Control of the symmetry breaking in double-well potentials by the resonant nonlinearity management

TL;DR

This paper studies how periodic modulation of nonlinearity in a Bose-Einstein condensate within a double-well potential can control symmetry-breaking effects, inducing trapping or detrapping depending on the nonlinearity sign.

Contribution

It introduces a model combining double-well potentials with time-periodic nonlinearity management, revealing resonance effects that control symmetry breaking in BECs.

Findings

FRM induces self-trapping in repulsive BECs via parametric resonance.

FRM causes detrapping in attractive BECs, possibly through higher-order resonance.

Oscillation frequencies relate to half or quarter of the modulation frequency.

Abstract

We introduce a one-dimensional model of Bose-Einstein condensates (BECs), combining the double-well potential, which is a well-known setting for the onset of spontaneous-symmetry-breaking (SSB) effects, and time-periodic modulation of the nonlinearity, which may be implemented by means of the Feshbach-resonance-management (FRM) technique. Both cases of the nonlinearity which is repulsive or attractive on the average are considered. In the former case, the main effect produced by the application of the FRM is spontaneous self-trapping of the condensate in either of the two potential wells in parameter regimes where it would remain untrapped in the absence of the management. In the weakly nonlinear regime, the frequency of intrinsic oscillations in the FRM-induced trapped state is very close to half the FRM frequency, suggesting that the effect is accounted for by a parametric resonance. In the case of the attractive nonlinearity, the FRM-induced effect is the opposite, i.e., enforced detrapping of a state which is self-trapped in its unmanaged form. In the latter case, the frequency of oscillations of the untrapped mode is close to a quarter of the driving frequency, suggesting that a higher-order parametric resonance may account for this effect.