Modulational Instability of Trapped Two-Component Bose–Einstein Condensates**Supported by the National Natural Science Foundation of China under Grant Nos 11764039, 11847304, 11865014, 11475027, 11274255 and 11305132, the Natural Science Foundation of Gansu Province under Grant No 17JR5RA076, and the Scientific Research Project of Gansu Higher Education under Grant No 2016A-005.

Abstract

The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.