Chaotic transport of a matter-wave soliton in a biperiodically driven optical superlattice

Under the effective particle approximation, we study the temporal ratchet effect for chaotic transport of a matter-wave soliton consisting of an attractive Bose–Einstein condensate held in a quasi-one-dimensional symmetric optical superlattice with biperiodic driving. It is known that chaos can substitute for disorder in Anderson's scenario [Wimberger S, Krug A, Buchleitner A. Phys Rev Lett 2002;89:263601] and only a higher level of disorder can induce Anderson localization for some special systems [Schwartz T, Bartal G, Fishman S, Segev M. Nature 2007;46:52], and a matter-wave soliton can transit to chaos with high or low probability in a high- or low-chaoticity region [Zhu Q, Hai W, Rong S. Phys Rev E 2009;80:016203]. Here we demonstrate that varying the driving phase to break the time reversal symmetry of the system can increase the size of the high-chaoticity region for low- and moderate-frequency regions. Consequently, the parameter region of the exponential spatial localization increases to the same size, and the low-chaoticity and delocalization region, which includes subregions of the ratchet effect and its inverse effect, correspondingly decreases. The positive dependence of the localization on the driving frequency is also revealed. The results indicate that a high-chaoticity region could replace higher disorder and assists in Anderson localization. From the results we suggest a method for controlling directed motion of a matter-wave soliton by adjusting the driving frequency and amplitude to strengthen or suppress, or even reverse, the temporal ratchet effect.