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Annual Meeting Optical Society of America

Atomic beam deflection in a quantum field

Pierre Meystre, E. Schumacher, Stig Stenholm, Ewan M. Wright

Published Jan 1, 1989• 3 citations
Publisher

Abstract

We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.

DOI
10.1364/oam.1989.thbb6

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Chinese Physics Letters•Dec 1, 1994•2 citations
We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.
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.
We have observed momentum transfer from a standing-wave light field to an atomic beam. The atomic beam is split symmetrically into two peaks whose separation increases with field strength. The short interaction time ensures that this deflection is due to induced forces; these are described using a semiclassical dressed-atom treatment, which gives good agreement with the data. In addition to the splitting, we have observed diffraction of the atomic beam due to the exchange of even numbers of photons with the field.
We study the interaction of a quantized single-mode standing-wave cavity field with a two-level atom de Broglie wave. For the sake of simplicity we consider the field to be far detuned and the atom to be moving in the Raman - Nath regime. We show that the Wigner function of the field is a superposition of the Wigner functions for the coherent states aligned on an arc in phase space. The back action of the measurement of the atomic internal state leads to the modification of the diagonal as well as of the off-diagonal elements of the field density matrix. We investigate the formation of nonclassical field states via atomic deflection and internal-state measurement and show that the coherence of the field and the interference between the constituent coherent states disappear in the limit of large interaction times. The width of the atomic momentum distribution allows us to determine the mean photon number and the width of the photon distribution. We find that, for an appropriate choice of the initial state of the atomic centre-of-mass motion, the form of the atomic momentum distribution is identical to that of the photon distribution. The field near a node or an antinode acts as a focusing or defocusing lens for atoms, depending on the detuning and on the initial internal state of the atom.
Atomic beam deflection in a quantum field is studied theoretically for the case of an atom passing through the mode of a resonant optical cavity. Deflection probability is calculated for a coupling rate g of order g/2{pi}=1 MHz, which is experimentally feasible in a short optical cavity. Atomic velocities are taken in the range of 1-10 m/s, which can be reached with current cooling and trapping techniques. We calculate deflection for a coherent state with mean photon number , and for a number state. For the parameters studied, the predicted scattering is in an intermediate regime between Raman-Nath and Bragg, but is closer to the former. We find significant deflection probability even for =1, indicating potential for a high level of sensitivity. We report on our progress in the experimental realization of this system with laser cooled sodium atoms as the atomic medium, and directions for future work are indicated.
By using the Wei-Norman's method, the deflection of an atomic beam with a large period quantized standing light wave is analyzed for the case with two-level atom and single-mode cavity field. It is concluded that after passing through the standing light wave in cavity, the atomic beam is split into infinite beams symmetrically, and each momentum shift for a split component is proportional to the interaction time. It is also shown that the output momentum distribution of atoms is sensitive to the statistical properties of the cavity field.