Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

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

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'.

Symmetry in Many-Body Physics

The harmony of nature is expressed through the implementation of symmetry providing optimal structures for complex systems from snowflakes to graphene lattices [...]

Formation of Matter-Wave Droplet Lattices in Multi-Color Periodic Confinements

In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion.