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arXiv:2507.19157 · Physical Review A

Probing the spatial distribution of k -vectors in situ with Bose-Einstein condensates

Samuel Gaudout, Rayan Si-Ahmed, Clément Debavelaere, Menno Door, Pierre Cladé, Saïda Guellati-Khélifa

Published Nov 11, 2025• 4 citations
arXivHTMLPDF

Abstract

The authors present a method that uses a Bose--Einstein condensate as a local probe to map, in situ, the photon momentum across a laser beam, revealing a striking extra-recoil. This approach offers a powerful tool for evaluating systematics due to wavefront distortions in atom interferometry.
DOI
10.1103/x2x9-dt38

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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.
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.
A pulsed atom laser derived from a Bose-Einstein condensate is used to probe a second target condensate. The target condensate scatters the incident atom laser pulse. From the spatial distribution of scattered atoms, one can infer important properties of the target condensate and its interaction with the probe pulse. As an example, we measure the s-wave scattering length that, in low energy collisions, describes the interaction between the |F = 1,m(F) = -1) and |F = 2,m(F) = 0) hyperfine ground states in (87)Rb.
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.
Bose-Einstein condensates in optical lattices have proven to be a powerful tool for studying a wide variety of physics. In this thesis a series of experiments using optical lattices to manipulate 87Rb Bose-Einstein condensates are described. 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 measured interferometrically using a two-pulse Ramsey interferometer. The two pulses were created using a one dimensional optical lattice. By measuring the resulting frequency as a function of the lattice detuning from the atomic resonance, we found a distinctive dispersive shape for the recoil frequency that fit the recoil momentum as nr~k. A one-dimensional optical lattice was used to modify the dispersion relation of the condensate in order to demonstrate the matter-wave analogue of Optical Parametric Generation (OPG) and Amplification (OPA) of photons. A condensate was loaded into a moving optical lattice with adjustable quasimomentum k0. As the value for k0 was varied, we observed elastic scattering into two distinct final momentum states k1