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Physical Review Letters

Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect

P. L. Gould, George A. Ruff, David E. Pritchard

Published Feb 24, 1986• 408 citations
Publisher

Abstract

We have observed the Kapitza-Dirac effect in the scattering of sodium atoms by a nearly resonant standing-wave laser field. The data clearly show diffraction peaks of the atomic momentum transfer at even multiples of the photon momentum. Theoretical predictions for an off-resonant, adiabatic interaction with a two-state system are in reasonable agreement with the data.

DOI
10.1103/physrevlett.56.827

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Abstract In their famous 1927 experiment, Davisson and Germer observed1 the diffraction of electrons by a periodic material structure, so showing that electrons can behave like waves. Shortly afterwards, Kapitza2 and Dirac3 predicted that electrons should also be diffracted by a standing light wave4. This Kapitza–Dirac effect is analogous to the diffraction of light by a grating, but with the roles of the wave and matter reversed. The electron and the light grating interact extremely weakly, via the ‘ponderomotive potential’5, so attempts to measure the Kapitza–Dirac effect had to wait for the development of the laser. The idea6 that the underlying interaction with light is resonantly enhanced for electrons in an atom led to the observation7 that atoms could be diffracted by a standing wave of light. Deflection of electrons by high-intensity laser light, which is also a consequence of the Kapitza–Dirac effect, has also been demonstrated8. But the coherent interference that characterizes wave diffraction has not hitherto been observed9, 10. Here we report the diffraction of free electrons from a standing light wave—a realization of the Kapitza–Dirac effect as originally proposed.

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The Kapitza-Dirac effect is the diffraction of a well-collimated particle beam by a standing wave of light. Why is this interesting? Comparing this situation to the introductory physics textbook example of diffraction of a laser beam by a grating, the particle beam plays the role of the incoming wave and the standing light wave the role of the material grating, highlighting particle-wave duality. Apart from representing such a beautiful example of particle-wave duality, the diffracted particle beams are coherent. This allows the construction of matter interferometers and explains why the Kapitza-Dirac effect is one of the workhorses in the field of atom optics. Atom optics concerns the manipulation of atomic waves in ways analogous to the manipulation of light waves with optical elements. The excitement and activity in this new field of physics stems in part from the realization that the shorter de Broglie wavelengths of matter waves allow ultimate sensitivities for diffractive and interferometric experiments that in principle would far exceed their optical analogues. Not only is the Kapitza-Dirac effect an important enabling tool for this field of physics, but diffraction peaks have never been observed for electrons, for which it was originally proposed in 1933. Why has this not been observed? What is the relation between the interaction of laser light with electrons and the interaction of laser light with atoms, or in other words what is the relation between the ponderomotive potential and the lightshift potential? Would it be possible to build interferometers using the Kapitza-Dirac effect for other particles? These questions will be addressed in this paper.

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Quantum mechanical diffraction is of particular interest, because it contradicts our everyday life experience. \nThis theoretical work considers the diffraction of electrons at standing waves of light, referred \nto as the Kapitza-Dirac effect. The work focuses on a special version of a Kapitza-Dirac effect in which \nthe electron interacts with three photons. The particular property of this 3-photon Kapitza-Dirac effect \nis, that the electron spin is rotated. \nThis work considers different relativistic and non-relativistic quantum mechanical wave equations \nwhich are described in momentum space. On one hand, the quantum dynamics of the diffracted electrons \nis solved numerically in momentum space and the properties of the 3-photon Kapitza-Dirac effect \nare investigated in detail. On the other hand, the quantum dynamics is solved via time-dependent \nperturbation theory and is compared with the numerical results. \nIn contrast to the originally proposed Kapitza-Dirac effect with two interacting photons, the number \nof absorbed and emitted photons by the electron is not equal for the 3-photon Kapitza-Dirac effect. \nTherefore, the diffraction process only appears for relativistic electron momenta in laser propagation \ndirection. Furthermore, a very high field strength of the laser beam is required for driving the Kapitza- \nDirac effect with a measurable diffraction probability. The electron spin is rotated along the axis of the \nmagnetic field of the laser beam, when it undergoes the diffraction process. The rotation angle of the \nspin rotation depends on the electron momentum component in laser polarization direction. Therefore, \nthe probability for flipping the electron spin can be tuned by choosing the electron momentum in \nthe direction of the laser polarization. An experimental investigation may by established by utilizing \nfuture X-ray laser facilities.

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We have observed the Kapitza-Dirac effect in the scattering of sodium atoms by a nearly resonant standing-wave laser field. The data clearly show diffraction peaks of the atomic momentum transfer at even multiples of the photon momentum. Theoretical predictions for an off-resonant, adiabatic interaction with a two-state system are in reasonable agreement with the data.
Abstract In their famous 1927 experiment, Davisson and Germer observed1 the diffraction of electrons by a periodic material structure, so showing that electrons can behave like waves. Shortly afterwards, Kapitza2 and Dirac3 predicted that electrons should also be diffracted by a standing light wave4. This Kapitza–Dirac effect is analogous to the diffraction of light by a grating, but with the roles of the wave and matter reversed. The electron and the light grating interact extremely weakly, via the ‘ponderomotive potential’5, so attempts to measure the Kapitza–Dirac effect had to wait for the development of the laser. The idea6 that the underlying interaction with light is resonantly enhanced for electrons in an atom led to the observation7 that atoms could be diffracted by a standing wave of light. Deflection of electrons by high-intensity laser light, which is also a consequence of the Kapitza–Dirac effect, has also been demonstrated8. But the coherent interference that characterizes wave diffraction has not hitherto been observed9, 10. Here we report the diffraction of free electrons from a standing light wave—a realization of the Kapitza–Dirac effect as originally proposed.
We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.
The diffraction of sodium atoms from a standing wave of near-resonant light is studied as a function of the atomic velocity component along the k vector of the wave. A simple theory is presented which quantitatively predicts the observed diffraction patterns and the decrease of the rms momentum transfer to the atoms with increasing velocity. This decrease results from the dephasing between the two counterpropagating traveling waves due to the first-order Doppler shift. In addition, these measurements have resolved the previous discrepancy between theory and experiment concerning the overall momentum transferred by a standing wave.
The Kapitza-Dirac effect is the diffraction of a well-collimated particle beam by a standing wave of light. Why is this interesting? Comparing this situation to the introductory physics textbook example of diffraction of a laser beam by a grating, the particle beam plays the role of the incoming wave and the standing light wave the role of the material grating, highlighting particle-wave duality. Apart from representing such a beautiful example of particle-wave duality, the diffracted particle beams are coherent. This allows the construction of matter interferometers and explains why the Kapitza-Dirac effect is one of the workhorses in the field of atom optics. Atom optics concerns the manipulation of atomic waves in ways analogous to the manipulation of light waves with optical elements. The excitement and activity in this new field of physics stems in part from the realization that the shorter de Broglie wavelengths of matter waves allow ultimate sensitivities for diffractive and interferometric experiments that in principle would far exceed their optical analogues. Not only is the Kapitza-Dirac effect an important enabling tool for this field of physics, but diffraction peaks have never been observed for electrons, for which it was originally proposed in 1933. Why has this not been observed? What is the relation between the interaction of laser light with electrons and the interaction of laser light with atoms, or in other words what is the relation between the ponderomotive potential and the lightshift potential? Would it be possible to build interferometers using the Kapitza-Dirac effect for other particles? These questions will be addressed in this paper.
Quantum mechanical diffraction is of particular interest, because it contradicts our everyday life experience. \nThis theoretical work considers the diffraction of electrons at standing waves of light, referred \nto as the Kapitza-Dirac effect. The work focuses on a special version of a Kapitza-Dirac effect in which \nthe electron interacts with three photons. The particular property of this 3-photon Kapitza-Dirac effect \nis, that the electron spin is rotated. \nThis work considers different relativistic and non-relativistic quantum mechanical wave equations \nwhich are described in momentum space. On one hand, the quantum dynamics of the diffracted electrons \nis solved numerically in momentum space and the properties of the 3-photon Kapitza-Dirac effect \nare investigated in detail. On the other hand, the quantum dynamics is solved via time-dependent \nperturbation theory and is compared with the numerical results. \nIn contrast to the originally proposed Kapitza-Dirac effect with two interacting photons, the number \nof absorbed and emitted photons by the electron is not equal for the 3-photon Kapitza-Dirac effect. \nTherefore, the diffraction process only appears for relativistic electron momenta in laser propagation \ndirection. Furthermore, a very high field strength of the laser beam is required for driving the Kapitza- \nDirac effect with a measurable diffraction probability. The electron spin is rotated along the axis of the \nmagnetic field of the laser beam, when it undergoes the diffraction process. The rotation angle of the \nspin rotation depends on the electron momentum component in laser polarization direction. Therefore, \nthe probability for flipping the electron spin can be tuned by choosing the electron momentum in \nthe direction of the laser polarization. An experimental investigation may by established by utilizing \nfuture X-ray laser facilities.