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Journal of Applied Physics

Kinetic momentum quantum effect in a superconducting closed loop composed of Josephson junctions

Tsutomu Yamashita, Yasuhiko Ogawa, Yutaka Onodera

Published May 1, 1979• 29 citations
Publisher

Abstract

Superconducting closed loops composed of N series Josephson junctions are discussed. The conditions to achieve the n quantum state of a fluxoid in the loop are analyzed. It is found that the n quantum state exists in Josephson loops having more than 4n pieces of junctions even if it is assumed that the inductance L in the loop is negligibly small. This n quantum state is achieved by an asymmetric current feed to the Josephson loop. The properties of the loop are easily explained by using a pendulum analog.

DOI
10.1063/1.326298

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Europhysics Letters (EPL)•Jan 1, 1996•7 citations
Superconducting closed loops composed of N series Josephson junctions are discussed. The conditions to achieve the n quantum state of a fluxoid in the loop are analyzed. It is found that the n quantum state exists in Josephson loops having more than 4n pieces of junctions even if it is assumed that the inductance L in the loop is negligibly small. This n quantum state is achieved by an asymmetric current feed to the Josephson loop. The properties of the loop are easily explained by using a pendulum analog.
The three-junction flux qubit (quantum bit) consists of three Josephson junctions connected in series on a superconducting loop. We present a numerical treatment of this device for the general case in which the ratio ${\ensuremath{\beta}}_{Q}$ of the geometrical inductance of the loop to the kinetic inductance of the Josephson junctions is not necessarily negligible. Relatively large geometric inductances allow the flux through each qubit to be controlled independently with on-chip bias lines, an essential consideration for scalability. We derive the three-dimensional potential in terms of the macroscopic degrees of freedom, and include the possible effects of asymmetry among the junctions and of stray capacitance associated with them. To find solutions of the Hamiltonian, we use basis functions consisting of the product of two plane wave states and a harmonic oscillator eigenfunction to compute the energy levels and eigenfunctions of the qubit numerically. We present calculated energy levels for the relevant range of ${\ensuremath{\beta}}_{Q}$. As ${\ensuremath{\beta}}_{Q}$ is increased beyond 0.50.50.5, the tunnel splitting between the ground and first excited states decreases rapidly, and the device becomes progressively less useful as a qubit.
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.
Abstract When the impedance of a Josephson junction is too low, the elements are connected in series. We connected two arrays with N series elements of Josephson junctions each (denoted 2N‐JJ loop) and tried to find conditions for it to operate coherently by investigating voltage‐current curves. the computer simulation showed that coherent operation is easier with this circuit than with a series connection of the elements when the elements have different junction parameters. Pb‐alloy tunnel‐type junctions were produced which have N = 2 and 3, and we found that voltage steps generated by application of rf current with frequency F have a voltige interval corresponding to NF. This agrees with the simulation results and indicates coherent operation.
We have theoratically and experimentally investigated the possibility of the phase mode operation of symmetrical four-junction Josephson interferometers (4J-loop), which are considered to play a key role as quantum logic devices for a Josephson switching system utilizing single-quanta as information bits, because of their excellent characters such as the kinetic momentum quantum effect and variety of the logic operations. The threshold characteristic, which is the most basic for Josephson interferometers to be operated in the phase mode and shows their fluxoid-quantum states, has experimentally been observed clearly for the first time for symmetrical 4J-loop's by using a novel radial-scanning, intensity-modulation technique, as predicted theoretically. It is characterized by a limited closed-shaped pattern. The number of the fluxoid-quantum states increases with LI0for the loops. Two different basic types of switching behaviors, a vortex-to-vortex and a vortex-to-voltage transition, have been confirmed, which have clearly been separated on the threshold characteristic, for the loops with LI0larger than\sim0.7\Phi_{0}The optimum LI0value for the phase mode operation of the loops has been found to be0.75\Phi_{0}\lsim LI_{0}\lsim 1.25\Phi_{0}. The desired performance of the phase mode operation of symmetrical 4J-loop has been confirmed by the shift motion of single fluxoids on the basis of the vortex-to-vortex transition of the loop. Finally, an application of such phase mode Josephson interferometers for pulse generators of Josephson sampling systems has been proposed.
The mutual coherent interaction of Josephson junctions in a multi-junction superconducting loop (MSL) in the limit of zero-loop inductance is theoretically investigated. For the loop containing 2 M junctions there are M coherent states corresponding to different values of effective flux ϕ eff in the loop. The stability analysis using the method of Floquet exponents shows the highest stability for the state with ϕ eff = 1/2. In this state, the MSL behaves like an oscillating magnetic dipole. The optimum stability is reached for the normalised bias current i b ≃ 2.5 and the McCumber parameter β C ≃ 0.5.