Two-photon direct frequency comb spectroscopy with chirped pulses

Thanks to the high peak intensities of ultrashort pulse trains that make up an optical frequency comb, conversion to much shorter wavelengths is readily available. Therefore direct frequency comb spectroscopy may offer the possibility of extending high-resolution spectroscopy to spectral regions that are unexplored so far. In this work, we investigate the impact of a chirp, i.e., a varying frequency across the pulses, on the excitation rate obtainable with two-photon direct frequency comb spectroscopy. Using the cesium $6\hspace{0.5em}{}^2{S}_{1/2}$-$8\hspace{0.5em}{}^2{S}_{1/2}$ two-photon transition at $822$ nm, we show that destructive interference of various quantum paths reduces the excitation rate with the inverse of the time bandwidth product of the exciting pulses.

Figure 1

Left: direct two-photon frequency comb spectroscopy. If one of the modes (${\omega }_0$) is tuned on resonance ($\Delta \omega =\frac{1}{2}{\omega }_{\mathit{eg}}-{\omega }_0=0$), all other modes combine pairwise to deliver the transition energy $\hslash {\omega }_{\mathit{eg}}$. Right: for constructive interference of all excitation paths, the modes of the frequency comb must be properly phased.

Figure 2

Top: Experimental setup. Two counter-propagating beams from a stabilized ps mode locked Ti:sapphire laser are superimposed in a 10 cm Cs vapor cell at room temperature. The pulses are chirped with a set of optical fibers (FI $=$ Faraday isolator, AOM $=$ acousto optic modulator, EOM $=$ electro optic modulator, PMT $=$ photomultiplier tube). Bottom: Image of the excitation volume with fluorescence at 456 nm from the decaying $8\hspace{0.5em}{}^2{S}_{1/2}$ via the $7\hspace{0.5em}{}^{2}P$ levels. The pulse collision volume, where the Doppler-free excitation takes place, appears as a bright spot in the center. Doppler-broadened excitation takes place all along the laser beam.

Figure 3

Example of the Doppler-free signal (count rate up to several kHz) from the pulse collision point shows two allowed hyperfine components ($F=3\to F=3$ and $F=4\to F=4$) of the $6\hspace{0.5em}{}^2{S}_{1/2}$-$8\hspace{0.5em}{}^2{S}_{1/2}$ transition.

Figure 4

Left: Normalized Doppler-free line strength versus time bandwidth product of the exciting pulses ($F=4$: $▴$ and $F=3$: $▾$). The solid line shows the theoretical line reduction according to Eq. (5) normalized to the unchirped transition rate. Right: The corresponding autocorrelation traces and pulse spectra after chirping with various chirp parameters (curves of-set for clarity). Top: Laser pulses are chirped by a single-mode polarization-maintaining fiber (PSM) of 1 m length. Center: The chirp is generated with a large-mode field diameter photonic crystal fiber (PCF) of 5 m length. Bottom: Same as center but for different fiber lengths and similar power levels: 0.3 m (84 mW), 1 m (81 mW), 2 m (86 mW), 5 m (95 mW), and 10 m (115 mW).