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Physical review. B, Condensed matter

Schrödinger cat states in a Josephson junction

Christopher C. Gerry

Published Apr 1, 1998• 24 citations
Publisher

Abstract

A proposal for the generation of a Schr\"odinger-cat-type state is made in the context Josephson junctions. The Bloch state description of the BCS state is used along with the pseudospin algebra description of the tunneling process. The cat state consists of a superposition of Bloch states associated with dc Josephson currents flowing in opposite directions across the junction. The states can be detected by the observation of interference fringes in the probability distribution of the eigenvalues of the Josephson current operator.

DOI
10.1103/physrevb.57.7474

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A proposal for the generation of a Schr"odinger-cat-type state is made in the context Josephson junctions. The Bloch state description of the BCS state is used along with the pseudospin algebra description of the tunneling process. The cat state consists of a superposition of Bloch states associated with dc Josephson currents flowing in opposite directions across the junction. The states can be detected by the observation of interference fringes in the probability distribution of the eigenvalues of the Josephson current operator.
Abstract In this work, we consider the feasibility of Schrödinger cat (SC) and N 00 N states formation by a convenient bosonic Josephson junction system in two-mode approximation. Starting with purely quantum description of two-mode Bose–Einstein condensate we investigate the effective potential approach that provides an accurate analytical description for the system with a large number of particles. We show that in the zero temperature limit SC states result from a quantum phase transition that occurs when the nonlinear strength becomes comparable with the Josephson coupling parameter. The Wigner function approach demonstrates the growth of the SC state halves separation and formation of N 00 N -like states (a Fock state superposition) with the particle number increase. We examine the possibility to attain the SC state at finite temperatures and a weak dissipation leading to appearing of some critical temperature; it defines the second-order phase transition from classical activation process to the SC state formation through the quantum tunneling phenomenon. Numerical estimations demonstrate that the critical temperature is sufficiently below the temperature of atomic condensation. The results obtained may be useful for experimental observation of SC states with small condensate Josephson junctions.
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.