Broadband Doppler-limited two-photon and stepwise excitation spectroscopy with laser frequency combs

Multiplex two-photon excitation spectroscopy is demonstrated at Doppler-limited resolution. We describe first Fourier-transform two-photon spectroscopy of an atomic sample with two mode-locked laser oscillators in a dual-comb technique. Each transition is uniquely identified by the modulation imparted by the interfering comb excitations. The temporal modulation of the spontaneous two-photon fluorescence is monitored with a single photodetector, and the spectrum of all excited transitions is revealed by a Fourier transform.

Figure 1

Frequency-domain illustration of the principle of dual-comb two-photon spectroscopy. For simplicity, we assume in this figure that the carrier-envelope offset frequency of the two frequency combs is equal to zero. Pairs of comb modes with the same sum frequency [$n^{\prime }{f}_{\mathrm{r}}$ for comb 1, $n^{\prime }(f_{\mathrm{r}}+\delta f_{\mathrm{r}})$ for comb 2] resonantly excite a two-photon transition at the optical frequency $f_0$. The excitation rate of the transition is modulated at the beat frequency $n^{\prime }\delta f_{\mathrm{r}}$, which is approximately equal to $\frac{f_0}{f_{\mathrm{r}}}\delta f_{\mathrm{r}}$. An intensity modulation of frequency $\frac{f_0}{f_{\mathrm{r}}}\delta f_{\mathrm{r}}$ is thus observed in the fluorescence radiated during decays to lower states. Because the frequency of the modulation is proportional to the transition frequency $f_0$, the two-photon excitation spectrum is revealed by Fourier transformation of the fluorescence intensity recorded versus time.

Figure 2

Experimental setup for dual-comb two-photon spectroscopy of atomic rubidium vapor. cw, continuous-wave; SHG, second-harmonic generation; PMT, photomultiplier tube; PD, photodiode.

Figure 3

(a) Experimentally relevant fine structure of rubidium. (b) Two portions of an unaveraged, corrected interferogram recorded at $T=393$ K with $\delta f_r=1$ Hz (red) and contributions to that interferogram from two-photon transitions (blue). The two-photon interferometric traces (blue) have been vertically-shifted for clarity. Two time scales are displayed. The laboratory time is the actual measurement time which accounts for the down-sampling nature of the technique. The effective time is the time delay between two pulses in a pair, one pulse from each comb.

Figure 4

Experimental dual-comb spectra. (a) Portions of the one- and two-photon excitation spectrum of Rb. The entire range of the one-photon excitation lines is shown in the upper-left part of the panel, while the main part zooms in to the individual one- and two-photon transitions (tick increment is 10 GHz). The spectrum, displayed at an unapodized resolution of 300 MHz, is recorded at $T=308$ K within 18 s measurement time. (b) Portion of the two-photon spectrum recorded at $T=393$ K (solid cyan: 18 s measurement time, unapodized resolution of 300 MHz; solid orange: 54 s measurement time, unapodized comb transform-limited linewidth of 4.4 MHz; dashed black: computed).

Figure 5

Portion of the absorption dual-comb spectrum of Rb at $T=308$ K and 300 MHz unapodized resolution.