Higher eigenmodes of matter wave solitons in parity-time symmetric complex potential

Abstract

Summary This work analyzes the higher eigenmodes of matter wave solitons in parity-time (PT) symmetric complex potential using variational and numerical methods. The dynamical states of the system have been investigated both in the linear and the nonlinear regime. In the linear case the particle number (power in optics) of the higher eigen mode remains constant for low values of imaginary part of the potential (gain/loss term). The system exhibits a spontaneous phase transition from PT symmetric regime to broken PT symmetric regime. The PT phase transition point depends on the strength of the imaginary component of the potential. The system has also been studied by applying the self-focusing cubic nonlinearity. For low values of the strength of the imaginary part of the potential the stable matter wave solitons are formed. The PT symmetric regime strongly depends on the strength of the nonlinear coefficient and the chemical potential (the propagation constant). For large values of the nonlinearity the particle number of the higher eigenmode increases which leads to the collapse of the solitons. The stable solitons are formed in a weak nonlinear system with low values of the strength of the imaginary potential. The variational results are found to be in close agreement with numerical results.