Technique for measuring atomic recoil frequency using coherence functions

Abstract

We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency r as a function of the time at which the third pulse is applied, allowing r to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.

Prospects for Precise Measurements with Echo Atom Interferometry

“…Specifically, the only momentum states contributing to the signal are those that differ byhq after SW3 and after SW2. 4 The non-uniform magnetic field produced by a stainless-steel vacuum chamber, and the gravity-induced Doppler shift limited previous experiments to T 10 ms [76,100,101]. diameter of d ∼ 1.7 cm and are circularly polarized in the same sense by a pair of λ/4 wave plates.…”

“…τ 3 (Ω eff ω q ) −1/2 ) the full-width at half-maximum (FWHM) of the fringe scales as 1/u 3 , as illustrated in Fig. 2(c) [54,56,101].…”

“…For the modified three-pulse AI described in this section, an additional SW pulse is applied between the first two pulses at t = δT, as shown in Fig. 2(b) [54,56,[100][101][102][103]. This pulse has the effect of diffracting the atom into higher-order momentum states that contribute additional harmonics of ω q to the temporal modulation of the macroscopic grating contrast.…”

“…We have developed a "modified" three-pulse echo AI 2 which exhibits increased sensitivity to atomic recoil compared to the aforementioned two-pulse configuration [57]. This modified geometry has been described in previous work using the formalism of coherence functions [100] and a full quantum-mechanical treatment that accurately describes the fringe shape [54,56,101]. In the same articles, we also discussed connections to δ-kicked rotors and quantum chaos, as well as scaling laws that apply to excitation with multiple SW pulses that have been used in other work [102,103].…”

Survival resonances in an atom-optics system driven by temporally and spatially periodic dissipation

“…This allows for precise determination of the period of a signal like that in Fig. 2(a), and thereby of the recoil frequency ω r = π/2T T [26] (which in turn can be used to determine the fine structure constant α [27]). The increase in precision yielded by the steep edges results from the enhancement of high-order diffraction due to the phase modulation provided by the off-resonance standing wave.…”