Dynamics of a macroscopic spin qubit in spin-orbit coupled Bose-Einstein condensates

We consider a macroscopic spin qubit based on spin-orbit coupled Bose-Einstein condensates, where, in addition to the spin-orbit coupling, spin dynamics strongly depends on the interaction between particles. The evolution of the spin for freely expanding, trapped, and externally driven condensates is investigated. For condensates oscillating at the frequency corresponding to the Zeeman splitting in the synthetic magnetic field, the spin Rabi frequency does not depend on the interaction between the atoms since it produces only internal forces and does not change the total momentum. However, interactions and spin-orbit coupling bring the system into a mixed spin state, where the total spin is inside rather than on the Bloch sphere. This greatly extends the available spin space making it three-dimensional, but imposes limitations on the reliable spin manipulation of such a macroscopic qubit. The spin dynamics can be modified by introducing suitable spin-dependent initial phases, determined by the spin-orbit coupling, in the spinor wave function.