The reverse AC-Josephson effect in 3He-B

No Heading We have investigated ³He Josephson currents under an externally applied ac-pressure modulation. The ³He-flow was driven by the motion of a flexible membrane through an array of 65 by 65 holes of 150 nm size in a 50 nm thick SiN wall. The membrane was deflected electrostatically. If a sinusoidal modulated electrostatic force was applied to the membrane, we could observe phase locking of the Josephson oscillations to the external ac-drive. As a result, a zero net flow through the weak link was observed while the membrane was stuck for many seconds at a non zero pressure position. For this pressure the Josephson frequency matched the ac-drive frequency. We could resolve the dynamics which led to this trapped, phase locked state. The dynamics looked quite similar to dynamics which took place when the system ended up in Helmholtz oscillations at the zero pressure difference equilibrium state.PACS numbers: 67.57.De, 67.57.Fg, 74.50.+r, 85.25.Cp     

Superfluid Phases of 3He in Aerogel

No Heading Formal derivation of criterion for selection of superfluid phases of ³He in aerogel is presented. At the strength of the derived criterion variation of the order parameter of B-like phase in magnetic field differs from that of B-phase of pure ³He. Possible observable consequence of this difference is discussed.PACS numbers: 67.57.Pq, 67.57.Bc, 67.57.De     

The Dynamic Texture of Superfluid 3He-B at Very Low Temperatures and in High Magnetic Fields

No Heading We report experiments using a pair of crossed vibrating wire resonators (VWRs) in the B phase of superfluid ³He in the zero temperature ballistic limit and in magnetic fields up to the B to A phase transition field of 340 mT. The VWRs are sensitive mechanical probes of energy gaps, textures and turbulent flow. In high magnetic fields the energy gap is no longer isotropic but significantly distorted, and the damping measured by the VWRs increases. With the crossed pair, we find that we can reduce the damping measured by one VWR when we increase the drive on the other one. We suggest that the reduction arises from the orientation of the surrounding texture by superflow and the screening of quasiparticles by the creation of superfluid turbulence.PACS numbers: 67.57.Fg, 67.57.Hi.     

Thermal phenomena in the flow of superfluid 3He through a weak link

No Heading We report on experiments performed with a weak link which was the only flow connection between two volumes of ³He. The deflection of a flexible wall between the volumes was measured to monitor the flow through the weak link as well as to measure the pressure difference across it. The temperature of the main volume was changed in steps of approximately 0.2 mK. After these temperature steps a fountain pressure developed and decayed on a time scale of several hundred seconds. This thermomechanical effect was found in normal and in superfluid ³He. We did not observe any influence of the quantum phase difference on the heat conductivity.PACS numbers: 67.57.De, 67.57.Fg, 74.50.+r, 85.25.Cp     

Temperature Dependence of the Josephson Current in the d-Wave Superconductor Junction Based on the 2-D Extended Hubbard Model

We present a theoretical study of the Josephson current in the d_x ^{2-y 2}-wave superconductor junction. We calculate the current-phase relation and the temperature dependence of the Josephson current for the (100) oriented and the (110) oriented junction using the two-dimensional (2-D) extended Hubbard model. We obtain the anomalous temperature dependence of the current in the (110) oriented junction which has been reported within the quasiclassical theory.     

Nonlocal Josephson electrodynamics

We present a review of the main results of the recently developed nonlocal Josephson electrodynamics. A nonlinear integro-differential equation for the phase difference is derived and its applicability to different problems is discussed. Fluxons and electromagnetic waves propagating along a tunnel junction are examined in detail. Features specific for the limiting case of a Josephson junction in a very thin film are considered.     

基于SNS型双路约瑟夫森结阵驱动方法研究

根据SNS型双路约瑟夫森结阵的驱动原理以及结阵分段特点,提出了平衡三进制驱动算法,实现了双路约瑟夫森结阵偏置状态的快速计算。根据约瑟夫森结阵的偏置状态以及组合方式,采用节点电压法,准确合成了双路阶梯波交流量子电压的台阶电压值,最终实现了最小分辨率为2个结,有效位为15位的交流量子电压输出。双路交流量子电压互测实验结果表明,合成交流量子电压的最大误差为0.06 μV,双路信号同步性测试实验中,两个通道的相位差为-0.01 μrad,证明了合成双路交流量子电压具有较高的幅值准确度和相位同步性。     

Weak link between conventional and unconventional superconductors

In this paper we consider the Josephson coupling between a conventional and an unconventional superconductor through a constriction. It is demonstrated that a weak link is very different from a tunnel junction. In particular, in an orientation where the coupling in a tunnel junction vanishes because of symmetry, the Josephson current in the case of a weak link can nevertheless be finite, albeit with the distinctive characteristics of(i) a current phase relationship with a period of 2/n, (ii) the critical current near but below the transition temperature T ₁ of the lower transition temperature superconductor is proportional to (1–(T/T ₁)) ^n/2, where n is an integer determined by the symmetry.     

S-N-S Josephson Weak Links in Superluid 3He-B

The Josephson current is calculated for an SNS junction consisting of two reservoirs of superfluid ³ He-B connected via thin cylindrical channels. The current-phase relations and maximal Josephson currents are calculated for channels of different diameter and length.     

Cross-Whisker Intrinsic Josephson Junction as a Probe of Symmetry of the Superconducting Order Parameter

As a test of the superconducting order parameter, we have developed an intrinsic Josephson junction by the name of cross-whisker junction. This junction was made using two Bi₂Sr₂CaCu₂O_8+d single crystal whiskers. Two whiskers were connected at their c planes with various cross-angles. Angular dependence of the critical current densities shows d-wave-like fourfold-symmetry. However, the angular dependence is much stronger than that of the conventional d_x ^{2-y 2} wave. The Jc shows its smallest value around 45 deg, which suggests that the Josephson penetration depth becomes longer. We have successfully observed a Fraunhofer pattern in the cross-whisker junction with cross-angle 45 deg.     

Quantum nondemolition measurement of the photon number in a Josephson-junction cavity

This paper proposes a quantum nondemolition measurement of the photon number in a Josephson-junction cavity. Under a current-biased Josephson junction with small capacitance, the Josephson phase fluctuates quantum-mechanically around its classical value due to the charging effect, and it couples to the photons in the junction cavity nonlinearly, which is necessary for the quantum nondemolition measurement. We show that the photon number in the junction cavity can be nondestructively measured by detecting the fluctuation of Josephson supercurrent through the junction.     

The Josephson Effect in Nanoscale Tunnel Junctions

In nanoscale Josephson junctions, the Josephson coupling energy is usually comparable with the charging energy of the junction and with the typical energy of thermal fluctuations. Under these circumstances, phase fluctuations imposed by the electromagnetic environment of the junction crucially affect the junction electrical behavior. In particular, they determine the maximum supercurrent the junction can sustain. We discuss this quantity in the case where the junction is not resistively shunted, so that the I V characteristics of the junction remains hysteretic. For a simple, yet realistic, unshunted junction model, we obtain detailed predictions of the shape of the supercurrent branch of the I V characteristic. Finally, we present experimental results supporting the theoretical analysis and which demonstrate that the supercurrent in an unshunted nanoscale Josephson junction can indeed be of the order of its critical current.     

Orbital Viscosity in Superfluid 3He-B in a Magnetic Field

No Heading Orbital viscosity is usually associated with the A phase of superfluid ³He which has a finite orbital angular momentum even in zero magnetic field. The B phase has no orbital angular momentum in zero magnetic field, but both spin and orbital angular momenta are induced by a field. The Leggett equations for spin dynamics assume that the orbital angular momentum can only charge on timescales much longer than those involved in spin dynamics. We calculate the orbital viscosity of the B phase in both the hydrodynamic and ballistic limits. At low temperatures the orbital viscosity becomes vanishingly small which gives rise to the possibility of coupled spin-orbit dynamics.PACS numbers: 67.57.Hi, 67.57.Lm     

Theory of the AC Josephson effect in triplet superconducting junction

The quasiparticle and AC Josephson current in superconductor / insulator / superconductor (S/I/S) junctions including a triplet p-wave superconductor are calculated for arbitrary transmission of the junction. As a triplet pairing state we select one of the unitary pairing states which is a promising candidate for the superconducting state in Sr ₂ RuO ₄ . In p-wave superconductor / insulator /p-wave superconductor junction, both quasiparticle current and AC Josephson current are enhanced near zero-bias voltage due to the existence of zero energy state of p-wave superconductors. For the s-wave superconductor/ insulator / p-wave superconductor junction, the quasiparticle current at low voltage is suppressed due to the energy gap of s-wave superconductor. The first Fourier component of the AC Josephson current vanishes due to the difference of the parity between the two superconductors.     

Macroscopic Quantum Phenomena in High Critical Temperature Superconducting Josephson Junctions

YBa₂Cu₃O_7?δ grain boundary bi-epitaxial Josepshon junctions (JJs) allow a very clear demonstration of Josephson current variation with the misorientation angle, consistent with the d-wave symmetry of the superconducting order parameter in cuprate, high temperature superconductors. Our bi-epitaxial junctions show a strong suppression of the first harmonic, I ₁ sin ø, of the current phase relation when tunneling from a lobe into a node of the superconducting gap function. In these configurations, the contribution of the second harmonic, I ₂ sin 2ø, becomes of the same magnitude as the first one, giving rise to a characteristic two-well Josephson potential as a function of phase ø instead of the usual single well. This characteristic intrinsic property has suggested proposals of a new class of qu-bit named “quiet” because of the existence a spontaneously degenerate fundamental state without the need of applying an external field. Our experiments probe the macroscopic quantum properties in a d-wave Josephson junction by measuring macroscopic quantum tunneling and energy level quantization. The switching current out of the zero voltage state is measured as a function of temperature down to 20 mK. The temperature variation of the width of an ensemble of switching events goes over from one, which is characteristic of a thermal activation of phase fluctuations to a temperature independent width which is a token of quantum tunneling of the phase. The transition regime is affected by the two-well potential in a 45^° misorientation junction as the second harmonic term gives rise to additional thermal transitions. The difference between quantized energy levels in the harmonic potential was determined by microwave spectroscopy. From the broadening of energy levels, it was possible to extract a Q-value of about 40 for the phase oscillations. The relatively high Q indicates quantum coherence over a sizeable time in d-wave junctions and gives hopes for a realization of a “quiet” high-T _c qu-bit. The contributions of V. L. Ginzburg to several different fields of physics are impressive and long standing. In superconductivity the Ginzburg–Landau theory, for instance, still represents a very powerful approach to model a huge number of different physical systems. High Temperature Superconductors (HTS) have strongly influenced research of the last 20 years and their d-wave order parameter symmetry represents one of the most intriguing features from both the fundamental point of view and some types of innovative long-term applications.     

Coherent Spin Precession in Superfluid 3He-B Excited in a Field Minimum at Low Temperatures

No Heading The persistent precessing domain (PPD) is an isolated region of coherent spin precession which is observed in the B phase of superfluid ³He at the lowest achievable temperatures. It has many unusual properties and its free decay can exceed 1000s at the lowest temperatures. Previous observations of the PPD were highly irreproducible but we now find the PPD to be very reproducible when there is a field minimum along the cell axis. Here we discuss measurements of the PPD as we control the magnetic field profile, allowing the depth of the minimum to be adjusted.PACS numbers: 67.57.Lm, 67.57.Jj, 67.57.Fg     

The Thermal Damping of an Aerogel Resonator in Superfluid 3He-B at Ultra Low Temperatures

No Heading We present measurements of the thermal damping of a cylindrical aerogel sample oscillating in superfluid. ³He-B in the low temperature regime. The measurements are made at low pressures where the ³He confined in the aerogel is normal. As in the case of conventional vibrating wire resonators, the thermal damping arises from quasiparticle collisions at the wire surface and is enhanced by many orders of magnitude by Andreev scattering from the superfluid backflow around the resonator. However, in the case of aerogel, incoming quasiparticles must be absorbed and thermalised within the aerogel before being re-emilled.PACS numbers: 67.57.Bc, 67.57.De, 67.57.Hi, 67.57.Pq.     

Dissipation in Superfluid 3He Weak Links

We suggest a new interpretation of the Berkeley data on the dissipation of superflow in Josephson junctions in superfluid ³He-B. The measurements are well described by the following relation between the current through a junction and the pressure head applied to it (current-pressure relation or CPR): $I = G_1 P + G_2 \sqrt P $ . The Berkeley group has proposed an explanation based on 1) ballistic removal of quasiparticles from the junction; 2) dissipative motion of the anisotropy axis of the order parameter inside the junction. We argue that part 1) of the model, which is responsible for the G ₂ part of the CPR, is invalid, since it presumes the existence, in the bulk, of quasiparticles with energies inside the superfluid gap. Part 2) which is responsible for the G ₁ term implies that the anisotropy axis of the order parameter strongly depends on the phase difference across the junction. Our agternative model is based on mechanisms well known in superconductors: dissipation due to time lag of inequilibrium order parameter and/or Andreev reflection of quasiparticles trapped inside the junction. For the parameters of the Berkeley experiment these models give the same order of magnitude for the G ₁ in the CPR, and are in rough agreement with the experiment. The nature of the G ₂ term remains mysterious. It could arise due to saturation of the current of Andreev-scattered quasiparticles if the quasiparticle relaxation time in the junction is considerably longer than in normal Fermi liquid.     

Fourth Sound Propagation in Superfluid 3He in Aerogel

No Heading Impurity effect on the fourth sound propagation in the superfluid ³He-aerogel system confined in a channel is discussed on the basis of a two-fluid theory in which phenomenological parameters are determined microscopically within the homogeneous scattering model.PACS numbers: 67.57.De, 67.57.Hi, 67.57.Pq.     

Tunnel Junction as a Noise Probe

The paper investigates theoretically effects of noise on low-bias parts of IV curves of tunnel junctions. The analysis starts from the effect of shot noise from an additional (noise) junction on the Coulomb blockaded Josephson junction in high-impedance environment. Asymmetry of shot noise characterized by its odd moments results in asymmetry of the IV curve of the Josephson junction. At high currents through the noise junction the IV curve is sensitive to electron counting statistics. The theory is generalized on another type of noise (phase noise of a monochromatic AC input) and on a normal Coulomb blockaded tunnel junction. The effect of shot noise on the IV curve of a superconducting Josephson junction in low-impedance environment is also analyzed. From this effect one can obtain information on the time necessary for an electron to tunnel through the junction responsible for shot noise. In summary, the analysis demonstrates, that the low-bias part of the IV curves of tunnel junctions can be a sensitive probe of various types of noise.