Abstract. Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantummechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1=2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwavespectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
The dynamic properties of a superconducting quantum interference device (SQUID) containing arrays of Josephson junctions in a superconducting loop, and in particular the case of a four-junction SQUID, is analyzed theoretically via computer simulations. It is shown that phase locking of Josephson junctions determines the dynamic behavior of the SQUID. In the case of a stable phase-lock state hysteretic I-V curves as well as unusual voltage-flux dependencies appear. The influence of a small spread in the Josephson junction parameters upon the stability of the phase-lock state is investigated in parameter space.
We investigate the behavior of dual three-Josephson-junction loops coupled through a mutual inductance in the classical regime. The energy levels and the circulating currents in the loops are calculated as a function of applied external magnetic flux. The calculation shows that the coupling effect leads to the sequential reversal of the circulating currents in the loops. We measured the magnetic flux due to the circulating currents with a DC-SQUID in a flux-locked loop configuration. We demonstrate that the states of the coupled system can be manipulated with a magnetic field. The observed magnetic flux agrees very well with the simulation results based on the measurement of an inductance associated with a superconducting wire. The observed reversal of the circulating currents is explained in terms of the noise-activated escape from the metastable state in a six-dimensional potential.
The Hamiltonian of a superconducting thin loop interrupted by a double-barrier Josephson junction is derived. The parameter ε, which takes account of the difference in the Josephson coupling of the two single junctions in the SISIS structure, is seen to allow variation of the energy gap ΔE01 between the ground state and the first excited flux number state of the system. An additional parameter γ, describing the coupling between the outer electrodes of the double-barrier Josephson junction, is introduced. Persistent currents in the system are studied in terms of the usual parameter α, representing the ratio between the Josephson energy and the magnetic energy, and of the externally applied flux.
An effective Hamiltonian is derived for two coupled three-Josephson-junction (3JJ) qubits. This is not quite trivial, for the customary ``free'' 3JJ Hamiltonian is written in the limit of zero inductance
L. Neglecting the self-flux is already dubious for one qubit when it comes to readout, and becomes untenable when discussing inductive coupling. First, inductance effects are analyzed for a single qubit. For small
L, the self-flux is a ``fast variable,'' which can be eliminated adiabatically. However, the commonly used junction phases are not appropriate ``slow variables,'' and instead one introduces degrees of freedom that are decoupled from the loop current to leading order. In the quantum case, the zero-point fluctuations (
LC oscillations) in the loop current diverge as $L\ensuremath{\rightarrow}0$. While their effect thus formally dominates over the classical self-flux, it merely renormalizes the Josephson couplings of the effective (two-phase) theory. In the coupled case, the strong zero-point fluctuations render the full (six-phase) wave function significantly entangled in leading order. However, in going to the four-phase theory, this uncontrollable entanglement is integrated out completely, leaving a computationally usable mutual-inductance term of the expected form as the effective interaction.