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Physical Review B

Persistent currents in the presence of nonclassical electromagnetic fields

Jerzy Dajka, M. Szopa, Apostol Vourdas, E. Zipper

Published Jan 9, 2004• 9 citations
Publisher

Abstract

Persistent currents in mesoscopic rings and cylinders threaded by a magnetostatic flux and also by monochromatic nonclassical electromagnetic fields are considered. The results depend on the quantum state of the nonclassical electromagnetic fields. It is shown that quantum and thermal noise in the field reduces the current and can change its character from diamagnetic to paramegnetic, and vice versa. Four different examples of nonclassical electromagnetic fields are considered (number eigenstates, coherent states with randomized phase, coherent states, and thermal states) and the corresponding currents are calculated. Two-mode entangled electromagnetic fields are also considered, and the effect of entanglement on the currents is studied.

DOI
10.1103/physrevb.69.045305

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Persistent currents in mesoscopic rings and cylinders threaded by a magnetostatic flux and also by monochromatic nonclassical electromagnetic fields are considered. The results depend on the quantum state of the nonclassical electromagnetic fields. It is shown that quantum and thermal noise in the field reduces the current and can change its character from diamagnetic to paramegnetic, and vice versa. Four different examples of nonclassical electromagnetic fields are considered (number eigenstates, coherent states with randomized phase, coherent states, and thermal states) and the corresponding currents are calculated. Two-mode entangled electromagnetic fields are also considered, and the effect of entanglement on the currents is studied.
Mesoscopic systems and the non-classical electromagnetic fields are of central importance for quantum information processing. Our aim is to present the significant impact of the non-classical radiation on the properties of persistent currents. We study mesoscopic rings or cylinders subject to both classical and non-classical magnetic flux. Our discussion is limited to oneand two-mode fields prepared in a given state. For the monochromatic radiation we study reduction of the current amplitude due to the quantum and classical noise in the field. We also present the change of the sign of the current from parato diamagnetic (and vice versa) controlled by the state of radiation. The effect of temperature will by shortly reviewed. There are two qualitatively distinct classes of two-mode fields: separable and entangled. This is reflected in the properties of the currents which become time-dependent for the fields in an entangled state. We investigate the effect of entanglement for the family of states with various amount of entanglement: from separable to Bell states quantified by the concurrence.
Circular superconducting devices with mesoscopic Josephson junctions are considered in the presence of a dc voltage bias V0{\mathit{V}}_{0}V0​ and of nonclassical electromagnetic fields. It is shown that when the voltage V0{\mathit{V}}_{0}V0​ is an integer multiple of a certain value, the current through the junction has a dc component. This is broadly similar to Shapiro steps in macroscopic Josephson junctions, but the details depend on the nature of the nonclassical electromagnetic field. Coherent states, squeezed states, and number eigenstates are considered and the corresponding Shapiro steps are studied in detail. The presence of thermal noise in the nonclassical fields is also considered and its effect on the results is studied.
Two mesoscopic SQUID rings which are far from each other, are considered. A source of two-mode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. Results for two different examples that involve microwaves in number states and coherent states are derived. It is shown that the quantum statistics of the tunnelling electron pairs through the Josephson junctions in the two rings, are correlated.
This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
Two mesoscopic SQUID rings which are far from each other, are considered.A source of twomode nonclassical microwaves irradiates the two rings with correlated photons.The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents.Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified.Results for two different examples that involve microwaves in number states and coherent states are derived.It is shown that the quantum statistics of the tunnelling electron pairs through the Josephson junctions in the two rings, are correlated.