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arXiv:quant-ph/0703149 · Journal of Prime Research in Mathematics

Open-Loop Control of Quantum Particle Motion: Effective Splitting in Momentum Space

Ahmad, Babar, Sergey Borisenok, Saifullah, Rozhdestvensky, Yuri

Published Mar 16, 2007• 0 citations
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Abstract

In this paper an effective quantum particle beam-splitter in the momentum space is realized in the frame of open-loop control scheme. We demonstrate for small interaction time that the splitting effect $\pm40\hbar k$ with summarized relative intensity in both main components is about 50 per cent from initial intensity of the atomic beam.

DOI
10.48550/arxiv.quant-ph/0703149

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In this paper an effective quantum particle beam-splitter in the momentum space is realized in the frame of open-loop control scheme. We demonstrate for small interaction time that the splitting effect ±40ℏk\pm40\hbar k±40ℏk with summarized relative intensity in both main components is about 50 per cent from initial intensity of the atomic beam.
Atomic beam splitter needs for the practical realization of nano-scale lithography by coherent scattering of the atoms. We consider the different types of atomic beam splitters, which could be used for the creation of the space structures with nano-scale period. We concentrate to a few main schemes of an interaction between an atom beam and optical radiation, which can produce a large angle splitting of atom beam into only two main momentum components: multi Bragg scattering an atom wave packet in standing wave; coherent splitting by scattering of an atom wave packet in standing wave with modulated intensity, when the intensity of the standing wave changes harmonically. We discuss also the experimental possibility of an atom selection in internal states for obtaining of space periodical structure with high clearance.
Control in multi-zone atomic beam splitters needs for the practical realization of nanoscale lithography by coherent scattering of the atoms. We propose an effective atomic beam splitter based on the interaction of three-level atom with the field of the standing optical waves having relative spatial shifts. It is shown, that using of several interaction zones of the standing waves having the different spatial shift it make possible to reach the splitting 2n/spl planck/k (where n is the number of zone) in each of lower three-level /spl Lambda/-atom state.
A theory of an atom beam splitter is developed involving the interaction of standing-wave field pulses with $\ensuremath{\Lambda}$-type atoms. The beam splitter consists of two interaction zones, both treated in the Raman-Nath approximation. There is an initial, off-resonant field (or fields) that prepares the initial atomic state, followed by interaction with a pair of standing-wave field pulses. Using this configuration one is able to create a large-angle beam splitter with a significant suppression of unwanted momentum components. The roles of relaxation and a frequency chirp are investigated, as are initial conditions for which both ground states of the $\ensuremath{\Lambda}$ scheme are prepared by the first field. It is shown that the scheme is rather robust against fluctuations of system parameters.
The probability of separating k particles from a beam of n classical distinguishable particles by a beam splitter is given by the Bernoulli distribution. When turning to indistinguishable Bose quantum particles, this distribution is preserved by a refined interplay between interference and stimulation effects. This behaviour is demonstrated in an experiment where pairs of photons interact with an optical beam splitter. The distinguishability of the photons within a pair is changed by varying the degree of coherence.
The methods of mathematical control theory are widely used in the modern physics, but still they are less popular in quantum science. We will discuss the aspects of control theory, which are the most useful in applications to the real problems of quantum optics. We apply this technique to control the behavior of the two-level quantum particles (atoms) in the modulated external optical field in the frame of the so called "semi classical model", where quantum two-level atomic system (all other levels are neglected) interacts with classical electromagnetic field. In this paper we propose a simple model of feedforward (open-loop) control for the quantum particle system, which is a basement for further investigation of two-level quantum particle in the external one-dimensional optical field.