Bloch oscillations of cold atoms in two-dimensional optical lattices

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 6, 2003, Pages 9-

  Kolovsky, A R ^a,b   Korsch, H J ^c  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b KIRENSKY INSTITUTE OF PHYSICS   (Russian Federation)

^c University of Koblenz Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85037213600     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.67.063601     Document Type: Article

References (28)

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20. There is some freedom in defining the scaled Planck constant. We use the scaling which sets the prefactor for (Formula presented) and (Formula presented) terms to unity. Then the scaled Planck constant is given by (Formula presented) for (Formula presented) and (Formula presented) for (Formula presented) Let us also note that intermediate values of (Formula presented) cannot be realized by using the laser beam configuration considered and thus are not discussed here.
21. Localized Wannier states (Formula presented) (not to be confused with Wannier-Stark states) can be defined as the Fourier expansion of the Bloch states (Formula presented) over the quasimomentum: (Formula presented)
22. To be more precise, there are two alternative sets of the eigenfunctions in the case of a separable potential: the set of localized functions corresponding to infinitely degenerate discrete levels, and the set of Bloch-like functions corresponding to energy bands of zero width. In the case of nearest-neighbor hopping (the so-called von Neumann neighborhood) the latter were studied in Ref. 22. See also the recent paper 23, which extends the results of Ref. 22 beyond the von Neumann neighborhood.
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