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Abstract
We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields of physics such as optics and Bose-Einstein condensates. We demonstrate that designing an optimal relation between the nonlinearity and the linear gradient strength provides extremely long-lived Bloch oscillations with little degradation. Such robust oscillations can be observed for a broad range of parameters and even for moderate nonlinearities and large enough values of linear potential. We also present an approximate analytical description of the wave packet’s evolution featuring a hybrid Bloch oscillating wave-soliton behavior that excellently corresponds to the direct numerical simulations.
Highlights
We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one
Correspondence and requests for materials should be addressed to R.D. www.nature.com/scientificreports/. Motion of such systems consists in their exact integrability, the physical explanation relies on the property of a specific nonlocal nonlinearity in such models which leads to stable Bloch modes at both band edges[16]
The competing effects of the nonlinearity, strength of linear potential and dispersion, are analyzed in Fig. 2(b) where we study the spread of the wave packet Δ(t) after sufficiently long evolution time, at t = 3000, for fixed linear gradients γ as function of the strength of the nonlinearity g
Summary
We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. A few years later, for atoms in optical lattices[8] and for coupled waveguides[9] BOs have been realized This proves that BOs can be considered in a broader context as a fundamental effect that may occur in systems which support wave propagation in media with periodically-varying parameters and with a linear potential. We fill this gap and introduce and analyze a physically-relevant non-integrable model which does show BO dynamics persisting for long times at considerable nonlinearities and linear gradients As it is demonstrated below, balance between the effects of the nonlinearity and the dispersion can be achieved in systems that contain an additional dimension besides the dimension corresponding to the direction of the linear gradient. This balance may result in the existence of very stable oscillatory motion of discrete-continuous soliton-like wave packets
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