Tunable energy-level inversion in spin-orbit-coupled Bose-Einstein condensates

A method to realize controllable inversion of energy levels in a\none-dimensional spin-orbit (SO)-coupled two-component Bose-Einstein condensate\nunder the action of a gradient magnetic field and harmonic-oscillator (HO)\ntrapping potential is proposed. The linear version of the system is solved\nexactly. By adjusting the SO coupling strength and magnetic-field gradient, the\nenergy-level inversion makes it possible to transform any excited state into\nthe ground state. The full nonlinear system is solved numerically, and it is\nfound that the results are consistent with the linear prediction in the case of\nthe repulsive inter-component interaction. On the other hand, the\ninter-component attraction gives rise to states of superposition and edge\ntypes. Similar results are also reported for the system with the HO trap\nreplaced by the box potential. These results suggest a possibility to realize\nany excited state and observe it in the experiment.\n