Variational Study of the Interacting Impurity Josephson Junction

Domenico Giuliano, Pasquale Sodano

Robert P. Erickson, David P. Pappas

We consider a superconducting phase qubit consisting of a monocrystalline sapphire Josephson junction with its symmetry axis perpendicular to the junction interfaces. Via the London gauge, we present a theoretical model of Fe3+ magnetic impurities within the junction that describes the effect of a low concentration of such impurities on the operation of the qubit. Specifically, we derive an interaction Hamiltonian expressed in terms of angular momentum states of magnetic impurities and low-lying oscillator states of a current-biased phase qubit. We discuss the coupling between the qubit and impurities within the model near resonance. When the junction is biased at an optimal point for acting as a phase qubit, with a phase difference of π/2 and impurity concentration no greater than 0.05%, we find only a slight decrease in the Q factor of less than 0.01%.

I. N. Askerzade, Ali Bozbey, Mehmet Cantürk

Michael Schecter, Dimitri M. Gangardt, Alex Kamenev

We overview the main features of mobile impurities moving in one-dimensional superfluid backgrounds by modeling it as a mobile Josephson junction, which leads naturally to the periodic dispersion of the impurity. The dissipation processes, such as radiative friction and quantum viscosity, are shown to result from the interaction of the collective phase difference with the background phonons. We develop a more realistic depleton model of an impurity-hole bound state that provides a number of exact results interpolating between the semiclassical weakly interacting picture and the strongly interacting Tonks–Girardeau regime. We also discuss the physics of a trapped impurity, relevant to current experiments with ultra cold atoms.

J. Kent Harbaugh, D. Stroud