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

Abstract

We provide an exact analytical model for the dynamics of a 1D Bose–Einstein condensate loaded in a bichromatic optical lattice. Although a host of exact solutions result from this novel method, we mainly concentrate on the solitonic excitations. The trapping potential and its depth of lattice frustration can be varied by tuning the power and the wavelengths of the two overlaying laser beams. Both attractive and repulsive regimes are thoroughly investigated. In the attractive domain, we obtain bright soliton, which reveals interesting variations with the depth of lattice frustration. Localization of the matter wave density is demonstrated as one of the applications in this regime. In the repulsive domain, dark soliton is obtained when the potential resembles an optical lattice. With appropriate tuning of the potential parameter, the dark soliton becomes modulated with an oscillatory background and gradually transforms to bright solitary trains.

Exact Analytical Model for Bose-Einstein Condensate at Negative Temperature

“…It clearly exhibits the axially compression of number density with β. This axial compression of atom number density can be attributed to the depth of lattice site and also the depth of lattice frustration 30,31 , gradually showing the localization of condensate atoms towards the central lattice site due to the presence of disorder potential 28 . This localization of atom density indicates the increase in negative temperature.…”

“…The motivation for considering BOL trap are threefold: (i) conversion to optical lattice (OL): BOL is generated by the superposition of two OL's of different wavelengths and intensities 22 . By tuning the power and the wavelength of the constituent laser beams, one can create a pure OL in a special case and vice-versa, allowing precise control over the shape of the trap profile; (ii) simulator for other systems like condensed matter physics in the context of supersolidity [23][24][25] ; (iii) rich in physical phenomena: a number of interesting phenomena are already observed in BOL making it a suitable test-bed for studying them in negative temperature scenario [26][27][28][29][30][31] . In addition to BOL, we have also added a linear trap for incorporating an overall asymmetry to the potential.…”

Long-time averaged dynamics of a Bose–Einstein condensate in a bichromatic optical lattice with external harmonic confinement

“…At low V 0 , the effect of lattice frustration is absent in our systems because the external harmonic trap suppresses it. With an increase of the lattice frustation depth, more intersite tunneling of the BEC is allowed [12] and the kinetic energy rises thereof. Indeed, the secondary OL in the presence of a primary OL of a high intensity (e.g.…”

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

“…In particular, the study of BEC under the action of geometrically frustrated OLs has drawn much interest [15][16][17][18]. Many complex phenomena have been found in this connection, including Anderson-like localization and negative absolute temperature [17,[19][20][21].…”

“…In particular, the study of BEC under the action of geometrically frustrated OLs has drawn much interest [15][16][17][18]. Many complex phenomena have been found in this connection, including Anderson-like localization and negative absolute temperature [17,[19][20][21]. Optical superlattices subjected to frustration offer potential for the development of tools which can hold and mould robust matter-wave states, such as solitons [22][23][24][25][26].…”