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arXiv:1711.08658 · Journal of Physics B Atomic Molecular and Optical Physics

Photon recoil momentum in a Bose–Einstein condensate of a dilute gas

Yu. A. Avetisyan, Victor A Malyshev, Evgenii Dmitrievich Trifonov

Published Mar 8, 2017• 3 citations
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Abstract

Abstract We develop a ‘minimal’ microscopic model to describe a two-pulse-Ramsey-interferometer-based scheme of measurement of the photon recoil momentum in a Bose–Einstein condensate of a dilute gas (Campbell et al 2005 Phys. Rev. Lett. 94 170403 ). We exploit the truncated coupled Maxwell–Schrödinger equations to elaborate the problem. Our approach provides a theoretical tool to reproduce essential features of the experimental results. Additionally, we calculate the quantum-mechanical mean value of the recoil momentum and its statistical distribution that provides a detailed information about the recoil event.

DOI
10.1088/1361-6455/aa654c

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Abstract We develop a ‘minimal’ microscopic model to describe a two-pulse-Ramsey-interferometer-based scheme of measurement of the photon recoil momentum in a Bose–Einstein condensate of a dilute gas (Campbell et al 2005 Phys. Rev. Lett. 94 170403 ). We exploit the truncated coupled Maxwell–Schrödinger equations to elaborate the problem. Our approach provides a theoretical tool to reproduce essential features of the experimental results. Additionally, we calculate the quantum-mechanical mean value of the recoil momentum and its statistical distribution that provides a detailed information about the recoil event.
Abstract Photon recoil upon light scattering by a Bose–Einstein condensate (BEC) of a dilute atomic gas is analyzed theoretically accounting for a weak interatomic interaction. Our approach is based on the Gross–Pitaevskii equation for the condensate, which is coupled to the Maxwell equation for the field. The dispersion relations of recoil energy and momentum are calculated, and the effect of weak nonideality of the condensate on the photon recoil is ubraveled. A good agreement between the theory and experiment [7] on the measurement of the photon recoil momentum in a dispersive medium is demonstrated.
A semiclassical theory is proposed to describe the light amplification in a Bose—Einstein condensate of a dilute atomic gas observed in [1]. Atomic states with well-defined momenta are taken as a basis of wave functions to derive the Maxwell—Bloch equations for the model of a dilute gas of atoms interacting with electromagnetic field. The evolution of light intensity and populations of coherent atomic states with different recoil momenta is described by solving these equations. The solutions obtained are used to demonstrate theoretically the effects observed in [1].
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.