Atomic-molecular Bose-Einstein condensates (BECs) offer brand new opportunities to revolutionize quantum gases and probe the variation of fundamental constants with unprecedented sensitivity. The recent realization of spin-orbit coupling (SOC) in BEC
s provides a new platform for exploring completely new phenomena unrealizable elsewhere. However, there is no study of SOC atomic-molecular BECs so far. Here, we find a novel way of creating a Rashba-Dresselhaus SOC in atomic-molecular BECs by combining the spin dependent photoassociation and Raman coupling, which can control the formation and distribution of a new type of topological excitation -- carbon-dioxide-like Skyrmion. This Skyrmion is formed by two half-Skyrmions of molecular BECs coupling with one Skyrmion of atomic BECs, where the two half-Skyrmions locates at both sides of one Skyrmion, which can be detected by measuring the vortices structures using the time-of-flight absorption imaging technique in real experiments.
We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in
the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.
We present the stability analysis of the dark states in the adiabatic passage for the linear and non-linear lambda and tripod systems in the presence of amplitude damping (losses). We perform an analytic evaluation of the real parts of eigenvalues of
the corresponding Jacobians, the non-zero eigenvalues of which are found from the quadratic characteristic equations, as well as by the corresponding numerical simulations. For non-linear systems, we evaluate the Jacobians at the dark states. Similarly to the linear systems, here we also find the non-zero eigenvalues from the characteristic quadratic equations. We reveal a common property of all the considered systems showing that the evolution of the real parts of eigenvalues can be split into three stages. In each of them the evolution of the stimulated Raman adiabatic passage (STIRAP) is characterized by different effective dimension. This results in a possible adiabatic reduction of one or two degrees of freedom.
