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Journal of the Physical Society of Japan

Coupling Effect in Dual Three-Josephson-Junction Loops in Classical Regime

Yoshihiro Shimazu

Published Jul 15, 2004• 2 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.73.1914

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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.
We analyze the influence of noise on magnetic properties of a superconducting loop which contains three Josephson junctions. This circuit is a classical analog of a persistent current (flux) qubit. A loop supercurrent induced by external magnetic field in the presence of thermal fluctuations is calculated. To connect with experiment, we calculate the impedance of a low-frequency tank circuit which is inductively coupled with the loop of interest. We compare the results with the results obtained in the quantum mode — when the three junction loop exhibits quantum tunneling of the magnetic flux. We demonstrate that the tank–loop impedance in the classical and quantum modes have different temperature dependence and can be easily distinguished experimentally.
This study shows that we can obtain an enhanced mutual coupling by using a superconducting quantum interference device (SQUID) containing a π-phase shift Josephson junction (π-junction). The π-junction can increase the current flowing in the loop inductance of the SQUID, thereby enhancing the magnetic flux generated in the inductance. Therefore, the effective self-inductance of the SQUID can increase, resulting in an increase in the mutual coupling. We use a 0-π SQUID formed by a conventional Josephson junction (0-junction) and a π-junction. Our numerical analysis for a simplified structure revealed that the ratio of effective to original self-inductance increased to 50. To confirm this, we measured the modulation patterns of critical current in dc-SQUIDs in which part of the loop inductance was replaced with a series of 0-π SQUIDs. The observed modulation pattern revealed that the effective self-inductance became more than 10-fold larger than the original self-inductance under the conditions that the applied current is a few μA while the critical current of the 0-junction in 0-π SQUIDs is 35 μA.
We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.
We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.
We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need two dc SQUID's in the connecting loop and the control fluxes threading the dc SQUID's must be in opposite directions. The coupling strength is analytically calculated as a function of the control flux at the coresonance point.
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.