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Chinese Physics

The spatial properties of atomic Raman–Nath diffraction

Liping Li, Zhang Li-yan, Peijun Song, Xiao-Tao Xie, Weibin Li

Published Aug 1, 2007• 1 citation
Publisher

Abstract

This paper obtains the exact analytical solution of atomic Raman–Nath diffraction in the coordinate representation and discusses the influence of different initial conditions and detunings on the atomic spatial population distribution. The phase difference between the dipole matrix element and initial atomic population may influence the atomic spatial population distribution after diffraction, which has never been discussed before as far as we know. It offers a method to measure the phase by the spatial population distribution, which is interesting in the study of quantum optics.

DOI
10.1088/1009-1963/16/8/045

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This paper obtains the exact analytical solution of atomic Raman–Nath diffraction in the coordinate representation and discusses the influence of different initial conditions and detunings on the atomic spatial population distribution. The phase difference between the dipole matrix element and initial atomic population may influence the atomic spatial population distribution after diffraction, which has never been discussed before as far as we know. It offers a method to measure the phase by the spatial population distribution, which is interesting in the study of quantum optics.
We present an analysis of atomic diffraction due to the interaction of an atomic beam with a pair of Gaussian light pulses. We derive a simple analytical expression for the populations in different diffraction orders. The validity of the obtained solution extends beyond the Raman-Nath regime, where the kinetic energy associated with different diffraction peaks is neglected, into the so-called channeling regime where accurate analytical expressions have not previously been available for the diffraction. Comparison with experimental results and exact numerical solutions demonstrate the validity of our analytical formula.
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.
A quantum theory of stimulated Raman scattering is established that takes into account the time-dependence of pump laser pulse, two-photon detuning and atomic populations, allowing the general transient and spatial propagation study of Raman memory. Heisenberg–Langevin and Maxwell equations for the collective atomic operators are solved analytically under adiabatic condition , where the electric field envelopes and the collective atomic operators vary slowly. The analytical solution of Stokes/anti-Stokes signal electric field operator is obtained. The spatial–temporal intensity of quantum signal field is studied numerically and analytically for different two-photon detunings and initial populations.
The properties of the phase evolution of two coupled atoms Raman interacting with squeezed vacuum field are studied using the Pegg-Barnett phase theory. The phase probability distribution and variance are calculated. The evolution of the phase probability distribution functions in some cases are given by curves in the polar coordinate system. The influence of Raman interaction between the coupled atoms with squeezed vacuum field, the dipole-dipole interaction between the atoms and the initial states of atoms on the phase properties are discussed.