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From microscopic to macroscopic description of Josephson dynamics in one-dimensional arrays of weakly-coupled superconducting islands

A. Giordano, Roberto De Luca

By starting from a microscopic quantum mechanical description of Josephson dynamics of a one-dimensional array of N coupled superconductors, we obtain a set of linear differential equations for the system order parameter and for additional macroscopic physical quantities. With opportune considerations, we adapt this description to two coupled superconductors, obtaining the celebrated Feynman model for Josephson junctions. These results confirm the correspondence between the microscopic picture and the semi-classical Ohta’s model adopted in describing the superconducting phase dynamics in multi-barrier Josephson junctions.By starting from a microscopic quantum mechanical description of Josephson dynamics of a one-dimensional array of N coupled superconductors, we obtain a set of linear differential equations for the system order parameter and for additional macroscopic physical quantities. With opportune considerations, we adapt this description to two coupled superconductors, obtaining the celebrated Feynman model for Josephson junctions. These results confirm the correspondence between the microscopic picture and the semi-classical Ohta’s model adopted in describing the superconducting phase dynamics in multi-barrier Josephson junctions.

Results in PhysicsJan 1, 20152 citations

Quantum theory of the small Josephson junction

Alwyn C. Scott

Physics Letters AJul 1, 19677 citations

"Normal" Josephson Junctions and Quantum Coherence

Lorin L. Vant-Hull, James E. Mercereau

Physical Review LettersSep 19, 196612 citations

Josephson junctions with nonsinusoidal current-phase relations based on heterostructures with a ferromagnetic spacer and their applications

N. V. Klenov, Н. Г. Пугач, Aleksei Sharafiev +2 more

A detailed review of theories describing the current-phase relations in Josephson junctions based on heterostructures with ferromagnetic layers is presented. The particular attention has been focused on the possibilities of making the so-called ϕ-junctions in which the ground state in the absence of the current is realized when the Josephson phase ϕ is nonzero. The recently popular speculations concerning the possibility of applying the Josephson π- and ϕ-junctions, which are made on the basis of heterostructures with ferromagnetic layers, to the formation of quantum bits (qubits) have been illustrated. An attempt to formulate the requirements for the characteristics of the Josephson heterostructures based on the first principles of the quantum-mechanical description of superconducting interferometers with a low inductance has been made.A detailed review of theories describing the current-phase relations in Josephson junctions based on heterostructures with ferromagnetic layers is presented. The particular attention has been focused on the possibilities of making the so-called ϕ-junctions in which the ground state in the absence of the current is realized when the Josephson phase ϕ is nonzero. The recently popular speculations concerning the possibility of applying the Josephson π- and ϕ-junctions, which are made on the basis of heterostructures with ferromagnetic layers, to the formation of quantum bits (qubits) have been illustrated. An attempt to formulate the requirements for the characteristics of the Josephson heterostructures based on the first principles of the quantum-mechanical description of superconducting interferometers with a low inductance has been made.

Physics of the Solid StateNov 1, 201024 citations

Effective description of tunneling in a time-dependent potential with applications to voltage switching in Josephson junctions

Christian Kraglund Andersen, Klaus Mølmer

We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features associated with voltage switching in Josephson junctions. Apart from applications as artificial atoms in quantum information studies, the Josephson junction may serve as an electric field sensitive detector, and our studies provide a detailed understanding of how the voltage switching dynamics couples to the electric field amplitude.We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features associated with voltage switching in Josephson junctions. Apart from applications as artificial atoms in quantum information studies, the Josephson junction may serve as an electric field sensitive detector, and our studies provide a detailed understanding of how the voltage switching dynamics couples to the electric field amplitude.

arXiv:1303.5644Physical Review AMay 15, 201316 citations

Macroscopic quantum mechanics: experiments on Josephson junctions

Vittorio Giulio Palmieri

Physica B Condensed MatterJul 1, 20000 citations

On the quantum-mechanical description of Josephson junctions

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