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Europhysics Letters (EPL)

Proposal for a Magneto-optical Beam Splitter for Atoms

Tilman Pfau, Charles S. Adams, J. Mlynek

Published Feb 1, 1993• 40 citations
Publisher

Abstract

In this letter we present a theoretical study of the coherent diffraction of three-level atoms from a light field with a polarization gradient (counterpropagating crossed linearly polarized beams) and a static magnetic field applied parallel to the laser propagation direction. We show that for a particular ratio of the laser field intensity and the magnetic-field strength, there occurs a resonance between the Larmor precession of the magnetic alignment and the Rabi oscillations. On resonance the atomic wave function is diffracted by an approximately triangular optical potential which leads to a very efficient coherent splitting of the atomic beam. The proposed configuration is particularly interesting in relation to atom interferometry, when efficient coherent beam splitters for atoms are required.

DOI
10.1209/0295-5075/21/4/010

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Physical Review A•Sep 1, 1994•6 citations
In this letter we present a theoretical study of the coherent diffraction of three-level atoms from a light field with a polarization gradient (counterpropagating crossed linearly polarized beams) and a static magnetic field applied parallel to the laser propagation direction. We show that for a particular ratio of the laser field intensity and the magnetic-field strength, there occurs a resonance between the Larmor precession of the magnetic alignment and the Rabi oscillations. On resonance the atomic wave function is diffracted by an approximately triangular optical potential which leads to a very efficient coherent splitting of the atomic beam. The proposed configuration is particularly interesting in relation to atom interferometry, when efficient coherent beam splitters for atoms are required.
A theoretical study of the coherent interaction of multilevel atoms with a magneto-optical potential is presented. The potential is formed by counterpropagating linearly polarized laser beams whose polarization vectors intersect at an angle cphi and a static magnetic field applied parallel to the laser propagation direction. For a particular ratio of the light and magnetic field amplitudes, the light shift at positions of purely circularly polarized light is equal to the Zeeman splitting. In this case, for a three-level atom, one of the eigenvalues has a triangular spatial form. The diffraction of atoms from this triangular phase grating is an efficient beam splitter. The splitting is symmetric for cphi=90\ifmmode^\circ\else\textdegree\fi{} and asymmetric for cphi90\ifmmode^\circ\else\textdegree\fi{}. In addition we show that at well-defined positions in the light field, the atom undergoes nonadiabatic transitions and thus by using state-selective detection, one could observe an interference pattern produced by an array of double slits.
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.
In this paper we review techniques to coherently split an atomic beam using the dipole force. We discuss the interaction of atoms with normal standing wave light field in the context of atomic beam splitters. The case where the atom enters the standing wave at a small angle such that Bragg diffraction and velocity selective resonances are observed is also considered. An alternative approach to realize a coherent beam splitter based on the optical Stern‐Gerlach effect is discussed. Finally we consider the interaction of atoms with a magneto‐optical potential formed by a polarization gradient light field and a static magnetic field. We show that the Stern‐Gerlach effect and the magneto‐optical potential produce a more effective beam splitting into states with high transverse momentum than diffraction from a normal standing wave.
We report an experimental demonstration of diffraction of He∗{\mathrm{He}}^{\mathrm{*}}He∗ atoms from a magneto-optical grating. The grating was produced by the interaction of three-level atoms with a light field of spatially varying polarization and a magnetic field. For a light shift matched to the Zeeman shift, a two-peaked diffraction pattern was observed, corresponding to a momentum splitting of 42\ensuremath{\Elzxh}k. The effect of changing the polarizations of the light field was investigated. The diffraction from the magneto-optical grating is compared directly with the diffraction of two-level atoms from a standing light wave and it is shown, that the magneto-optical interaction leads to more efficient coupling into high order momentum states.
We investigate schemes for the clean splitting of beams of three-level atoms using two standing-wave laser fields within an optical cavity. The proposed beam splitter is shown to work for atoms in the \ensuremath{\Lambda} ladder, and ssV configurations. For appropriate values of Rabi frequencies and detunings, we obtain a triangular type of potential for the atomic states of interest. As well as modeling the coherent evolution of the systems, we have used quantum Monte Carlo wave-function methods to model the effects of spontaneous emission on the resulting diffraction pattern, finding significant differences between the three configurations. We also investigate the limits of the Raman-Nath approximation for our systems, using the symmetric split-operator technique to include the effects of the kinetic term in the Hamiltonian. We also present the results of calculations in which the split output beams are recombined, demonstrating the expected interference for differently prepared input beams. In comparison with two-level beam splitters using a single standing wave, we obtain a superior splitting, while, in comparison with magneto-optical beam splitters, our system possesses the worthwhile practical advantages of experimental simplicity.
The simulated magneto-optical force, which in the presence of a longitudinal static magnetic field is exerted on atoms resonant with the high-intensity light field of two counterpropagating, linearly polarized laser beams with an angle of \ensuremath{\sim}45\ifmmode^\circ\else\textdegree\fi{} between their directions of polarization, is described in the dressed-atom picture. This allows an easy calculation of the force on atoms at rest, illustratively explains its nonzero wavelength average, and provides an intuitive understanding of its dependence on the atomic velocity. For a simple atomic model transition (J=0\ensuremath{\leftrightarrows}J'=1) the velocity-dependent force is calculated by considering the motion along the dressed states and using the Landau-Zener model for the nonadiabatic transitions at the avoided level crossings. It is shown that for a certain relation between Larmor and optical Rabi frequency a perfectly diabatic motion takes place, leading to a disappearance of the velocity-tuned (doppleron) resonance structure.