Bose–Einstein condensate in a bichromatic optical lattice: an exact analytical model

Ajay Nath and Utpal Roy

Laser Phys. Lett. 11 (2014) 115501: doi:10.1088/1612-2011/11/11/115501


We provide the first exact analytical method to investigate the dynamics of ultracold atoms trapped in geometrically frustrated optical lattices like bichromatic optical lattice (BOL).

The theoretical and experimental investigations on this system have attracted enormous attention in current literature. Overlapping two optical lattices of different depths and incommensurate wavelengths results in the formation of geometrical frustration in BOL. A variety of interesting physical phenomena have been reported in some of the recent experiments (Roati G et al 2008 Nature

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). However, no exact analytical solution for Bose-Einstein condensate in BOL potential was reported so far.

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On the other hand, it is an extremely non-trivial task to analytically solve the dynamical equation, even for a particular predefined potential. So far, the exact analytical solution is possible only for a few confinements: harmonic, periodic and double-well. Motivated by the above statement, in this letter we go beyond previous studies by considering 1D-Bose-Einstein condensate loaded in a tunable BOL with space and time modulated nonlinearities, gain or loss. Explicit localized bright (Fig. 1 & 3) and dark (Fig. 2 & 4) solitary wave excitations are reported using an exact analytical technique.

We reveal that the laser power and wavelength are the natural experimental tuning parameters for the modulation of condensate density. We find bright solitary waves in attractive interaction in this system which exhibits interesting variations with the depth of lattice frustration.

In the repulsive domain, we obtain localized dark soliton when the potential resembles an optical lattice. Interestingly, by tuning the potential parameter, the dark soliton gradually becomes modulated with the oscillatory background and finally transforms to bright solitary trains.