Dynamical Phase Transitions and the Kibble Zurek Mechanism in Spin-Orbit Coupled BECs

We investigate non-equilibrium dynamics using a spin-orbit coupled Bose-Einstein condensate with a tunable optical matching lattice in momentum space. Based on previous work with self-trapping in a double well dispersion relation, we explore the phase space in order to study second-order phase transitions relating to the Kibble Zurek Mechanism (KZM). This is realized by combining two fixed-angle Raman beams to couple the spin and linear momentum of the atoms. Momentum space dynamics are induced by an appropriate quench protocol with the Raman detuning. An added weak optical lattice is used to enhance the coupling between the spin-orbit coupled states. Spin and momentum resolved imaging provides a single-state resolution with a high number of atoms. By probing phase space across critical points, we measure the delay time associated with the KZM. This presentation highlights the current work and future research on dynamical phase transitions and the KZM.