Research Seminar in Mathematics - Tunable spin-orbit-coupled Bose-Einstein condensates in deep optical lattices

Speaker

Prof. F.Kh. Abdullaev, Physico-technical Institute, Tashkent, Uzbekistan.

Abstract

Binary mixtures of Bose-Einstein condensates (BECs) trapped in deep optical lattices and subjected to equal contributions of Rashba and Dresselhaus spin-orbit coupling(SOC)are investigated in the presence of a periodic time modulation of the Zeeman field. SOC tunability is explicitly demonstrated by adopting a mean-field tight-binding model for the BEC mixture and by performing an averaging approach in the strong modulation limit. In this case, the system can be reduced to an unmodulated vector discrete nonlinear Schr\’’odinger equation with a rescaled SOC tuning parameter α, which depends only on the ratio between amplitude and frequency of the applied Zeeman field. We consider the attractive interaction case and focus on the effect of the SOC tuning on the localized ground states. The dependence of the spectrum of the linear system on α has been analytically characterized. The stability of ground states in the presence of the modulating field has been demonstrated by real-time evolutions of the original (unaveraged) system. Localization properties of the ground state induced by the SOC tuning, and a parameter design for possible experimental observation, have also been discussed.