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Physical Review A

Momentum transfer for an optical transition in a prepared two-level atom

A. Zh. Muradyan, H. L. Haroutyunyan

Published Jun 5, 2000• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.62.013401

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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\Elzxhk\ensuremath{\Elzxh}k\ensuremath\Elzxhk 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\Elzxhk.\ensuremath{\Elzxh}k.\ensuremath\Elzxhk. 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.
It is shown that a two-level atom, being initially in general superposition state of ground and excited energy levels with mutually different momentum distributions there, gets a large scale evolution in the energy levels momentum distribution. As a consequence the mean momentum of each individual energy level also gets large scale changes, more than the own momentum hbar k of the photon. Because of not completeness of the literature under the hand, we are not sure that this simple phenomenon isn't known in quantum theory of atom-photon interactions or, particularly, in the interferometry of atomic matter waves. One of main purposes of this article is our request to the leading specialists to respond and if the phenomenon is known, send the corresponding references. Thoroughly is discussed the special case, when 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 that in such conditions the mentioned phenomenon can be presented as a transformation of the resonant Kapitza-Dirac splitting of atomic states into the Stern-Gerlach type splitting.
We investigate the diffraction of a three-level atom from a "walking" light wave composed of counterpropagating traveling waves of different frequencies. The coupling of the two nondegenerate internal ground states by means of an off-resonant Raman transition resonantly couples the initial external momentum state to only one other momentum state. This happens even in the Raman-Nath regime, where the interaction time is short enough that momentum transfer is not constrained by phase-matching conditions. The final momentum state depends on the initial internal state of the atom and the relative directions of the two traveling waves. By using multiple diffraction regions, this process can be used to coherently split a beam of atoms into two beams that are widely separated in momentum space. This type of beam splitter would be useful in the building an atom interferometer.
It is shown that the population Rabi oscillations in a lossless two-level atom, interacting with a monochromatic electromagnetic field, in general, are convergent in time. The well-known continuous oscillations take place because the restricted choosing of initial conditions, that is, when the atom is chosen on ground or excited level before the interaction, simultaneously having a definite value of momentum there. The convergence of Rabi oscillations in atomic wave-packet states is a direct consequence of the Doppler effect on optical transition rates (Rabi frequencies): it gradually leads to ``irregular'' chaotic-type distributions of momentum in ground and excited energy levels, smearing the amplitudes of Rabi oscillations. Conjointly with Rabi oscillations, the coherent accumulation of momentum on each internal energy level monotonically diminishes too.
We study the deflection of an atomic system with a resonant multilevel energy structure in classical and quantized wave light fields. We obtain that the shape of the momentum distribution is very sensitive to the energy level structure, whereas its moments are not. Comparison with a two-level case is made. PACS: 32.80, 33.80, 42.50 During the last two decades a remarkable development in mechanically manipulating atomary particles with resonant laser light has taken place (for a review, see for example [1, 2] and references therein). In addition to trapping and cooling of particles, the deflection of particles by a laser beam offers interesting possibilities, for example, to construct atomic interferometers or beam splitters [2-4]. This problem has been studied extensively both theoretically [2, 5, 8] and experimentally [9-12]. The fact that the momentum distribution caused by the scattering is connected to the quantum statistical properties of the scattered light has been known for some time [13]. Recently, one has also realized that the quantum statistics of the light causing the scattering can be important [14]. At low photon numbers, for example, the initial field state strongly influences the resulting momentum distribution. A related effect is that a standing wave and two counterpropagating traveling plane waves of equal emplitudes cause a different diffraction pattern when fields are treated quantum mechanically [15]. Most previous work on the deflection of particles by light fields used two-level atoms. In this paper we study how resonant multilevel systems scatter when they traverse a plane wave. In practical applications, molecules or highly excited atoms have similar energy structures as the models we use in this work. In most cases, we assume that the Raman-Nath regime is valid, i.e., the kinetic energy of the particle can be neglected. However, the field coupling is assumed to be sufficiently strong to make multiple scattering events possible. Our results show that the final momentum distribution of a multi-level system can strongly deviate from that of a two-level atom. It is of interest that the momentum distributions for resonant ladder systems are in general superpositions of few or several distributions similar to that of a two-level system. We also study the expectation values related to the momentum distribution and show that the spread in momentum is remarkably independent of the system considered. The absorption and reabsorption of photons during the scattering process causes the photon distribution to be smoothed out, and for long times a steady state is reached. The cases we studied did not show a creation of sub-Poissonian light. Our model and assumptions are described and discussed in Sect. 1. Some of the general properties of the momentum distribution are discussed in Sect. 2. In Sect. 3 we derive the generating function of the moments of momentum change in Raman-Nath regime. The main part of the paper is contained in Sects. 4 and 5, in which the momentum distribution itself is discussed for several model systems. In Sect. 4 a semiclassical field is assumed and in Sect. 5 a quantum field is used. The effects of the scattering on the field photon statistics are studied in Sect. 6. The final discussion of the results is given in Sect. 7.
The exchange of momentum between atoms and photons in a deflection experiment is usually described by different formalisms depending on whether the interaction time T is shown or long compared with the radiative lifetime tau R . The authors present a new approach to this problem leading to a single theoretical expression valid in both limits and therefore allowing the transition between them to be studied. They interpret in this way the resonant Kapitza-Dirac effect and the optical Stern and Gerlach effect appearing in the short-time limit (T<< tau R ) as well as the deflection profiles usually deduced from a Fokker-Planck equation in the long-time limit (T>> tau R ). The transition between these two regimes is interpreted in terms of momentum transfer due to absorption and stimulated emission of laser photons, convoluted by the distribution of recoil due to spontaneously emitted photons.
In the optical Stern-Gerlach effect, the interaction of a traveling two-level atom with the electromagnetic field of an optical cavity causes a splitting of the atomic trajectory. One may ask if it is possible to single out particular initial configurations of the system that will lead to selective scattering, in which the atoms follow only one trajectory. We show that these configurations consist of a coherent superposition of the atomic internal states, and of a field phase state or a field coherent state, with a precise phase relation between the two subsystems: The same configurations which produce the so-called atomic coherent trapping in the Jaynes-Cummings model.