R. de Bruyn Ouboter

The thermodynamic properties of liquid 3He−4He mixtures between 0 and 20 atm in the limit of absolute zero temperature

Abstract The presently existing thermodynamic data of liquid 3 He- 4 He mixtures between 0 and 20 atm in the limit of absolute zero temperature are presented in a coherent way, without reference to models, through constructing the thermodynamic surface e( n 3 , n 4 ), where e is the energy density and n 3 , n 4 are the molar densities. The chemical potentials are the partial derivative of e. The construction is made through the information contained in the existing thermodynamical data. The geometrical meaning of the surface whose coordinates are the energy density and the molar densities of both components is explained. In the pressure range considered the energy density and the chemical potentials are determined as a function of the molar densities. Details of the thermodynamic functions are summarized in the tables at the end of the article. Special attention is given to the saturated solution curve and the one-phase region in which the energy density appears to be expandable not in integral but in fractional powers of the 3 He density.

Thermal activation in the quantum regime and macroscopic quantum tunnelling in the thermal regime in a metabistable system consisting of a superconducting ring interrupted by a weak junction: Part II: Thermal activation in the quantum regime (continuation)

Abstract Under certain circumstances a superconducting ring containing a weak superconducting junction, a SQUID, has two metastable magnetic flux states separated by a potential barrier ΔU. If the junction has a small capacitance stochastic magnetic flux transitions are observed even at very low temperatures. This article mainly concerns the intrinsic thermal activation in the quantum regime, where the mean energy of the oscillator, corresponding to the metastable potential wells, is different from the equipartition value kT due to the high frequencies and low temperature involved in our experiments. We have found strong deviations from the classical thermodynamic activation theory of Kramers where the transition rate is proportional to exp( -ΔU kT ). We are able to explain our experimental findings by replacing the classical equipartition value kT for the mean energy in the exponent with the value for the mean excitation energy of the Brownian motion of a quantum oscillator, accounting for the appropriate damping.

The London moment for high temperature superconductors

Inside a stationary superconductor the magnetic field is zero, as described by the London equations. These equations also describe the development of a magnetic field in a superconductor when it is set into rotation. The generated magnetic moment is called the London moment. We show that the high-Tc superconductors develop a London moment of the same magnitude as the conventional superconductors and discuss the consequences of this for the interpretation of the London penetration depth.

Flux transition mechanisms in superconducting loops closed with a low capacitance point contact

Abstract Flux transitions in a superconducting ring containing a weak link have been investigated both theoretically and experimentally. For low capacitance junctions it is shown that in addition to thermally induced transitions a second mechanism, macroscopic quantum tunneling, might play a role and that this effect will become dominant at lower temperatures.

Multi-terminal SQUID controlled by the transport current

Abstract A theory is offered for a multi-terminal SQUID (MTS), i.e., a superconducting ring interrupted with a Josephson multi-terminal junction. The behaviour of the MTS which is governed by the two independent control parameters, the transport current and the applied magnetic flux, is described. The steady state domain and the critical current in the transport circuit as a function of the external magnetic flux in the ring is obtained. The total magnetic flux in the ring is a multi-valued function from the applied magnetic flux for all values of the self-inductance of the ring. The MTS presents a system in which the structure of macroscopic quantum states can be transformed by the current through the current-driven Josephson junction as well as by the external magnetic field.

On the thermodynamics of a superconducting ring interrupted by a weak superconducting junction

Abstract A superconducting ring interrupted by a weak Josephson junction can have two metastable magnetic flux states separated by a potential energy barrier in case an external magnetic field of appropriate strength is applied. The thermodynamic Gibbs surface of this system is constructed: i.e. the relevant part of the magnetic Gibbs potential as a function of the applied magnetic flux and the temperature is shown. The relevant contribution to the entropy and the self-induced circulating current are the corresponding partial derivatives of the Gibbs function. From the Gibbs function and the entropy the magnetic enthalphy is found. The calculations presented here are of relevance in interpreting thermodynamic fluctuation phenomena in the total embraced magnetic flux which are determined by the magnetic availability of the system with respect to the surroundings fixed by the temperature of the heat reservoir and the external magnetic field.

On the thermodynamics of a superconducting ring interrupted by a weak superconducting junction: II (continuation)

A superconducting ring interrupted by a weak Josephson junction can have two metastable magnetic flux states separated by a potential energy barrier in case an external magnetic field of appropriate strength is applied. In our previous article, part I, the thermodynamic Gibbs surface of this system was constructed together with the relevant contribution to the entropy being the negative of the corresponding partial derivative of the Gibbs function. The calculations presented here in part II are an extension and of relevance in interpreting thermodynamic fluctuation phenomena in the total embraced magnetic flux which are determined by the magnetic availability of the system with respect to the surroundings fixed by the temperature of the heat reservoir and the external magnetic field. The magnetic availability of this system, being the minimum work an external source must perform to bring the small system reversibly from a state of equilibrium with the surroundings to a given non-equilibrium state, is constructed. In a few examples the dynamics of the flux transition mechanism is investigated by calculating the change of the temperature of the system with respect to the temperature of the surroundings and of the corresponding availability potential.

Metabistability in superconducting rings interrupted by a weak junction

Abstract Under certain circumstances a superconducting ring containing a weak superconducting junction (a SQUID) has two metastable magnetic flux states separated by a potential barrier when an external magnetic field is applied of appropriate strength. If the junction has a small capacitance, even at low temperatures where kT is very much smaller than the barrier height ΔU intrinsic magnetic flux transitions are observed from one metastable flux state into an other and vice versa, or in other words a weak “persistent supercurrent” switches stochastically from one direction into the opposite. This flux transition mechanism at very low temperatures might be interpreted as due to macroscopic quantum tunnelling, a new macroscopic quantum effect.

Fabrication of inherently stable and adjustable contacts of atomic size

As dimensions of devices shrink new phenomena are revealed. We present a technique which allows the dimension of a point contact to ‘‘shrink’’ down to a single atom. Furthermore, this technique enables us to adjust a tunnel barrier between two inherently stable electrodes. Utilizing this technique we show that it is possible to apply a pressure or a tensile force on a single atom contact and study the resulting effects on the transport properties of this microscopic structure.

Thermal activation in the quantum regime and macroscopic tunnelling in the thermal regime in a metabistable system consisting of a superconducting ring interrupted by a weak junction: Part III: Macroscopic quantum tunnelling in the thermal regime

Abstract When an external magnetic flux close to half a flux quantum is applied to a superconducting ring containing a weak superconducting junction, a SQUID, there can exist two metastable magnetic flux states by a potential energy barrier. If the junction has a sufficiently small capacitance, at very low temperatures intrinsic stochastic magnetic flux transitions due to macroscopic quantum tunnelling from one metastable flux state into another and vice versa are observed. Experiments are described showing macroscopic quantum tunnelling effects in an evaporated Nb device performed in a glass dilution refrigerator. A statistical analysis of the sampled data is made showing the measured distribution of the flux transitions in agreement with a pure stochastic transition process with a Poisson distribution. The measurements of the mean lifetimes are — in two ways — out of keeping with the theoretical predictions of the dissipative two-state Boson model. Firstly, although at fixed temperature the mean lifetime depends exponentially on the bias in the potential energy, a thermal quasi-Boltzmann distribution has not been found. Secondly, the mean lifetime of the two flux states in case of zero bias, symmetrical potential energy, does not clearly show the predicted T 1−2α dependence. It is conjectured that the system may not behave perfectly isothermal, because when a flux transition takes place between the metastable potential wells some energy will be dissipated possibly causing a temporary temperature rise due to self-heating. This effect is discussed in part II in relation with the data of the thermal activation experiments obtained with the same type of devices.