Relative phase and Josephson dynamics between weakly coupled Richardson models

Buccheri, Francesco and Trombettoni, A. (2013) Relative phase and Josephson dynamics between weakly coupled Richardson models. PHYSICAL REVIEW B, 87 (17). ISSN 2469-9950

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Abstract

We consider two weakly coupled Richardson models to study the formation of a relative phase and the Josephson dynamics between two mesoscopic attractively interacting fermionic systems: our results apply to superconducting properties of coupled ultrasmall metallic grains and to Cooper- pairing superfluidity in neutral systems with a finite number of fermions. We discuss how a definite relative phase between the two systems emerges and how it can be conveniently extracted from the many-body wavefunction: we find that a definite relative phase difference emerges even for very small numbers of pairs (∼ 10). The Josephson dynamics and the current-phase characteristics are then investigated, showing that the critical current has a maximum at the BCS-BEC crossover. For the considered initial conditions a two-state model gives a good description of the dynamics and of the current-phase characteristics.

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