Quantum scattering of droplets by wells and barriers in one-dimensional Bose-Bose mixtures

TL;DR

This paper studies how one-dimensional quantum droplets scatter from potential wells and barriers, revealing velocity-dependent reflection, transmission, and phase effects with implications for droplet interactions.

Contribution

It provides analytical and numerical analysis of droplet scattering, identifying critical velocities, phase shifts, and regimes of reflection and transmission in Bose-Bose mixtures.

Findings

Sharp transition between reflection and transmission at critical velocity.

Small droplets form symmetric trapped modes; large droplets form asymmetric trapped states.

Reflectionless wells induce a π-phase shift affecting collisions.

Abstract

We investigate, both analytically and numerically, the scattering of quasi-one-dimensional quantum droplets from P\"oschl-Teller potential wells and barriers. For attractive wells, we find a sharp transition between complete reflection and transmission at a critical incident velocity for both small and large flat-top droplets. The scattering interactions differ: small, soliton-like droplets form a spatially symmetric trapped mode at the critical velocity, showing their compressibility and coherence characteristics, while large droplets develop a spatially asymmetric trapped state, revealing incompressibility and internal structure. The critical velocity depends non-monotonically on atom number: it rises in the small, compressible-droplet regime, falls in the incompressible, flat-top regime, and turns at the crossover point. We also show that the reflectionless well generates a $\pi$-phase shift, strongly altering droplet-droplet collisions relative to free space. The persistence of a confined mode after collisions between trapped and incident droplets depends sensitively on their relative phase. For the repulsive barrier, we identify regimes of complete reflection, partial return, and full transmission, depending on incident velocity, barrier height, and particle number. Our predictions match direct numerical simulations in all cases.