Three-dimensional Talbot optical superlattice produced by bichromatic cosine-Gaussian light beams

Abstract

In this paper, we show the use of the combination of co-propagating cosine-Gaussian laser beams to generate a deep three-dimensional (3D) optical superlattice for resonant particles (atoms, ions and similar ones). The method is based on the Talbot effect, non-diffracting properties of the cosine-Gaussian light beams and 3D rectification of a gradient force in a strong bichromatic field.

Opto-thermophoretic superlattice for atoms

“…2z 0 ≲ l coh ∼ c/Γ. Under the conditions described in sections 2.2 and 2.3, RcGF turns out to be the main factor determining the translational particle dynamics in the region D. Note that in the considered case of the collinear combination of the counterpropagating CGBs ( 9) and ( 10) the scattering forces generated by different components of the fields mutually compensate each other, and thus, for implementing OTSL smaller intensities are needed than in the case of the Talbot OTSL produced by the combination of co-propagating CGBs [27].…”

“…Now, we consider the case when the period of the OTSL is considerably smaller than the CGB envelope radius, λ w ≫ 1 (the case of a large number of trapping cells in the region D, see section 3.1). Then, to find the solution of Smoluchowski diffusion equation (27), we use the multiscale asymptotic method [35]. For this purpose, we introduce 'slow' transverse variables, r ′ j = r j /λ w , r ′ t = r ⊥ /λ w (where j = x, y) and treat r z as a 'fast' variable of the problem.…”

“…For this purpose, we introduce 'slow' transverse variables, r ′ j = r j /λ w , r ′ t = r ⊥ /λ w (where j = x, y) and treat r z as a 'fast' variable of the problem. We seek for the solution of equation (27) in the form of a power series expansion in λ −1…”

“…Ťi (r ′ t ) at l ⩾ 0. Substituting this expansion into equation (27), comparing the coefficients of 1/λ m and taking into account the z-periodicity of n, we obtain equations for finding the principal term of the asymptotic expansion…”