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Physica Scripta

Generalized Bloch states of a two-level atom in the field of counterpropagating waves: application to the Kapitza–Dirac diffraction problem

G. A. Muradyan, Atom Zh. Muradyan

Published Oct 5, 2015• 2 citations
Publisher

Abstract

The Bloch-state approach to atomic translational states is extended out of adiabatic following and Raman–Nath approximations, taking into account the possible transfer of population from the initially populated internal energy level. The presented theory suggests a notion of potential energy corresponding to the initially populated internal state, and makes a generalization in the treatment of energy spectrum band-gap structure. Applying the theory to off-resonant Kapitza–Dirac diffraction and two-pulse standing wave atom interferometer (for the study of non-coherent processes in the cold atomic gases) we discuss the ability of the present approach for large-angle split multipath atom interferometry.

DOI
10.1088/0031-8949/90/11/115401

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The Bloch-state approach to atomic translational states is extended out of adiabatic following and Raman–Nath approximations, taking into account the possible transfer of population from the initially populated internal energy level. The presented theory suggests a notion of potential energy corresponding to the initially populated internal state, and makes a generalization in the treatment of energy spectrum band-gap structure. Applying the theory to off-resonant Kapitza–Dirac diffraction and two-pulse standing wave atom interferometer (for the study of non-coherent processes in the cold atomic gases) we discuss the ability of the present approach for large-angle split multipath atom interferometry.
The problem of resonant Kapitza – Dirac diffraction is solved in Raman – Nath approximation out of familiar Bessel function approximation (applicable in zero and very large resonance detuning cases). It shows new and promising results for the atom optics and atom interferometry if the atomic momentum state has been prepared in a form of discrete Gaussian distribution. Namely, instead of monotonic broadening within the Bessel function approximation, our formula yields in splitting of initial distribution into two identical peaks, whith preserving form, which symmetrically move away from the distribution center for the interaction time. A table-shaped form for the ultimate momentum distribution also is in frame of new distributions. As to relaxation processes, they have only quantitative influence on the pattern of diffraction.
We investigate the diffraction of a three-level atom from a "walking" light wave composed of counterpropagating traveling waves of different frequencies. The coupling of the two nondegenerate internal ground states by means of an off-resonant Raman transition resonantly couples the initial external momentum state to only one other momentum state. This happens even in the Raman-Nath regime, where the interaction time is short enough that momentum transfer is not constrained by phase-matching conditions. The final momentum state depends on the initial internal state of the atom and the relative directions of the two traveling waves. By using multiple diffraction regions, this process can be used to coherently split a beam of atoms into two beams that are widely separated in momentum space. This type of beam splitter would be useful in the building an atom interferometer.