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

TL;DR

This paper proposes a method to controllably invert energy levels in a spin-orbit-coupled Bose-Einstein condensate, enabling transformation of excited states into ground states through adjustable parameters, with potential experimental realization.

Contribution

It introduces a controllable energy-level inversion technique in SO-coupled BECs using magnetic and trapping parameters, supported by exact linear solutions and numerical nonlinear analysis.

Findings

Energy-level inversion achieved by tuning SO coupling and magnetic gradient.

Linear system solved exactly, nonlinear results consistent with linear predictions.

Attractive interactions lead to superposition and edge states.

Abstract

A method to realize controllable inversion of energy levels in a one-dimensional spin-orbit (SO)-coupled two-component Bose-Einstein condensate under the action of a gradient magnetic field and harmonic-oscillator (HO) trapping potential is proposed. The linear version of the system is solved exactly. By adjusting the SO coupling strength and magnetic-field gradient, the energy-level inversion makes it possible to transform any excited state into the ground state. The full nonlinear system is solved numerically, and it is found that the results are consistent with the linear prediction in the case of the repulsive inter-component interaction. On the other hand, the inter-component attraction gives rise to states of superposition and edge types. Similar results are also reported for the system with the HO trap replaced by the box potential. These results suggest a possibility to realize any excited state and observe it in the experiment.