Phase engineering of chirped rogue waves in Bose-Einstein condensates with a variable scattering length in an expulsive potential

TL;DR

This paper explores how phase engineering and temporal modulation of parameters in Bose-Einstein condensates can generate and control chirped rogue waves, revealing new ways to manipulate matter wave dynamics.

Contribution

It introduces a method to produce and control chirped rogue waves in BECs via phase imprinting and parameter modulation, using a transformation to an integrable KE equation.

Findings

Derived conditions for modulational instability leading to rogue waves.

Explicit first- and second-order chirped rogue wave solutions.

Demonstrated control of rogue wave evolution through temporal parameter modulation.

Abstract

We consider a cubic Gross-Pitaevskii (GP) equation governing the dynamics of Bose-Einstein condensates (BECs) with time-dependent coefficients in front of the cubic term and inverted parabolic potential. Under a special condition imposed on the coefficients, a combination of phase-imprint and modified lens-type transformations converts the GP equation into the integrable Kundu-Eckhaus (KE) equation with constant coefficients, which contains the quintic nonlinearity and the Raman-like term producing the self-frequency shift. The condition for the baseband modulational instability of CW states is derived, providing the possibility of generation of chirped rogue waves (RWs) in the underlying BEC model. Using known RW solutions of the KE equation, we present explicit first- and second-order chirped RW states. The chirp of the first- and second-order RWs is independent of the phase imprint. Detailed solutions are presented for the following configurations: (i) the nonlinearity exponentially varying in time; (ii) time-periodic modulation of the nonlinearity; (iii) a stepwise time modulation of the strength of the expulsive potential. Singularities of the local chirp coincide with valleys of the corresponding RWs. The results demonstrate that the temporal modulation of the s-wave scattering length and strength of the inverted parabolic potential can be used to manipulate the evolution of rogue matter waves in BEC.