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arXiv · 1602.01001

Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well potentials

Krzysztof B. Zegadlo·Nir Dror·Marek Trippenbach·Miroslaw A. Karpierz·Boris A. Malomed
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Abstract

We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and BEC. The order in which the SSB and self-trapping transitions take place with the growth of the nonlinearity strength depends on the height of the central barrier of the DWP: the SSB happens first if the barrier is relatively high, while self-trapping comes first if the barrier is lower. The SSB of the leaky modes is characterized by specific asymmetry of their radiation tails, which, in addition, feature a resonant dependence on the relation between the total size of the system and radiation wavelength. As a result of the SSB, the instability of symmetric modes initiates spontaneous Josephson oscillations. Collisions of freely moving solitons with the DWP structure admit trapping of an incident soliton into a state of persistent shuttle motion, due to emission of radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.

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Krzysztof B. Zegadlo, Nir Dror, Marek Trippenbach, Miroslaw A. Karpierz, Boris A. Malomed. 2016-02-02. Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well potentials. https://doi.org/10.1103/physreva.93.023644

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