trap with occupation number N. Experimental addition spectra are compared with Monte Carlo simulations for the actual trap geometry, confirming the ordered state of electrons over helium in the island