Dual-frequency-comb two-photon spectroscopy

This thesis reports on experimental demonstrations of a novel direct frequency-comb spectroscopic technique for the measurement of one- and two-photon excitation spectra. An optical-frequency-comb generator emits a multitude of highly coherent laser modes whose oscillation frequencies are evenly spaced and uniquely determined by only two measurable and adjustable radio-frequency parameters and the integer-valued mode number. Direct frequency-comb spectroscopy can traditionally be performed by scanning the comb lines of the frequency comb across the transitions of interest and measuring a signal that is proportional to the excitation by all comb lines in concert. Since the modes that contribute to the excitation cannot be singled out, transition frequencies can only be measured modulo the comb-line spacing with this scheme. The so arising limitations are overcome by the technique presented here, where the first frequency comb is spatially overlapped with a second frequency comb. Both combs of this so-called dual-comb setup are ideally identical except for having different carrier-envelope frequencies and slightly different repetition rates. The interference between the two combs leads to beat notes between adjacent comb lines, forming pairs (with one line from each comb) with an effectively modulated excitation amplitudes. Consequently the probability of excitation by any given comb-line pair is also modulated at the respective beat-note frequency. These beat-note frequencies are spaced by the repetition-rate difference and uniquely encode for individual comb-line pairs, thus enabling the identification of the comb lines causing an observed excitation. In a first demonstration, Doppler-limited one-photon excitation spectra of the transitions 5S_{1/2}-5P_{3/2} (at 384 Thz/780 nm), 5P_{3/2}-5D_{3/2}, and 5P_{3/2}-5D_{5/2} (both at 386 Thz/776 nm), and two-photon spectra of the 5S_{1/2}-5D_{5/2} (at 2x385 Thz/2x778 nm) transition, agreeing well with simulated spectra, are simultaneously measured for both stable Rb isotopes. Within an 18-s measurement time, a spectral range of more than 10 THz (20 nm) is covered at a signal-to-noise ratio (SNR) of up to 550. To my knowledge, this is the first demonstration of both dual-comb-based two-photon spectroscopy and fluorescence-based dual-comb spectroscopy. In a follow-up experiment probing the same sample and two-photon transitions, the Doppler-resolution limit is overcome by implementation of an anti-resonant ring configuration. Cancellation of the first-order Doppler effect makes it possible to resolve 33 hyperfine two-photon transitions. The highly resolved (1 MHz point spacing), narrow transition-linewidth (5 MHz), accurate (systematic uncertainty of ~340 kHz), high-SNR (10^4) spectra are shown to be consistent with basic simulation-based predictions. As the spectral span is, in principle, only limited by the bandwidths of the excitation sources, the acquisition of Doppler-free two-photon spectra spanning 10s of THz appears to be in reach. To my knowledge, this is the first demonstration of Doppler-free Fourier-transform spectroscopy. Lastly, the possibility of extending the technique's scope to applications in the field of biochemistry, such as two-photon microscopy, are explored. To that end, first high-speed, low-resolution (>>1 GHz) experiments are carried out identifying comb-stabilization requirements and measurement constraints due to the limited dynamic range of the presented highly multiplexed spectroscopic technique.