Creating moving gap solitons in spin-orbit-coupled Bose-Einstein condensates

Abstract

It is known that the balance between dispersion and nonlinearity may generate solitons [1, 2]. Engineering dispersion and nonlinearity becomes a merited means to control over the existence of solitons and their dynamics. There is a particular kind of engineered dispersion, which is in the form of an avoided energy level crossing with an energy gap that forbids propagation of linear waves. The balance between such dispersion and nonlinearity places solitons inside the energy gap. Due to their specific location, they are named as gap solitons [3, 4]. Generalized massive Thirring models, possessing this dispersion as well as nonlinearity, become an ideal platform to theoretically stimulate gap solitons [5–11]. In experiments, periodic potentials can carry out energy gap opening in dispersion. The observation of gap solitons has been implemented experimentally in various nonlinear periodic optical systems, including fiber Bragg gratings [12], waveguide arrays [13], optically induced photonic lattices [14– 16], temporal lattices [17], and microcavities with periodic modulations [18]. In atomic Bose-Einstein condensates (BECs), optical lattices and spin-orbit coupling are responsible for dispersion engineering [19, 20]. Energy gaps can be opened up around Brillouin zone edges by optical lattices. Gap solitons are predicted theoretically [21, 22] and observed experimentally [23] inside these gaps. The study on matter-wave gap solitons in optical lattices soon represents an active research field [1, 2, 24–27]. Spin-orbit coupling, which can be implemented experimentally by Raman dressing of atomic hyperfine states [28], can modify dispersion in an interesting way that is different from optical lattices. The spin-orbit-coupled dispersion features many degenerated energy minima and has local avoided crossings [29]. It was predicted long time ago that the local spin-orbit-coupled energy gap can mimic generalized massive Thirring model and can support the existence of gap solitonlike solutions [30–34]. However, until now their experimental observations are not yet achieved. A possible experimental challenge may lay in preparation. In order to decorate BECs with spin-orbit coupling, Raman lasers are always ramped up adiabatically