Anomalous Tunneling of Phonon Excitations between Two Bose-Einstein Condensates

Abstract

We discuss the tunneling of phonon excitations across a potential barrier separating two condensates. It is shown that a strong barrier proves to be transparent for the excitations at low energy epsilon. Moreover, the transmission is reduced with increasing epsilon in contrast to the standard dependence. This anomalous behavior is due to the existence of a quasiresonance interaction. The origin of this interaction is a result of the formation of a special well determined by the density distribution of the condensate in the vicinity of a high barrier.

Phase dependence of phonon tunnelling in bosonic superfluid–insulator–superfluid junctions

“…Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT qualitatively the same as that for the rectangular potential barrier [13] in the case of current-free condensate. Moreover, comparing equation (28) to equation (A.16) in appendix, we can see that the relation between the supercurrent and the phase difference for the δ-function potential is also qualitatively the same as that for the rectangular potential.…”

“…This means that the potential barrier is transparent for the low-energy excitations. This behaviour of the transmission coefficient, called anomalous tunnelling, has been predicted for a current-free condensate [13,14]. We can see from equation (61) that the peak width decreases as ϕ approaches ϕ c π/2, and it becomes infinitesimal for ϕ → ϕ c .…”

“…The anomalous tunnelling is predicted also for this rectangular potential barrier [13]. When the barrier is so high that 1/κ 0 ξ, e…”

“…which expresses the conservation law of the energy flux [13]. It is obvious that the reflection coefficient R and transmission coefficient T are defined from equation (43) as…”

“…where q expresses the current of the condensate fraction in dimensionless form and equation (13) corresponds to the equation of continuity. In dimensional form, the current is expressed ashq n 0 /m.…”