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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Diffraction of atoms by a standing wave at Gaussian initial momentum distribution of amplitudes

Artur Mikhailovich Ishkhanyan

Published Dec 28, 1999• 0 citations
Publisher

Abstract

The role of the initial state preparation of the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum- mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from the maximum possible amount (determined by the limiting speed of stimulated photon re-emission acts) to zero. Consequently, for Gaussian atoms the standing wave presents an effective mirror with controllable reflection angle.

DOI
10.1117/12.375301

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 28, 1999•1 citation
The role of the initial state preparation of the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum- mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from the maximum possible amount (determined by the limiting speed of stimulated photon re-emission acts) to zero. Consequently, for Gaussian atoms the standing wave presents an effective mirror with controllable reflection angle.
The role of the initial-state preparation in the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum-mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from a maximum possible value (determined by the limiting speed of stimulated photon re-emission) to zero. Consequently, the standing wave presents an effective mirror for Gaussian atoms, the reflection angle being controllable.
The influence of the initial-state preparation on the diffraction of atoms in the field of a standing wave is discussed. The solution of the coherent scattering problem for rather general initial conditions involving initial atomic wave-packet splitting in the momentum space is obtained. A different effect of narrowing of the interference fringes of the diffraction pattern caused by secondary interference during the standing-wave scattering is discovered. The effect takes place at a specific type of initial wave-packet splitting involving two translation states whose momenta differ by even photon momenta, corresponding to the same, ground or excited, internal state. It is shown that a higher-order narrowing can be achieved using binomial wave packets. Further, another case that causes an asymmetrically narrowed diffraction is presented. An atomic-beam-splitting technique based on the preparation of atoms by STIRAP is proposed.
A model of the asymmetric coherent scattering process (caused by initial atomic wave-packet splitting in the momentum space) taking place at the large detuning and adiabatic course of interaction for an effective two-state system interacting with a standing wave of laser radiation is discussed. We show that the same form of initial wave-packet splitting may lead to different, in general, diffraction patterns for opposite, adiabatic and resonant, regimes of the standing-wave scattering. We show that the scattering of the Gaussian wave packet in the adiabatic case presents refraction (a limiting form of the asymmetric scattering) in contrast to the bi-refringence (the limiting case of the high-order narrowed scattering) occurring in the resonant scattering.
Atoms interacting with a standing wave are diffracted into even multiples of photon momentum. We argue that the spreading of the atomic momentum is analogous to the fanning out of Bloch vectors of an ensemble of two-level systems in coherent optics. It is shown that a continuous, time-proportional phase increment of the standing wave reverses the dynamics of the atoms and generates momentum echoes. Monte Carlo wave-function simulations are performed to see how the scheme works for realistic atomic models, taking spontaneous emission into account. Application of the echo formation to lifetime measurements of atoms is proposed.
Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.
The influence of the initial state preparation by an interaction with resonant traveling waves on the anomalous standing wave scattering of a two-level system with magnetic sublevels for arbitrary coherency (1) between the atomic sublevels and (2) between the polarizations of counterpropagating waves is discussed. The potential of the magnetic sublevels and light polarization in the formation of specific types of split initial momentum distributions is pointed out. It is found a new effect of narrowing of the interference fringes of the diffraction pattern taking place at particular case of the initial wave packet splitting involving two translation states, whose momenta differ by two photon momenta, corresponding to the same energy level. It is shown that this narrowing can be combined with the known asymmetric scattering.