Bi-state SuperfluidH3eWeak Links and the Stability of JosephsonπStates

Abstract

We have discovered new features of the current-phase relation, I͑f͒, in superfluid 3 He weak links. Firstly, we find that at any given temperature there are two distinct I͑f͒ functions that characterize the weak link. Secondly, both functions continuously develop an unusual form that ultimately leads to the previously reported p state. The observed form of I͑f͒ has recently been predicted for unconventional quantum fluids such as 3 He, high-T c superconductors, and Bose-Einstein condensates. The two distinct states are likely to originate from the textural degree of freedom in superfluid 3 He. PACS numbers: 67.57. -z, 74.50. + r At temperatures not too far below the superfluid transition ͑T c 0.93 mK͒, the current-phase relation for 3 He aperture-array weak links is given by the dc-Josephson expression, I͑f͒ I c sinf, where I c is referred to as the link's critical current [1,2]. In this regime experiments have revealed several dynamic phenomena which are analogous to known effects in superconducting weak links: Josephson oscillations [3], plasma mode motion [4], homodyne current spikes [5], and Shapiro steps [6].The experiments also revealed a new phenomenon: the existence at lower temperatures of a metastable state, characterized by a p phase difference across the link [7]. The appearance of such a state implies that the system's energy has a local minimum at f min p, a feature not yet observed experimentally for conventional superconductors.Several theories have been advanced to explain the physics that gives rise to such minimum [8][9][10]. To test these theories it is necessary to determine the I͑f͒ function of the weak links with better precision. In order to improve on our earlier measurements we have built an elaborate acoustic shield surrounding our experiment in order to decrease noise caused by acoustical disturbances in the environment. Pressure driven fluctuations have been reduced (relative to our earlier work) by at least 1 order of magnitude, and important properties heretofore hidden, particularly near f p, have now become visible.We use a double diaphragm cell (which is described more completely elsewhere [3]) to study the dynamics of the weak links. This cell consists of a flat cylindrical container bounded on the top and bottom with metallized flexible plastic membranes of known stiffness. The weak link (a square array of 65 3 65 holes, each nominally 100 nm diameter separated by 3 mm, in a 50 nm thick SiN wall [11]) is mounted in the lower membrane. The top membrane's position is monitored with a SQUID-based displacement transducer [12]. This cell is immersed into liquid 3 He-B (at zero ambient pressure) which also fills the inside region.By applying a step voltage between the bottom diaphragm and the adjacent rigid electrode we create an initial pressure head across the weak link which eventually relaxes due to dissipation. A sufficiently large impulse sends the system into the Josephson oscillation regime; i.e., the phase is winding through angles greater than 2p and the average pressure he...

Pinhole calculations of the Josephson effect in3He−B

“…We consider this explanation unlikely because apparently the apertures in Ref. [5] are not hysteretic, and also because it is difficult to understand why exactly half of the apertures could behave differently. The second alternative is that the π state appears trivially in a coherent array if an isotextural π state appears in each of the apertures independently.…”

“…In this paper we study superfluid 3 He, where the Josephson effect was experimentally confirmed over ten years ago by Avenel and Varoquaux [2,3]. However, more recent experiments in Berkeley have raised new questions [4,5] which we are going to address here.…”

“…They are characterized by a single maximum supercurrent J c and a negative derivative at φ = π, J ′ (π) < 0. The experiments at Berkeley used a 65 × 65 array of small apertures in 3 He-B [4,5]. At high temperatures J(φ) was found to be sinusoidal.…”

Theory of Josephson Phenomena in Superfluid 3He

“…The former case resembles the Kulik-Omel'yanchuk result (2): at high temperatures I(φ) is sinusoidal but at lower tem- FIGURE 5. Measured current-phase relationships for a 65 × 65 array of 100 nm diameter apertures in 50 nm thick wall [16].…”

Phase oscillations in superfluid 3 He - B weak links

“…This could dress our dynamic π states from oscillations of the density depression at pores, producing fine structure in the oscillation modes. In fact, bistability between two types of π oscillations has been reported [21].…”