Theory of Quantum Gap Solitons

Ray‐Kuang Lee, Elena A. Ostrovskaya, Yuri S. Kivshar +1 more

We study quantum-noise squeezing and quantum correlations of gap solitons in a Bose-Einstein condensate loaded into a one-dimensional optical lattice. By employing a linearized quantum theory we find that quantum-noise squeezing of gap solitons, produced during their evolution, is enhanced compared with the atomic solitons in a lattice-free case due to intrasoliton structure of quantum correlations induced by the Bragg scattering in the periodic potential. We also show that nonlinear interaction of gap solitons in dynamically stable bound states can produce strong atom-number correlation between the soliton pairs.

A. S. Chirkin

Szu-Cheng Cheng

A one-band effective-mass (EFM) theory was developed to study the properties of the localized states of a Bose-Einstein condensate (BEC) in a periodic optical potential with either attractive or repulsive atom interactions. The localized states of the BEC are solitons in the gaps or gap solitons. The analytic solutions of the gap solitons are a Bloch function from periodicity, modulated by a soliton envelope function of the nonlinear Schrödinger equation. The soliton width is determined by the detuning chemical potential from the band edge. The detuning chemical potential in the nonlinear Schrödinger equation indicates that not all the atoms in the condensate are used for forming gap solitons, and that some atoms form the background of nonlinear modes. The background atoms are determined by the chemical potential at the band edge. The gap solitons form on top of the background atoms. PACS numbers: 03.75.Lm, 03.75.Kk, 05.30.Jp I.

Lai Yinchien

Andreas Sizmann

Zhang Ming-Rui, Yongliang Zhang, Jiang Xun-Ya +1 more

We systematically investigate the motion of slowly moving matter–wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross–Pitaevskii equation.