Fig. 8: Atom interferometry of sub-Doppler cooled GMOT atoms in the compact LPAI sensor head.

a Three-level atomic system for stimulated Raman transitions. \(\left|{g}_{1}\right\rangle =\left|F=1,{m}_{F}=0\right\rangle \), ground state 1; \(\left|{g}_{2}\right\rangle =\left|F=2,{m}_{F}=0\right\rangle \) ground state 2; \(\left|e\right\rangle \), excited state; Δ, single-photon detuning; δ, two-photon detuning which depends on the Doppler shift; Ω_Raman, effective Rabi frequency of Raman beams; Ω₁, single-photon Rabi frequency of \(\left|{g}_{1}\right\rangle \to \left|e\right\rangle \) transition; Ω₂, single-photon Rabi frequency of \(\left|{g}_{2}\right\rangle \to \left|e\right\rangle \) transition. b Space-time trajectory of atomic wavepackets during LPAI. A three-light-pulse sequence, \(\frac{\pi }{2}\to T\to \pi \to T\to \frac{\pi }{2}\), coherently addresses the ground states of the atoms and provides the state-dependent momentum kicks, ℏk_eff ≈ 2ℏk, where p₀ is the initial atomic momentum; T, the free-evolution time between Raman pulses; k_eff, the effective wavenumber of stimulated Raman transition; k, the wavenumber (2π/λ) of a single Raman beam. c Scan of the interrogation time showing the LPAI chirped fringe for T = 0.0 ms to 4.5 ms. The fringe chirping results from the Doppler shift of the cold atoms relative to the Raman beams as the atoms accelerate due to gravity. Each data point in the plot is an average of three data points and a slowly-varying offset was removed. The data is fit to a chirped sinusoid⁹²\(\cos \left({k}_{{{{{{\rm{eff}}}}}}}\,{g}_{{{{{{\rm{k}}}}}}}\left({T}^{2}+{\tau }_{{{{{{\rm{\pi }}}}}}}(1+\frac{2}{\pi })T\right)+{\phi }_{0}\right)\), where τ_π is the π-pulse duration, g_k is gravity, and ϕ₀ is an arbitrary phase factor. We measured g = 9.79316(2)ms⁻² with the statistical uncertainty of Δg/g = 2.0 × 10⁻⁶ without vibration isolation. Plots (d) and (e) provide a detailed view of the chirped fringe of (c) for T = 2.0 ms to 2.1 ms and T = 4.0 ms to 4.1 ms, respectively. The measurement data rate is 10 Hz.