Eigenstates of a small Josephson junction coupled to a resonant cavity

Abstract

We carry out a quantum-mechanical analysis of a small Josephson junction coupled to a single-mode resonant cavity. We find that the eigenstates of the combined junction-cavity system are strongly entangled only when the gate voltage applied at one of the superconducting islands is tuned to certain special values. One such value corresponds to the resonant absorption of a single photon by Cooper pairs in the junction. Another special value corresponds to a two-photon absorption process. Near the single-photon resonant absorption, the system is accurately described by a simplified model in which only the lowest two levels of the Josephson junction are retained in the Hamiltonian matrix. We noticed that this approximation does not work very well as the number of photons in the resonator increases. Our system shows also the phenomenon of "collapse and revival" under suitable initial conditions, and our full numerical solution agrees with the two level approximation result.

Cooperative effects in Josephson junctions in a cavity in the strong coupling regime

“…It should be expected that the same should happen for the QAMP producing a classical radiation field. The origin of decoherence on Josephson junctions is to be understood but it could not be excluded that revival and collapse effects of Rabi oscillations may be at work as happens in the weak coupling regime 12,13 . We have shown how, in the strong coupling limit as devised by Nakamura's group, several collective effects as Rabi oscillations and quantum amplification could appear in Josephson junctions coupled by a radiation field.…”

“…The strong coupling regime has the advantage that can be theoretically described by a two-level model 10,11 . Validity of the two-level model to describe the behavior of Josephson junctions has been proved by Stroud and AlSaidi 12,13 . They considered the case of weak coupling where the so called rotating wave approximation does apply 14 .…”

“…being ∆ the separation between the ground and the first excited state in a Cooper pair 12,13 , ω the frequency of the field in the cavity, g the coupling between the junction and the cavity, a † and a creation and annihilation operators, (1) is just the Dicke model that we have specialized to a single qubit with Pauli matrices. This generalizes immediately to any number of qubits putting…”

Quantum measurement of a coupled nanomechanical resonator–Cooper-pair box system

“…29,30 A connection to CQED may be made by noting that at the charge degeneracy point (n g Ϫnϭ1/2) the Hamiltonian given here, rewritten in the basis of noninteracting energy eigenstates, becomes identical to the two-level atom, single cavity mode Hamiltonian of CQED:…”

Long Josephson junction in a resonant cavity

“…[13][14][15][16][17][18][19] This regime is relevant when the junctions are very small, so that the noncommutation of the Cooper pair number operator and the phase operator is important. In this regime, the states of the junction ͑or junctions͒ and the cavity become entangled, and uniquely quantum phenomena such as Rabi oscillations may be detectable in suitable experiments.…”