Dissipative dynamics of a Josephson junction in the Bose gases

Abstract

The dissipative dynamics of a Josephson junction in the Bose-gases is considered within the framework of the model of a tunneling Hamiltonian. The effective action which describes the dynamics of the phase difference across the junction is derived using functional integration method.The dynamic equation obtained for the phase difference across the junction is analyzed for the finite temperatures in the low frequency limit involving the radiation terms. The asymmetric case of the Bose-gases with the different order parameters is calculated as well.

Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space

“…As a result, an overlap between two wave functions at both sides of the barrier provides a measure for the tunneling amplitude of the particle. Potential barriers of this sort have been realized in quantum devices [9] that make use of Josephson tunneling [12] and in the recently achieved optical traps [13].…”

Dissipative dynamics of the Josephson effect in binary Bose-Einstein-condensed mixtures

“…In order to comprehend the dynamics of the relative phase differences ϕ 1 and ϕ 2 across the junction, we should analyze the behavior of the response functions α ik (τ ) and β ik (τ ) as a function of time. Note that the contribution of the terms G ik and F ik to the response functions α ik and β ik is much smaller than that of the first two others [28]. The order-of-magnitude smallness is about a ratio of the noncondensate density to the condensate density or about gas parameter (na 3 ) 1/2 ≪ 1.…”

“…Taking into account (2), we arrive finally at the following generalization of the effective action compared with that in the one-component condensed system [28]…”

“…As both α i =k = 0 and β i =k = 0, the Josephson equations split into two decoupled equations for each component of a mixture. In this case no interference in the mass currents appears and the response functions together with nonzero diagonal coefficients α ii , β ii go over to the quantities corresponding to the case of a single-component Bose-condensed gas [27,28].…”

“…In this paper, we will generalize the energy dissipation effects in the Josephson dynamics to the case of the binary Bose-condensed systems, employing functional integration approach of Ref. [28]. We will derive the expression for the effective action depending on two relative phases ϕ 1 and ϕ 2 between two condensed mixtures connected by a pointlike tunneling junction.…”