The role of the Josephson-Anderson equation in superfluid helium

Packard, R. E.

doi:10.1103/revmodphys.70.641

Cited by 97 publications

(54 citation statements)

References 38 publications

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“…Smartly designed SQUID devices with several Josephson junctions and a quantized flux serve as sensible detectors of magnetic field and electromagnetic waves, which, in their turn, are utilized in industry, research, and medicine [95][96][97][98]101]. Recently oscillatory effects inherent to superfluid 3 He [102][103][104] and 4 He [103][104][105], which are similar to the Josephson one, were used to construct superfluid helium quantum interference devices (SHeQUIDs) [106].…”

Section: Introductionmentioning

confidence: 99%

dc Josephson Current Between an Isotropic and a d-Wave or Extended s-Wave Partially Gapped Charge Density Wave Superconductor

Gabovich¹,

Li²,

Войтенко³

2012

Superconductors - Materials, Properties and Applications

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Section: Introductionmentioning

confidence: 99%

dc Josephson Current Between an Isotropic and a d-Wave or Extended s-Wave Partially Gapped Charge Density Wave Superconductor

Gabovich¹,

Li²,

Войтенко³

2012

Superconductors - Materials, Properties and Applications

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“…In order to observe quantum effects the objects moving in the liquid have to be smaller than the superfluid healing length. This length, which determines the width of the vortex states as well [12,13], is about 50 nm in superfluid 3 He. Silicon beams with a width of 80 nm have already been fabricated [14].…”

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confidence: 99%

Nanomechanical vibrating wire resonator for phonon spectroscopy in liquid helium

Kraus¹,

Erbe²,

Blick³

2000

Nanotechnology

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We demonstrate how to build a vibrating wire resonator for phonon excitation in liquid helium. The resonator is designed as a nanoscopic mechanically flexible beam machined out of a semiconductor/metal-hybrid. Quenching of the mechanical resonance around 100 MHz by phonon excitation in liquid 4 He at 4.2 K is shown. First measurements operating the nanoresonator in a dilution of 3 He/ 4 He at 30 mK are presented. 62.30.+d, 67.40.Vs, 07.10.Cm Vibrating wire resonators (VWR) are standard bolometers for the quantum fluids 3 He/ 4 He [1]. The general idea is to immerse a metallic wire into superfluid helium and to induce a mechanical vibration by applying a magnetic field while simultaneously sending an alternating current through the wire. Usually these wires are resonating at several kHz with deflections on the order of some microns. The wire moving in the superfluid will generate a phonon flux, which is directed parallel to the plane of motion of the wire. With these macroscopic wires excitations in 4 He are usually not found, since the Landau critical velocity is not in the accessible range.Here we present a new approach to build such phonon radiators for applications in spectroscopy of quantum liquids. In contrast to previous resonators operating in the kHz-range only, we focus on the realization of wires or more specifically on suspended hybrid Si/metal-beams with nanometer dimensions and hence resonance frequencies up to 1 GHz [2,3]. We will first discuss processing of the nanostructures and then proceed to the experimental setup. Moreover, we show measurements allowing us to calibrate the attenuation of the nano-VWR in liquid 4 He. Finally, we show first results on resonating nano-VWRs in 3 He/ 4 He at 30 mK.The beams are machined from commercially available Silicon-on-Insulator (SOI) wafers with a top layer thickness of 205 nm and a sacrificial layer of 400 nm. Optical lithography and evaporation of 180 nm NiCr-Au/Ti are used to define the necessary bond pads and an etch mask (Ti), which is then removed in the wet etch step. An electron beam writer (JEOL 6400) is used to define the nanomechanical resonator, consisting finally of the metallic line on top (Au) and the Si supporting membrane. In the following step the sample is etched in a reactive ion etcher (RIE) using CF 4 as an etchant. The section of the sample, which is not covered by metal, is milled down by 200 nm. Finally the sacrificial layer is removed using diluted (2%) hydro-fluoric acid (HF) at an etch-rate of 10 nm/sec.In the right inset of Fig. 1 the suspended beam is shown in a scanning electron beam micrograph: The beam is freely suspended between two tuning gates, coupling capacitively. The beam has a length of 1 µm, a width of 200 nm, and the gates are covered by a 50 nm Au layer. The gates can be applied to tune the mechanical 1

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“…The knowledge of the phase drop γ across the barrier, combined with the knowledge of the (spatially-constant) current j flowing across the weak-link, allows to construct the current-phase relation of the system. This is a powerful characterization of the weak link, allowing for instance to distinguish different regimes ranging from deep tunneling to hydrodynamic flow [24][25][26]. In the context of BECs, the current phase-relation has been computed so far for infinite systems with open boundary conditions, a static weak link, and a given injected flow [23,38].…”

mentioning

confidence: 99%

“…As order parameter of the phase, both the continuous and discontinuous phase transitions we choose the difference between the phase accumulated around the ring ν and phase drop across the barrier, a quantity which is experimental accessible [22]. The phase drop across the barrier, together with the current flowing through the ring, also provides the currentphase relation [22,23] -an optimal characterization of the ring-superfluid junction [24][25][26][27][28].…”

mentioning

confidence: 99%

Parity-symmetry breaking and topological phases in a superfluid ring

Zhang

Piazza

et al. 2016

Phys. Rev. A

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We study analytically the superfluid flow of a Bose-Einstein condensate in a ring geometry in presence of a rotating barrier. We show that a phase transition breaking a parity symmetry among two topological phases occurs at a critical value of the height of the barrier. Furthermore, a discontinuous (accompanied by hysteresis) phase transition is observed in the ordered phase when changing the angular velocity of the barrier. At the critical point where the hysteresis area vanishes, chemical potential of the ground state develops a cusp (a discontinuity in the first derivative). Along this path, the jump between the two corresponding states having a different winding number shows strict analogies with a topological phase transition. We finally study the current-phase relation of the system and compare some of our calculations with published experimental results. In the limit of a vanishing barrier, the state with topological defects adiabatically connect two rotation-invariant states with different winding number . A second-order phase transition takes place two times as a function of Ω [19], first as the system enters the state with topological defects from the first rotational-invariant state 1 and then as it leaves the former by entering the second rotational-invariant state 2 . This scenario changes in presence of any finite-size obstacle that breaks the rotational symmetry of the ring, wherein the topological defects are always dynamically unstable [20], so that, in general, two topologically different states cannot be adiabatically connected. This has been recently confirmed experimentally with a barrier moving inside a toroidal BEC [21], where hysteresis appears in the transition between states with different topological winding number. The unstable branch of the hysteresis loop corresponds to the state with topological defects, and the angular velocity at which the metastable state decays (through phase slippage [7]) into the ground state generalizes the Landau critical velocity to the weak-link case [16,20].In this manuscript, we show that with a barrier rotating at the angular velocity Ω c = /2mR 2 , with R and m the radius of the ring and the atomic mass, respectively, the ground state of the system becomes degenerate when the height of the barrier is smaller than a critical value V < V c . The degeneration arises from a parity symmetry breaking that provides two

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The role of the Josephson-Anderson equation in superfluid helium

Cited by 97 publications

References 38 publications

dc Josephson Current Between an Isotropic and a d-Wave or Extended s-Wave Partially Gapped Charge Density Wave Superconductor

dc Josephson Current Between an Isotropic and a d-Wave or Extended s-Wave Partially Gapped Charge Density Wave Superconductor

Nanomechanical vibrating wire resonator for phonon spectroscopy in liquid helium

Parity-symmetry breaking and topological phases in a superfluid ring

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