Helicoidal spin–orbit coupling induced novel nonlinear dispersion relation and Landau–Zener tunneling dynamics
Geng Zhao, Haibin Tang, Junyan Yao +4 more
Abstract Spin–orbit (SO) coupling enriches the single-particle dispersion relation, inducing dramatic change of the ground state phase and non-equilibrium quantum dynamics. Here, the nonlinear energy spectrum and Landau–Zener (LZ) tunneling dynamics in helicoidal SO coupled Bose–Einstein condensates are studied. The interplay of atomic interactions and helicoidal SO coupling results in novel nonlinear energy spectrum and LZ tunneling dynamics. Two distinct helicoidal SO avoided crossing points in the energy spectrum are predicted, i.e. a normal avoided crossing point characterized with degenerate eigenenergies and non-degenerate eigenstates, and an abnormal avoided crossing point analogous to the exceptional point in non-Hermitian system characterized with both degenerate eigenenergies and eigenstates. When the effective atomic interaction beyond a threshold, normal and abnormal loops emerge at the corresponding crossing points successively. Particularly, by adjusting the system parameters (e.g. atomic interactions), the two avoided crossing points and loops can co-exist in different bands, and the two loops even collide and merge. When the atoms are accelerated and move adiabatically along the energy band, atoms can steadily cross the normal avoided crossing point and normal LZ tunneling dynamics takes place at the edge of the normal loop, while an abnormal LZ tunneling dynamics is excited successively at the abnormal avoided crossing point and the edge of the abnormal loop. The two avoided crossing points and loops result in distinct LZ tunneling dynamics. Furthermore, the helicoidal SO coupling induces spatial symmetry broken of energy band, resulting in nonreciprocal LZ tunneling, i.e. the tunneling probabilities for right-ward and left-ward sweeping are different. The novel energy spectrum and tunneling dynamics are further understood with the help of the evolution of fixed points in classical Hamiltonian phase space. We provide a theoretical evidence for experimental probing and manipulation of nonlinear dispersion relation and quantum tunneling dynamics in ultracold atomic gases.
New Journal of Physics•Jul 1, 2025•1 citation