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Physical Review Letters

Difference between a Photon’s Momentum and an Atom’s Recoil

Kurt Gibble

Published Aug 14, 2006• 48 citations
Publisher

Abstract

When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.

DOI
10.1103/physrevlett.97.073002

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When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.
In an atom interferometry experiment, the output phase shift depends on the wave vector of photons and the recoil momentum in optical transitions. This Letter puts forward a hypothesis that in light-atom interaction, the atom wave function could provide a transverse confinement to photons and thus could affect the mean recoil momentum. We propose a model to analyze the photon effective wave vector in a monochromatic optical field and calculate the relative shift of |k[over →]_{eff}| to k when an atom with a 3D Gaussian wave function absorbs one photon in a Gaussian beam. This shift could lead to a systematic effect related to the spatial distribution of atoms and the transverse beam profile in high-precision experiments based on atom interferometry.
A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was determined with a two-pulse light grating interferometer using near-resonant laser light. The results show that the recoil momentum of atoms caused by the absorption of a photon is n variant Planck's k, where n is the index of refraction of the gas and k is the vacuum wave vector of the photon. This systematic effect must be accounted for in high-precision atom interferometry with light gratings.
We derive the general frequency shift of a microwave atomic clock due to resonant dipole forces acting on the atomic wave functions during the Ramsey interactions. We explicitly demonstrate that only dressed-state populations in position space contribute significantly to the frequency shift and that the de Broglie phases of the dressed-state wave functions do not contribute. In addition, we show that momentum changes in the second Ramsey interaction normally produce negligible frequency shifts in comparison to those from the first Ramsey interaction.
We investigate theoretically and by numerical simulations the effects of the atomic recoil on the frequency and fringe contrast of microwave atomic frequency standards. Such effects arise because of the influence of external degrees of freedom on the phases and the spatial positions of the interfering wave packets. We show under which conditions such effects lead to a frequency shift and examine the loss of contrast of the interference signal (Ramsey fringes). We use an interferometric description to model the frequency standards, treating simultaneously internal and external degrees of freedom. We consider multiple momentum exchanges in 3D between the atoms and the standing microwave field inside the cavity leading to a large number of wave packets that leave the cavity with different momenta. At detection, these wave packets interfere giving rise to Ramsey fringes that are modulated by the interference of the external states of the wave packets. Similar treatments have proved efficient when treating ID recoil effects in standing laser waves. We apply this theoretical model numerically to laser cooled atomic fountain frequency standards and investigate the behaviour of the observed signal as a function of the frequency standard parameters (microwave power, launching height, etc.). Finally, we discuss possible experimental methods that could be used to observe such effects.
Light carries momentum which induces on atoms a recoil for each photon absorbed. In vacuum, for a monochromatic beam of frequency ν, the global momentum per photon is bounded by general principles and is smaller than hν/c leading to a limit on the recoil. However, locally this limit can be broken. In this Letter, we give a general formula to calculate the recoil in vacuum. We show that in a laser beam with a distorted optical field, there are regions where the recoil can be higher than this limit. Using atoms placed in those regions we are able to measure directly the extra recoil.