Tunneling dynamics in exactly solvable models with triple-well potentials

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.

Tunneling and quantum localization in chaos‐driven symmetric triple well potential: An approach using quantum theory of motion

“…Tunneling also plays very important roles in some of the major biological processes like photosynthesis, protein activation, self‐repair of DNA, and enzymatic catalysis . Study of tunneling by placing the quantum particle in symmetric double well potential, asymmetric double wells are very common practice although the use of “breathing” double well and triple well potentials has become popular in recent times.…”

“…Tunneling also plays very important roles in some of the major biological processes like photosynthesis, protein activation, self-repair of DNA, and enzymatic catalysis. [10] Study of tunneling by placing the quantum particle in symmetric double well potential, asymmetric double wells [11,12] are very common practice although the use of "breathing" double well [13,14] and triple well potentials [15][16][17][18][19][20] has become popular in recent times.Since the ideas of quantum computation and building of quantum computers have taken shapes, tunneling in driven quantum systems has been an emerging area of research and with the development in quantum cryptography, the importance increases many folds. In early nineties, Lin and Ballentine have theoretically predicted the tunneling enhancement in a driven double well, [21,22] known as chaos assisted tunneling (CAT) [23][24][25] while in 1991 Grossmann and his group have done the first theoretical work on coherent destruction of tunneling (CDT), [26] later confirmed by many other researchers.…”

Solution of the “Classical” Schrödinger equation for a driven symmetric triple well: A comparison with its classical counterpart

“…The effect of viscosity on the isomerization process, rate of isomerization, reaction path analysis, are some of the studies in this respect. The advantage of triple well potential is that the transition of particle from one well to other is spatial symmetry guided and thus the driven triple well potential is a very useful model for atomtronic devices . Also, the idea of resonant tunneling and quantum fluctuation can be applied to the coherent tunneling via adiabatic passage, vanishing central‐well population in adiabatic transport, etc.…”

“…For dynamical study, although double well potential and harmonic well are mostly used by researchers, the study using triple well potential is not very uncommon. [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] In study of reaction dynamics of isomerization process among three species, triple well potential is a very good model as the three wells can represent the three species. [36][37][38][39][40][41] The effect of viscosity on the isomerization process, [35] rate of isomerization, [36,38,39,41] reaction path analysis, [37] are some of the studies in this respect.…”

“…Since early days, periodically driven quantum well potentials are seemed to be very important research models for studying phenomena like tunneling and its control, may be enhancement or suppression, quantum localization of particle, simple quantum chaos using Fermi accelerator, etc. For dynamical study, although double well potential and harmonic well are mostly used by researchers, the study using triple well potential is not very uncommon . In study of reaction dynamics of isomerization process among three species, triple well potential is a very good model as the three wells can represent the three species .…”