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arXiv:cond-mat/0603854 · Journal of Physics Condensed Matter

Correlated nanoscopic Josephson junctions

Stefano Bellucci A, Michele Cini, Pasquale Onorato, Enrico Perfetto

Published Aug 4, 2006• 0 citations
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Abstract

We discuss correlated lattice models with a time-dependent potential across a barrier and show how to implement a Josephson-junction-like behavior. The pairing occurs by a correlation effect enhanced by the symmetry of the system. In order to produce the effect we need a mild distortion which causes avoided crossings in the many-body spectrum. The Josephson-like response involves a quasi-adiabatic evolution in the time-dependent field. Besides, we observe an inverse-Josephson (Shapiro) current by applying an AC bias; a supercurrent in the absence of electromotive force can also be excited. The qualitative arguments are supported by explicit exact solutions in prototype 5-atom clusters with on-site repulsion. These basic units are then combined in ring-shaped systems, where one of the units sits at a higher potential and works as a barrier. In this case the solution is found by mapping the low-energy Hamiltonian into an effective anisotropic Heisenberg chain. Once again, we present evidence for a superconducting flux quantization, i.e. a Josephson-junction-like behavior suggesting the build-up of an effective order parameter already in few-electron systems. Some general implications for the quantum theory of transport are also briefly discussed, stressing the nontrivial occurrence of asymptotic current oscillations for long times in the presence of bound states.

DOI
10.1088/0953-8984/18/33/s23

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ac Josephson effect in one-dimensional Tomonaga-Luttinger liquid (TLL) adiabatically connected to superconducting electrodes is theoretically investigated. It is found that density fluctuations due to repulsive electron-electron interactions in TLL inhibit Josephson oscillations, whereas they do not affect time-independent current part. We also show that the fluctuations reduce supercurrent noise caused by multiple Andreev reflections. This indicates that the quantum fluctuations in TLL disturb the superconducting phase coherence spreading across the junction.
There exists a large number of experimental and theoretical results supporting the picture of macroscopic qubits implemented by nanoscopic Josephson junctions of three different types -- charge qubit, flux qubit and phase qubit. The standard unified description of such systems is based on the formal quantization of the phenomenological Kirchhoff equations for the corresponding circuits. In this paper a simplified version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions. For these models the state-dependent individual tunneling of Cooper pairs couples ground pair states with excited pair states what leads to a more complicated structure of the lowest lying energy levels. In particular, the highly degenerate levels emerge, which act as probability sinks for the qubit. These models allow also for the coupling to phonons as an efficient mechanism of relaxation for all types of junctions. The alternative formulas concerning basic spectral parameters of superconducting qubits are presented and compared with the experimental data. Finally, the question whether small Josephson junctions can be treated as macroscopic quantum systems is briefly discussed.
The direct-current (dc) Josephson effect provides a phase-sensitive tool for investigating superfluid order parameters. We report on the observation of dc Josephson supercurrents in strongly interacting fermionic superfluids across a tunneling barrier in the absence of any applied potential difference. For sufficiently strong barriers, we observed a sinusoidal current-phase relation, in agreement with Josephson's seminal prediction. We mapped out the zero-resistance state and its breakdown as a function of junction parameters, extracting the Josephson critical current behavior. By comparing our results with an analytic model, we determined the pair condensate fraction throughout the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover. Our work suggests that coherent Josephson transport may be used to pin down superfluid order parameters in diverse atomic systems, even in the presence of strong correlations.
With the recent technical breakthroughs, physicists fully play with the beauty of quantum mechanics. In this theoretical work on the mesoscopic Josephson effect, we take advantage of the collaborations with experimentalists as well as the exchanges between the cold atoms and condensed matter communities. We consider various systems based on the Josephson junction, beginning with its quantum description in the underdamped regime. Using the Keldysh formalism, we obtain the current-voltage characteristics from the classical to the zero temperature regime and the quantum Smoluchowski equation in the quasi-classical limit. We then study the quantum dynamics of a phase qubit realized with a SQUID in a novel configuration where tunneling events occur through two quartic barriers. The escape rate in this camel-back potential, calculated with the instantons technique, allows us to describe the experiments. Circuit quantum electrodynamics predicts that a lasing effect appears when a qubit is coupled to a resonant cavity. We consider the case of a charge qubit and also that of a transmon which exploits the Purcell effect. With the Lindbladian we obtain the density matrix from which we derive the spectrum of the output field. Finally, we study a gas of cold atoms in a ring shape trap comprising a barrier, thus creating a Bose Josephson junction. The low energy physics is described through the correlation functions with the Luttinger liquid theory. We show that the quantum fluctuations in the ring induce a renormalization of the Josephson energy.
Bosons with density-dependent hopping on a one dimensional lattice have been shown to emulate anyonic particles with fractional exchange statistics. Leveraging this, we construct a Josephson junction setup, where an insulating barrier in the form of a Mott-insulator is sandwiched between two superfluid phases. This is obtained by spatially varying either the statistical phase or the strength of the on-site interaction potential on which the ground state of the system depends. Utilizing numerical methods such as exact diagonalization and density renormalization group theory, the ground state properties of this setup are investigated to understand the Josephson effect in a strongly correlated regime. The dynamical properties of this model for different configurations of this model are analyzed to find the configurations that can produce the Josephson effect. Furthermore, it is observed that continuous particle flow over time is achievable in this proposed model solely by creating an initial phase difference without any external biasing.