Fano-like Resonance due to Interference with Distant Transitions

Narrow optical resonances of atoms or molecules have immense significance in various precision measurements, such as testing fundamental physics and the generation of primary frequency standards. In these studies, accurate transition centers derived from fitting the measured spectra are demanded, which critically rely on the knowledge of spectral line profiles. Here, we propose a new mechanism of Fano-like resonance induced by distant discrete levels and experimentally verify it with Doppler-free spectroscopy of vibration-rotational transitions of ${\mathrm{CO}}_2$. The observed spectrum has an asymmetric profile and its amplitude increases quadratically with the probe laser power. Our results facilitate a broad range of topics based on narrow transitions.

Figure 1

Principle of the nonlinear Fano resonance in low-lying states of molecules. (a) The experimental arrangement for the absorption spectrum measurement of moving molecules, probed by a standing wave field with wavelength $\lambda$. (b) Energy level diagram. (c),(d) Simplified energy level diagram for a molecule with speed $V$ in the laboratory frame (c) and in the molecular frame (d).

Figure 2

(a) Schematic of an asymmetric absorption profile of a static molecule obtained by scanning the probe laser in the molecular frame. (b) Numerically calculated absorption spectrum for a molecule ensemble interacting with a standing-wave field. (c),(d) Detailed absorption features around the line center evaluated by the full model (triangle points) and effective model (circular points), with modulation of $\delta /2\pi =-0.02$ and $-0.12\mathrm{MHz}$, respectively. with Fano factors $q$ of $-0.19$ and $-0.67$, respectively.

Figure 3

(a) $q$ and the shift of the fitted center frequency ${\omega }_s/2\pi$ versus the modulation $\delta /2\pi$. (b) $q$ versus ${\gamma }_{12}/2\pi$ for different modulation amplitudes. (c) $q$ versus transverse speed $V_t$ with a beam waist width of 0.5 mm for the standing-wave field. The label of curves [$\delta /2\pi$ (MHz),${\gamma }_{12}/2\pi$ (${10}^{-5}\mathrm{Hz}$)] indicates the modulation and linewidth of $|2⟩$. (d) Absorption spectra of the noted points in (e). (e) $q$ versus $\delta /2\pi$ and ${\gamma }_{12}/2\pi$. Points $p_1$, $p_2$ and HD are located at $\delta /2\pi =-0.12,-0.32,-0.022\mathrm{MHz}$ and ${\gamma }_{12}/2\pi =1.3\times {10}^{-4},2.0\times {10}^{-5},3.42\times {10}^{-6}\mathrm{Hz}$, respectively. Unless specified, all parameters are the same as those in Fig. 2.

Figure 4

(a) Experimental configuration of cavity ring-down spectroscopy (CRDS) of ${}^{13}\mathrm{C}{}^{16}{\mathrm{O}}_2$ with a typical observed spectrum given in the inset. (b) Experimental configuration of wavelength modulated cavity enhanced absorption spectroscopy(WM CEAS) of ${}^{12}\mathrm{C}{}^{16}{\mathrm{O}}_2$, along with a typical observed spectrum. Note that the signal acquired by WM CEAS essentially presents the first derivative of the normal absorption spectrum and the modulation effect has been included in the fit. (c) Dependence of $q$ on ${\gamma }_{12}/2\pi$ in the ${}^{13}\mathrm{C}{\mathrm{O}}_2$ measurements (purple circles) and theory (pink range and blue line) with a standing wave field intensity of $I=1.83\times {10}^8\mathrm{W}/{\mathrm{m}}^2$. (d) Dependence of the $q$ on the standing-wave field intensity $I$ in ${}^{12}\mathrm{C}{\mathrm{O}}_2$ measurements (red circles) and theory (pink range and blue line) with ${\gamma }_{12}/2\pi =1.63\times {10}^{-6}\mathrm{Hz}$.