F. W. J. Hekking

Correlated tunneling into a superconductor in a multiprobe hybrid structure

We consider tunneling in a hybrid system consisting of a superconductor with two or more probe electrodes which can be either normal metals or polarized ferromagnets. In particular we study transport at subgap voltages and temperatures. Besides Andreev pair tunneling at each contact, in multi-probe structures subgap transport involves additional channels, which are due to coherent propagation of two particles (electrons or holes), each originating from a different probe electrode. The relevant processes are electron cotunneling through the superconductor and conversion into a Cooper pair of two electrons stemming from different probes. These processes are non-local and decay when the distance between the pair of involved contacts is larger than the superconducting coherence length. The conductance matrix of a three-terminal hybrid structure is calculated. The multi-probe processes enhance the conductance of each contact. If the contacts are magnetically polarized the contribution of the various conduction channels can be separately detected.

Interference of two electrons entering a superconductor.

The subgap conductivity of a normal-superconductor (NS) tunnel junction is thought to be due to tunneling of two electrons. There is a strong interference between these two electrons, originating from the spatial phase coherence in the normal metal at a mesoscopic length scale and the intrinsic coherence of the superconductor. We evaluated the interference effect on the transport through an NS tunnel junction. We propose the layouts to observe drastic Aharonov-Bohm and Josephson effects

Subgap conductivity of a superconductor–normal-metal tunnel interface

At low temperatures, the transport through a superconductor--normal-metal tunnel interface is due to tunneling of electrons in pairs. We show that the rate for this process is often determined by the interference of the electron waves on a space scale determined by the coherence length. Therefore, the subgap current strongly depends on the layout of the electrodes within this space scale. The approach developed allows us to evaluate the subgap current for different layouts of interest.

INTERACTION CONSTANTS AND DYNAMIC CONDUCTANCE OF A GATED WIRE

We show that the interaction constant governing the long-range electron-electron interaction in a quantum wire coupled to two reservoirs and capacitively coupled to a gate can be determined by a low-frequency measurement. We present a self-consistent, charge and current conserving, theory of the full conductance matrix. The collective excitation spectrum consists of plasma modes with a relaxation rate which increases with the interaction strength and is inversely proportional to the length of the wire.

Observation of Transition from Escape Dynamics to Underdamped Phase Diffusion in a Josephson Junction

We have investigated the dynamics of underdamped Josephson junctions. In addition to the usual crossover between macroscopic quantum tunnelling and thermally activated (TA) behaviour we observe in our samples with relatively small Josephson coupling E_J, for the first time, the transition from TA behaviour to underdamped phase diffusion. Above the crossover temperature the threshold for switching into the finite voltage state becomes extremely sharp. We propose a (T,E_J) phase-diagram with various regimes and show that for a proper description of it dissipation and level quantization in a metastable well are crucial.

Coherent oscillations in a superconducting multilevel quantum system

We have observed coherent oscillations in a multilevel quantum system, formed by a current-biased dc SQUID. These oscillations have been induced by applying resonant microwave pulses of flux. Quantum measurement is performed by a nanosecond flux pulse that projects the final state onto one of two different voltage states of the dc SQUID, which can be read out. The number of quantum states involved in the coherent oscillations increases with increasing microwave power. The dependence of the oscillation frequency on microwave power deviates strongly from the linear regime expected for a two-level system and can be very well explained by a theoretical model taking into account the anharmonicity of the multilevel system.

Andreev Current-Induced Dissipation in a Hybrid Superconducting Tunnel Junction

We have studied hybrid superconducting microcoolers made of a double superconductor-insulator-normal metal tunnel junction. Under subgap conditions, the Andreev current is found to dominate the single-particle tunnel current. We show that the Andreev current introduces additional dissipation in the normal metal equivalent to Joule heating. By analyzing quantitatively the heat balance in the system, we provide a full description of the evolution of the electronic temperature with the voltage. The dissipation induced by the Andreev current is found to dominate the quasiparticle tunneling-based cooling over a large bias range.

Quantum jump approach for work and dissipation in a two-level system.

We apply the quantum jump approach to address the statistics of work in a driven two-level system coupled to a heat bath. We demonstrate how this question can be analyzed by counting photons absorbed and emitted by the environment in repeated experiments. We find that the common nonequilibrium fluctuation relations are satisfied identically. The usual fluctuation-dissipation theorem for linear response applies for weak dissipation and/or weak drive. We point out qualitative differences between the classical and quantum regimes.

JOSEPHSON CURRENT THROUGH A LUTTINGER LIQUID

We study the Josephson effect through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. The interactions are treated in the framework of the one-channel Luttinger model. At zero temperature, the Josephson critical current is found to decay algebraically with increasing distance between the junctions. The exponent is proportional to the strength of the Coulomb interaction. If the Luttinger liquid has a finite size, the Josephson current depends on the total number of electrons modulo 4. These parity effects are studied for the ring, coupled capacitively to a gate-voltage and threaded by a magnetic flux. The Josephson current changes continuously as a function of the gate voltage and {\em stepwise} as a function of the magnetic flux. The electron-electron interaction introduces {\em qualitatively} new features compared to the non-interacting case.

Current-current correlations in hybrid superconducting and normal-metal multiterminal structures

We consider a hybrid system consisting of two normal metal leads weakly connected to a superconductor. Current-current correlations of the normal leads are studied in the tunneling limit at subgap voltages and temperatures. We find that only two processes contribute to the cross-correlation: the crossed Andreev reflection (emission of electrons in different leads) and the elastic cotunneling. Both processes are possible due to the finite size of the Cooper pair. Noise measurements can thus be used to probe directly the superconducting wave function without the drawbacks appearing in average current measurements where the current is dominated by direct Andreev reflection processes. By tuning the voltages it is possible to change the sign of the cross-correlation. Quantitative predictions are presented both in the diffusive and ballistic regimes.