Lower energy excitations and unique collective dynamics in a spin-tensor–momentum coupled Bose–Einstein condensates

Spin tensor–momentum coupling (STMC) in Bose–Einstein condensates (BECs) induces rich ground-state phases and multicritical points for phase transition. However, the physics of STMC BECs at the multi-critical point remains unexplored. Particularly, the collective dynamics, which can provide an ideal way to identify the multi-critical point and explore the novel dynamics of STMC system at the multi-critical point, has never been discussed. Here, considering the atomic interactions, the collective dynamics in a nonuniform STMC BECs is presented analytically and numerically. Particularly, the frequency of the breathing mode is derived by taking into account the local current of the condensate, allowing for a theoretical investigation of the impact of STMC on breathing dynamics. A tricritical point is predicted and novel physical phenomena at this point are observed: different types of energy bands merge, first- and second-order phase transitions meet, and unique collective dynamics occurs. The strongest softening of the lower frequency collective modes at the tricritical point is observed, while the higher frequency collective modes show a linear (parabolic) structure near the phase transition point when the system is below (above) the tricritical point, making the collective dynamics below and above the tricritical point is distinct. Softening of collective modes between two plane wave phases are observed in STMC system, which cannot occur in the ordinary SO coupled BECs. The tricritical point implies unique physics of STMC system, which can be well manipulated by spin-dependent interaction, STMC strength and external trapping potential. We provide a dynamical way to identify the tricritical point and establish a theoretical evidence for deep understanding and experimental manipulation of novel quantum physics in STMC systems.