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arXiv:quant-ph/0209108 · Physical Review A

Momentum transfer using chirped standing-wave fields: Bragg scattering

Vladimir S. Malinovsky, P. R. Berman

Published Aug 27, 2003• 16 citations
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Abstract

We consider momentum transfer using frequency-chirped standing-wave fields. Atom-beam splitter and mirror schemes based on Bragg scattering are presented. It is shown that a predetermined number of photon momenta can be transferred to the atoms in a single interaction zone.
DOI
10.1103/physreva.68.023610

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We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.
A theory of Bragg scattering of atoms is presented in which atoms are scattered by counterpropagating optical fields having different frequencies. It is shown that, for this geometry, the system reduces to that encountered in the pump-probe spectroscopy of two or multilevel systems. As a result, one can tune the Bragg resonances by varying the frequency difference between the optical fields. The possiblity of using these techniques to construct an atom-beam splitter, whose output arms are separated in momentum space by a hundred photon momenta, is discussed.
Atoms undergo two types of momentum changes as they pass across a near-resonant standing wave. First, their transverse momentum spreads. Second, if the atoms cross the field at an angle, they undergo Bragg scattering from the periodic structure provided by the wave. Classically, this behavior can be understood in terms of traveling waves: the atom catalyzes the transfer of momentum from one traveling wave to the other, thereby changing its own transverse momentum. In the quantum regime, however, there is an essential difference between scattering by two running waves and by a standing wave. With running waves, we can in principle know which of the two waves has exchanged a unit of momentum with the atom. In contrast, a standing wave is an inseparable quantum unit whose average momentum remains zero at all times. This unity is imposed by the fixed mirrors that establish the standing wave. These act as infinite sinks of momentum. Quantum mechanics forbids one even in principle to determine, via a field measurement from which traveling wave the atom picked up its momentum. To demonstrate this point, we discuss the diffraction and deflection of an atom in both a standing wave and a superposition of two counter-propagating running waves.
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.