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Physical review. B, Condensed matter

Geometric phase in a mesoscopic Josephson junction with classical driving source

Bin Shao, Jian Zou, Qian‐Shu Li

Published Oct 1, 1999• 16 citations
Publisher

Abstract

We examine a mesoscopic Josephson junction driven by the time periodic field and solve its time-dependent Schr\"odinger equation with the help of the time dependent invariant of the Hamiltonian operator. We show that the state of the system can evolve a generalized squeezed state if the junction is prepared initially in its $n\mathrm{th}$ excited state. It also turns out to be possible to produce coherent and ordinary squeezed states for the mesoscopic junction system. The explicit expression of the nonadiabatic geometric phase of the system is also obtained.

DOI
10.1103/physrevb.60.9714

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We examine a mesoscopic Josephson junction driven by the time periodic field and solve its time-dependent Schr"odinger equation with the help of the time dependent invariant of the Hamiltonian operator. We show that the state of the system can evolve a generalized squeezed state if the junction is prepared initially in its nthn\mathrm{th}nth excited state. It also turns out to be possible to produce coherent and ordinary squeezed states for the mesoscopic junction system. The explicit expression of the nonadiabatic geometric phase of the system is also obtained.
We examine an effective bosonic Hamiltonian describing a mesoscopic Josephson junction driven by a sinusoidal magnetic field. We study the effects caused by the Josephson nonlinearity and find that an initial vacuum state of the junction can evolve into a class of superposition state of coherent states. Further, we investigate the reduced quantum fluctuation of the junction variables and the dynamics of the supercurrent. Our results show that, due to the effect of Josephson nonlinearity, the time evolution of the supercurrent can exhibit the collapse and revival even when the junction is driven by a classical field.
In this paper, we examine a mesoscopic LC circuit with alternating source and solve its time-dependent Schrödinger equation by selecting a proper Hermitian invariant operator. We study LR geometric phase in mesoscopic circuit system. Our results indicate that LR geometric phase is present at all times. In the evolution of the circuit system, it is a geometric phase factor accumulated by the wavefunction of external source's interaction with circuit system after nonadiabatic and noncyclic evolution. Its property lies in that it depends on the evolution path of the system wavefunction in the parameter space.