Tunneling dynamics in exactly-solvable models with triple-well potentials

TL;DR

This paper develops a method using N=4 Supersymmetric Quantum Mechanics to analyze tunneling in exactly solvable triple-well potentials, revealing controllable tunneling behaviors relevant to atomtronics.

Contribution

It introduces explicit formulas for potentials, wavefunctions, and propagators in triple-well models using N=4 SQM, enabling detailed tunneling analysis.

Findings

Observation of Josephson-type tunneling transition

Identification of partial wave packet trapping

Non-monotonic tunneling dependence on potential shape

Abstract

Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein condensate dynamics, we apply a general technique of N=4 extended Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well potentials, i.e. symmetric and asymmetric. Expressions of quantum-mechanical propagators, which take into account all states of the spectrum, are obtained, within the N = 4 SQM approach, in the closed form. For the initial Hamiltonian of a harmonic oscillator, we obtain the explicit expressions of potentials, wavefunctions and propagators. The obtained results are applied to tunneling dynamics of localized states in triple-well potentials and for studying its features. In particular, we observe a Josephson-type tunneling transition of a wave packet, the effect of its partial trapping and a non-monotonic dependence of tunneling dynamics on the shape of a three-well potential. We investigate, among others, the possibility of controlling tunneling transport by changing parameters of the central well, and we briefly discuss potential applications of this aspect to atomtronic devices.