Asymmetric Tunneling of Bose-Einstein Condensates

Abstract

In his celebrated textbook, Quantum Mechanics-Nonrelativistic Theory, Landau argued that, for single particle systems in 1D, tunneling probability remains the same for a particle incident from the left or the right of a barrier. This left-right symmetry of tunneling probability holds regardless of the shape of the potential barrier. However, there are a variety of known cases which break this symmetry, e.g. when observing composite particles. First, we set about proving Landau's argument, as no rigorous proof currently exists. We then computationally show breaking of the left-right tunneling symmetry for the Bose-Einstein condensates (BEC) in 1D, modeled by the Gross-Pitaevskii equation. By varying the parameter, g, of inter-particle interaction in the BEC, we demonstrate the transition from symmetric (g = 0) to asymmetric tunneling is a threshold phenomenon. Our computations employ experimentally feasible parameters such that these results may be experimentally demonstrated in the near future. We conclude by suggesting applications of the phenomena to design atomtronic diodes, synthetic gauge fields, Maxwell's demons, and blackhole analogues.

Tunneling Gravimetry

“…Such barriers can be generated [25,26] or painted [27] experimentally with the help of spatial light modulators [28,29], digital (micro)mirror devices [26,30], and acousto-optic deflectors [31,32]. Tunneling [33][34][35] leads to a transmission of the incident mater wave though the barrier. It is a purely quantum mechanical effect without any classical counterpart.…”