Dual-frequency Doppler-free crossover resonance with suppressed magnetic-field sensitivity for compact optical frequency standards

TL;DR

This work addresses the need for robust, portable optical frequency references by evaluating a dual-frequency ground-state crossover resonance in the $D$1 line of rubidium. The authors implement a two-laser, bichromatic spectroscopy scheme to compare the conventional DFSDS resonance at $δ=0$ with the large $δ$ ground-state crossover, showing that the latter offers high contrast and narrow linewidth with greatly suppressed sensitivity to magnetic-field fluctuations. Theoretical analysis attributes asymmetry and residual shifts at nonzero ellipticity to the dispersive contributions of ground-state coherences to absorption, and experiments demonstrate over an order-of-magnitude improvement in frequency stability under $B$-field perturbations when locking to the crossover. These findings indicate the crossover resonance as a promising reference for compact, field-deployable optical standards, with practical implications for metrology and navigation devices.

Abstract

We report the observation and characterization of a high-contrast dual-frequency Doppler-free ground-state crossover resonance in the D1 line of 87Rb.The crossover appears at a two-photon detuning exceeding the natural linewidth of the excited state and is formed by the optical pumping effect. Unlike the previously proposed resonance at zero two-photon detuning, which we show becomes sensitive to magnetic-field fluctuations due to residual ellipticity of the optical fields-resulting in frequency shifts and profile asymmetry-the crossover resonance is largely immune to this effect. Our theoretical analysis attributes the observed sensitivity to the dispersive contribution of ground-state coherences to absorption. Stability measurements under magnetic-field fluctuations demonstrate that using the crossover resonance provides more than an order-of-magnitude improvement, making it a promising reference for frequency stabilization in compact, field-deployable optical standards.

Figures (9)

• Figure 1: Schematic of the experimental setup. ECDL---extended-cavity diode laser, OI---optical isolator, EOM---electro-optic modulator, P---polarizer, $\lambda/2$---half-wave plate, $\lambda/4$---quarter-wave plate, PBS---polarizing beam splitter, BS---beam splitter, AOM---acousto-optic modulator, ND---neutral density filter, M---mirror, PD---photodetector, FPD---fast photodetector.
• Figure 2: Dual-frequency Doppler-free spectra of $^{87}$Rb D$_1$ line taken at crossed polarizations of the counter-propagating waves for different values of two-photon detuning $\delta$ and magnetic field $B_z$. The horizontal axis represents the detuning of the laser carrier frequency from the value given by the sum of the $F_g=2 \rightarrow F_e=2$ transition frequency and half of the ground-state hyperfine splitting.
• Figure 3: Schematic diagram of the energy levels for the D$_1$ line of $^{87}$Rb. The vertical lines represent first-order sidebands of counter-propagating fields for three laser carrier frequency detunings at a fixed two-photon detuning $\delta$. The lower part of the figure illustrates the Maxwell distribution of longitudinal atomic velocities and highlights the velocity groups that interact with the resonant optical components.
• Figure 4: Dependence of the $(1,2)\rightarrow 2$ resonance amplitude on the two-photon detuning (a). The first points correspond to Fig. \ref{['Resonances']} c and ig. \ref{['Resonances']} d. Dependence of the resonance amplitude (b) and width (c) on the longitudinal magnetic field.
• Figure 5: Doppler-free resonances for two values of longitudinal magnetic field $B_z$ in the case of elliptically polarized field $\vec{\mathcal{E}}_2$: $\delta=0$ MHz (a) and $\delta=100$ MHz (b). Dependences of the beatnote frequency shift on the change in the magnetic field magnitude $\Delta B_z$ in the case of elliptically polarized field $\vec{\mathcal{E}}_2$ (c). The inset shows the blue curve with a rescaled vertical axis.