Hydrodynamics studies of spin-orbit-coupled Bose systems

Abstract

The importance of spin-orbit coupling has been well-known in the fields of atomic physics and solid state physics. With advanced techniques in controlling ultracold atomic gases, it is now possible to create and manipulate spin-orbit coupling in highly controllable ways. Such successes in laboratory have ignited a lot of theoretical and experimental studies owing to its potential application in future technologies like quantum computer.

The effects of spin-orbit coupling on Bose-Einstein condensate have been discussed in numerous publications, but so far little has been investigated in the normal phase where temperature is above the condensation temperature. In the first half of this thesis, I will derive the hydrodynamical equations for a spin-orbit coupled Bose gas in its normal state. Because of spin-orbit coupling, the resulting equations are more complicated than usual, with coupling between spin and density degrees of freedom. However, several interesting phenomena, including the occurrence of persistent spin helix and the decay of spin helical structure can be obtained analytically and I discuss these in detail.

In the second half of the thesis, I study the elementary excitations of a homogeneous Bose-Einstein condensate with spin-orbit coupling. Due to non-linearity of phonon dispersion, it is possible that a single phonon of a given momentum decays into two phonons of different momentum while conserving total momentum and energy. It is long known in helium-4 as the Beliaev decay. Now the effect of spin-orbit coupling on Beliaev decay is investigated in detail. In particular, it is found that at the transition point between the two ground state phases (plane wave and zero momentum phases), phonon is softened and the Beliaev decay changes qualitatively.