Generation of higher harmonics in dipolar Bose–Einstein condensates trapped in periodically modulated potentials

Abstract

We consider a quasi-one-dimensional Bose–Einstein condensate with contact and long-range dipolar interactions, under the action of the time-periodic modulation applied to the harmonic-oscillator and optical-lattice trapping potentials. The modulation results in generation of a variety of harmonics in oscillations of the condensate’s width and centre-of-mass coordinate. These include multiple and combinational harmonics, represented by sharp peaks in the system’s spectra. Approximate analytical results are produced by the variational method, which are verified by systematic simulations of the underlying Gross–Pitaevskii equation. This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.

Introduction to ‘New trends in pattern formation and nonlinear dynamics of extended systems’

“…The spontaneous formation of a coherent density wave (supersolid) in a BEC, which was predicted by the theory far ago [ 26 , 27 ], has been discovered in experiments [ 28 ]. In [ 29 ], a dipolar BEC trapped by a combination of harmonic-oscillator (HO) and optical-lattice (OL) potentials is considered. The action of a time-periodic modulation of the HO frequency and/or OL depth is studied in the framework of an appropriate modification of the Gross–Pitaevskii equation, by means of a variational approximation and by direct numerical solution.…”