Inelastic time dependent tunnelling of m

Tunnelling of ultra-cold atoms across a periodically displaced optical barrier exhibits characteristic inelastic effects as well as remarkable transparency at energies for which the same barrier, if stationary, would be opaque. Such phenomena could be observed with sodium Bose–Einstein condensate wavepackets and could be exploited for atom–laser sideband generation. Resonant tunnelling through a static double barrier is a well understood phenomenon extensively studied to tailor the transport properties of low-dimensional semiconductor structures. We explore a scenario where barrier spatial oscillations are not so fast, resulting in a weakly resonant tunnelling regime that markedly modifies the transmission of tunnelling particles. For sufficiently large amplitudes of oscillations, the interplay of barrier dynamics and wavepacket properties leads to significant inelastic processes that could enhance the efficiency of sideband generation in atom lasers. Specifically, we study the dynamics of a Gaussian atomic wavepacket moving across a harmonic square barrier experiencing oscillations in position. Our analysis demonstrates the conditions under which a transparency peak occurs, highlighting the necessity for wavepackets with narrow energy spreads, typical of those from Bose–Einstein condensates.