Scattering by an oscillating barrier: Quantum, classical, and semiclassical comparison

Abstract

We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the scattered particle, while also providing the foundation for semiclassical theory. We use the semiclassical approach to selectively add quantum-mechanical effects such as interference and diffraction. We find good agreement between the quantum and semiclassical momentum distributions. Our methods and results can be used to understand quantum and classical aspects of transport mechanisms involving time-varying potentials, such as quantum pumping.

Quantum paddlewheel with ultracold atoms in waveguides

“…These parameters are accessible in experiments (compare with Table I in Ref. [43]). The quantum regime can be explored with wavepackets of BEC with interactions suppressed by Feshbach resonances, available for most species for which BEC has been created, including 39 K [39].…”

“…It would be actually simpler to use wavepackets of BEC instead as assumed here, since there would be no need for reservoirs at the end of the channels as when one literally mimics mesoscopic transport. There has already been progress in implementing the wavepacket approach in experiments on scattering by time-varying potentials, as described in a recent paper [43] some of us were involved in. That paper focused on an oscillating barrier, but the same setup can be used to create a paddlewheel pump, by introducing periodic translation of the barrier.…”

“…Additional features [43] need to be added to the semi-classical picture to incrementally describe those, which is not essential for the purpose of this paper. The primary conclusion here is that Fig.…”

Atom chip apparatus for experiments with ultracold rubidium and potassium gases

“…We have successfully loaded near-degenerate thermal 87 Rb atoms from the Z-wire trap into the atom chip dipole trap (see Figure 12(d)), which we are using for experiments in the vicinity of the atom chip. 36 In the MOT cell, we have successfully loaded atoms into the crossed dipole trap (see Figure 12(c)) from the magnetic trap by operating both traps simultaneously and performing RF evaporative cooling, following the method of reference: 14 we obtain a phase space density of 10 −4 with up to 6 × 10 6 87 Rb at μK-level temperatures and a 14 s lifetime in the retro-reflected 6 W dipole trap. We are optimizing the alignment of the crossed dipole trap lasers in preparation for evaporative cooling to higher phase space densities by lowering the trapping laser intensities.…”

Ballistic atom pumps

“…Our quantum calculations are performed in the same fashion as in [62], and are based on propagating the wave packet with the time-dependent Schrödinger equation via a split-step operator method [64]. We determine the net particle transport in these systems by the following process: 1) For each initial momentum, launch particles toward the barriers from the left, and compute and record the fraction transmitted and reflected.…”