Persistence of equilibrium states in an oscillating double-well potential

TL;DR

This paper explores how parametric drives influence the stability of equilibrium states in nonlinear coupled wave systems, with implications for controlling optical and matter wave tunneling in oscillating double-well potentials.

Contribution

It demonstrates that parametric drives can stabilize or destabilize equilibrium states, providing a new method to control nonlinear wave dynamics in oscillating double-well systems.

Findings

Drive can stabilize or destabilize equilibrium states.

Parametric drive influences symmetry breaking bifurcation points.

Analytical averaging methods support numerical results.

Abstract

We investigate numerically parametrically driven coupled nonlinear Schrodinger equations modelling the dynamics of coupled wavefields in a periodically oscillating double-well potential. The equations describe among other things two coupled periodically-curved optical waveguides with Kerr nonlinearity or horizontally shaken Bose-Einstein condensates in a double-well magnetic trap. In particular, we study the persistence of equilibrium states of the undriven system due to the presence of the parametric drive. Using numerical continuations of periodic orbits and calculating the corresponding Floquet multipliers, we find that the drive can (de)stabilize a continuation of an equilibrium state indicated by the change of the (in)stability of the orbit. Hence, we show that parametric drives can provide a powerful control to nonlinear (optical or matter wave) field tunneling. Analytical approximations based on an averaging method are presented. Using perturbation theory the influence of the drive on the symmetry breaking bifurcation point is discussed.