Generation of vortex molecule in Bose-Einstein condensate by twisted light von Yuxiong Duan

Since its first realization in the 1990s, atomic Bose-Einstein condensate (BEC), a novel state of matter close to 0 Kelvin, has been an active research subject. In the last decade, studies have shown that it can be utilized as a clean and highly controllable platform for simulating various effects of solidstate physics. One prominent example is the spin-orbit coupling (SOC), which can be artificially induced by an external light field. In the exploration of different SOC schemes, a special type of light, twisted light, has attracted much attention. It is also known as optical vortex, which possesses an orbital angular momentum in addition to its spin angular momentum. The idea is to transfer the twisted light's orbital angular momentum to the condensate during the atomic transition. On the one hand, exotic spin vortices can be sculpted in the Bose matter wave. On the other hand, this process creates a spinorbitalangularmomentum coupled condensate. In this dissertation, we perform a thorough theoretical study of the above system. We will demonstrate the creation of vortex molecule in a spinor BoseEinstein condensate by twisted light. To arrive at this result, our bottomtotop discussion will cover three topics: selection rules, spinorbit interaction and quantum phase transition. We first deal with the electronic transition of a single atom induced by twisted light. We calculate the transition matrix element and derive the conditions for an allowed transition, i.e. the selection rules. We then take a further step by considering the centerofmass motion of the atom. We go beyond the paraxial regime of twisted light and investigate the dipole transition of a multilevel atom. We show the transfer of coupled spin and orbital angular momentum from a light to an atom. Finally, we return to the discussion of BEC by adding the collision between atoms. This nonlinear interaction leads to a spontaneous symmetry breaking of the system and enriches its ground-state phases. In particular, our numerical results show exotic phases with a structure of vortex molecule. We characterize the various vortex molecules and analyze their role in the symmetry breaking and quantum phase transitions.