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Quantum Electronics

Momentum state preparation of a two-level atom using Kapitza – Dirac diffraction

A. E. Movsisyan, G. A. Muradyan

Published Sep 30, 2014• 1 citation
Publisher

Abstract

We report a theoretical study on the possibility of preparing different types of momentum state distributions by two successive resonant Kapitza – Dirac diffractions. It is shown that table-shaped and Gaussian distributions can be obtained as well as the initial single-momentum state can be almost completely reconstructed by the end of the second phase of scattering. We outline the interferometric purposes for which these distributions can be promising. The advantage of the method proposed is the weak dependence of the scattering patterns of interest on such parameters of the system as the field intensity and interaction time.

DOI
10.1070/qe2014v044n09abeh015250

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We report a theoretical study on the possibility of preparing different types of momentum state distributions by two successive resonant Kapitza – Dirac diffractions. It is shown that table-shaped and Gaussian distributions can be obtained as well as the initial single-momentum state can be almost completely reconstructed by the end of the second phase of scattering. We outline the interferometric purposes for which these distributions can be promising. The advantage of the method proposed is the weak dependence of the scattering patterns of interest on such parameters of the system as the field intensity and interaction time.
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.
In a momentum space, the resonant Kapitza–Dirac effect is described by the difference Schrödinger equation the step of which is the two-photon recoil momentum. For the interferometry of a multipath atom, the case of intense counter-propagating waves is of interest, when the number of generated momenta can reach to some tens. After that, in an intermediate stage of calculations, the discrete momentum distribution is regarded as a continuous one, and the Taylor expansion is applicable to it. This approximation preserves the spectrum of a diffraction well, in particular, the formation of a pair of almost monopulse states from the initial Gaussian distribution.
We consider the interaction of a traveling optical wave with a resonant two-level atom, which is initially in its general superposition state, i.e., in the superposition state of the ground and excited internal energy levels and simultaneously has mutually different momentum distributions, corresponding to each of these internal energy levels. We show that during the interaction, the atom periodically gets large-scale changes in these momentum distributions. As a consequence, a portion of the atomic momentum of the states, corresponding to each internal energy level, gets large-scale changes too, much more than the momentum $\ensuremath{\Elzxh}k$ of an absorbed/emitted photon. The amount of momentum that a photon transfers between the atomic internal energy levels is in general more than its own momentum $\ensuremath{\Elzxh}k.$ The special case is discussed in which the atom's preliminary superposition state is created as a result of interaction of the atom with the resonant standing wave. Also it is pointed out that in appropriate time intervals the mentioned phenomenon can be presented as a transformation of the resonant Kapitza-Dirac splitting of atomic states into the Stern-Gerlach-type splitting.