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Annual Meeting Optical Society of America

Doppleron-catalyzed Bragg resonances in atom optics

S. Glasgow, P. Meystre, N. Wilkens

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Effective atomic beam splitters providing large scattering angles are central to atom optics and atom interferometry. Their most common optical realization relies on first-order Bragg scattering, which generates a splitting of the atomic wave function in momentum space. For typical atomic beam velocities of the order of 100 m/s, 2ħk produces very small scattering angles. Higher-order Bragg scattering is of questionable practicality, because of the need for atom–field interaction times that scale exponentially with the scattering order. Attempts at solving this problem include the introduction of multiple laser beams, the use of three-level transition schemes, and the application of velocity-tuned, or Doppleron, resonances. We present a novel scheme that uses a Doppleron resonance as a catalyst to speed up a high-order Bragg resonance by orders of magnitude. This effect occurs when the atom–field frequency detuning is such that the Bragg resonance and the Doppleron resonance become degenerate. Alternatively, in the band-theoretical description of the near-resonant Kapitza–Dirac effect, the Doppleron resonance is required to occur either at the center or at the boundary of the first Brillouin zone.

DOI
10.1364/oam.1992.tuaaa4

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Effective atomic beam splitters providing large scattering angles are central to atom optics and atom interferometry. Their most common optical realization relies on first-order Bragg scattering, which generates a splitting of the atomic wave function in momentum space. For typical atomic beam velocities of the order of 100 m/s, 2ħk produces very small scattering angles. Higher-order Bragg scattering is of questionable practicality, because of the need for atom–field interaction times that scale exponentially with the scattering order. Attempts at solving this problem include the introduction of multiple laser beams, the use of three-level transition schemes, and the application of velocity-tuned, or Doppleron, resonances. We present a novel scheme that uses a Doppleron resonance as a catalyst to speed up a high-order Bragg resonance by orders of magnitude. This effect occurs when the atom–field frequency detuning is such that the Bragg resonance and the Doppleron resonance become degenerate. Alternatively, in the band-theoretical description of the near-resonant Kapitza–Dirac effect, the Doppleron resonance is required to occur either at the center or at the boundary of the first Brillouin zone.
Atomic Kapitza-Dirac Bragg regime scattering is a multiphoton process in which a neutral atom undergoes a change of momentum through an interaction with a coherent light source. When the Bragg conditions are met, the outgoing atom beams are spatially quantized. Counterpropagating lasers act as pump and probe scattering from far-off-resonant excited intermediate electronic states, leaving the atoms in the electronic ground state with quantized transverse momentum. Each nontrivial scattering event imparts transverse velocity and therefore kinetic energy to the deflected atoms through recoil. In the Bragg regime, the loss of energy in the light fields is equal to the gain of kinetic energy in the atom. Energy nonconserving intermediate states, which are described by nonadiabatic contributions, are not accounted for by first-order off-resonant states. By comparing the solutions of increasing orders of off-resonant intermediate states, it becomes clear that calculating the correct Pendell\"osung frequencies and phases requires including an ever increasing number of off-resonant states in proportion to the square root of the field strength.
We study theoretically the diffraction of atoms by a standing-wave light field. Conceptually the text is divided into two parts. In the first part we deal with the coherent interaction only. We use a band theoretical approach to describe the laser-atom interaction, and to characterize two-beam resonances (Dopplerons and Bragg resonances). These two-beam resonances are major candidates to develop effective atom beam splitters. We study the interaction with classical light fields as well as with quantum fields. In the second part we take incoherent processes, i.e. spontaneous emission, into account and present a numerical scheme for the solution of the generalized optical Bloch equations. This scheme is based on the split-operator technique, and we use it to study numerically the influence of spontaneous emission on the diffraction process. We compare our results with recent experimental data, and investigate the impact of spontaneous emission on the performance of two-beam resonances.
We report on a technique to split an atomic beam coherently with an easily adjustable splitting angle. In our experiment metastable helium atoms in the ∣1s2s3S1M=1⟩|{1s2s}{^{3}S}_{1}\phantom{\rule{0.3em}{0ex}}M=1⟩∣1s2s3S1​M=1⟩ state diffract from a polarization gradient light field formed by counterpropagating ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarized laser beams in the presence of a homogeneous magnetic field. In the near-adiabatic regime, energy conservation allows the resonant exchange between magnetic energy and kinetic energy. As a consequence, symmetric diffraction of ∣M=0⟩|M=0⟩∣M=0⟩ or $|M=\ensuremath{-}1⟩$ atoms in a single order is achieved, where the order can be chosen freely by tuning the magnetic field. We present experimental results up to sixth-order diffraction ($24\ensuremath{\hbar}k$ momentum splitting, i.e., 2.21 m/s in transverse velocity) and present a simple theoretical model that stresses the similarity with conventional Bragg scattering. The resulting device constitutes a flexible, adjustable, large-angle, three-way coherent atomic beam splitter with many potential applications in atom optics and atom interferometry.
We perform an experimental and theoretical study of a novel distributed quasi-Bragg splitter for cold atoms propagating in crossed optical waveguides. The atoms are guided by horizontal red-detuned laser beams which cross with an angle of roughly 90°. The lattice formed by the interference between the two waveguides is used as a quasi-Bragg splitter to continuously deflect the atomic flux from one waveguide into the other. In the limit of strong waveguide confinement and depending on the velocity of the cloud, three main regimes are observed corresponding (1) to the absence of reflection, (2) to partial reflection and (3) to full reflection into the second waveguide. In view of the application to atom interferometry, the condition to split the cloud into mainly two equally-populated fragments is only met in the highest velocity regime, where the fraction of reflected and transmitted atoms can be controlled by tuning the lattice height. A diagnostic of the momentum distribution shows that a quasi-Bragg splitter with the occupation of mainly two momentum states is achieved in this regime. This behaviour can be understood by considering the band structure associated with the potential in the crossing region and agrees with numerical simulations of the atomic dynamics.
Multi-photon Doppleron resonances are investigated for the diffraction of atoms by a classical standing-wave optical field in the regime where energy conservation limits the diffraction orders. In this regime, atomic recoil is incorporated into the description, and consideration of the dynamical shift of the resonance condition from the purely kinematic results becomes critical to observing the desired diffraction of the atomic wave function. Special attention is given to the development of a technique for evaluating the resonances which constitutes a significant simplification of the usual degenerate perturbation theory approach for a quantum-mechanical Hamiltonian. Also developed is a specialized off-resonant atom-field interaction which is shown to be maximally efficient at producing high-order diffraction of the atomic wave function. Suggestions for its implementation are given.