Lineshape-asymmetry-caused shift in atomic interferometers

Abstract

We investigate the shift caused by asymmetry of spectroscopic lineshape in atomic interferometers, which has not previously been discussed in the scientific literature. This asymmetry arises because laser field is frequency-chirped not only during the free-evolution intervals of atoms, but also during the Ramsey pulses. As a result, the effective detuning from the working atomic transition during the pulses also depends on the chirping rate, which, in turn, leads to the lineshape-asymmetry-caused shift (LACS). It is shown that this shift has an inverse cubic dependence of $\propto 1/T^3$ on the duration of the interval between the Ramsey pulses $T$, which markedly contrasts with the $\propto 1/T^2$ dependence typical in atomic interferometry. Therefore, the metrological importance of this shift substantially increases for compact atomic interferometers with a short baseline. For example, for interferometers-gravimeters using two-photon transitions in rubidium atoms, at $T\sim 1$~ms we estimate the LACS shift and its variations at the level of 0.1-1~mGal, while for $T\sim 100$~$μ$s this can reach a value of 0.1-1~Gal.

Figures (4)

• Figure 1: Standard scheme of a Mach–Zehnder type atomic interferometer gravimeter.
• Figure 2: Typical forms of dependencies: (a) total signal $N_e(\widetilde{\alpha})$; (b) interference contribution $|K_{2e}(\widetilde{\alpha})|^2$; (c) substrate ($|K_{1e}(\widetilde{\alpha})|^2+|K_{3e}(\widetilde{\alpha})|^2$). Calculation parameters: $\tau\Omega_0=\pi/2$, $T=10\tau$, $\Delta_{\rm D}=0$.
• Figure 3: Demonstration of the shift in the position of the extremum at the central Ramsey resonance in the dependence $N_e(\widetilde{\alpha})$ under $\Delta_{\rm D}\neq 0$.
• Figure 4: (a) Dependence of the dimensionless function $\xi^{}_1(T/\tau)$ in the expression (\ref{['shift_dep']}) at $T\gg \tau$. (b) Dependence of the dimensionless function $\xi^{}_2(T/\tau,|{\bf k}_{\rm eff}|\bar{v}/\Omega_0)$ on $T/\tau$ in the expression (\ref{['LACS_v']}) for several fixed values of $|{\bf k}_{\rm eff}|\bar{v}/\Omega_0$ (indicated in the plot).