Several small Josephson junctions in a Resonant Cavity: Deviation from the Dicke Model

TL;DR

This study explores the quantum dynamics of multiple Josephson junctions in a resonant cavity, revealing deviations from the Dicke model due to additional dipole-dipole interactions, and demonstrates observable collective oscillations.

Contribution

It introduces a modified Hamiltonian for Josephson junctions in a cavity, highlighting an extra interaction term and confirming collective oscillation enhancement beyond the Dicke model.

Findings

Oscillation frequency scales with √N, indicating collective behavior.

Additional dipole-dipole interaction term modifies the standard Dicke model.

Enhanced oscillations remain observable despite junction differences.

Abstract

We have studied quantum-mechanically a system of several small identical Josephson junctions in a lossless single-mode cavity for different initial states, under conditions such that the system is at resonance. This system is analogous to a collection of identical atoms in a cavity, which is described under appropriate conditions by the Dicke model. We find that our system can be well approximated by a reduced Hamiltonian consisting of two levels per junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but contains an additional term resembling a dipole-dipole interaction between the junctions. This extra term arises when states outside the degenerate group are included via degenerate second-order (L\"{o}wdin) perturbation theory. As in the Dicke model, we find that, when N junctions are present in the cavity, the oscillation frequency due to the junction-cavity interaction is enhanced by $\sqrt{N}$. The corresponding decrease in the Rabi oscillation period may cause it to be smaller than the decoherence time due to dissipation, making these oscillations observable. Finally, we find that the frequency enhancement survives even if the junctions differ slightly from one another, as expected in a realistic system.