Quantum-Noise-Limited Optical Frequency Comb Spectroscopy

We achieve a quantum-noise-limited absorption sensitivity of $1.7\times {10}^{-12}{\mathrm{cm}}^{-1}$ per spectral element at 400 s of acquisition time with cavity-enhanced frequency comb spectroscopy, the highest demonstrated for a comb-based technique. The system comprises a frequency comb locked to a high-finesse cavity and a fast-scanning Fourier transform spectrometer with an ultralow-noise autobalancing detector. Spectra with a signal-to-noise ratio above 1000 and a resolution of 380 MHz are acquired within a few seconds. The measured absorption line shapes are in excellent agreement with theoretical predictions.

Figure 1

Schematic of the experimental setup. Er:fiber femtosecond laser is locked to a high-finesse optical cavity containing a gas sample. An electro-optic modulator (EOM) is used to phase modulate the comb light at 14 MHz, and the cavity reflected light is dispersed by a reflection grating and imaged on two photodetectors (PD1 and PD2) in order to create error signals at two different wavelengths. The feedback is sent to laser current controller and to a PZT inside the laser cavity. The cavity transmitted light is coupled through a polarization-maintaining fiber into a fast-scanning Fourier transform spectrometer. The two outputs of the interferometer (beams 1 and 2) are incident on two photodiodes of the autobalancing photodetector. The beam of a cw 780 nm external cavity diode laser (ECDL), used for frequency calibration, is propagating parallel to the frequency comb beam and incident on a separate detector (not shown). P—polarizer, (P)BS—(polarizing) beam splitter cube, $\lambda /4$—quarter wave plate, $\lambda /2$—half wave plate.

Figure 2

(a) The centerburst of double-sided interferograms acquired in 3 s with one photodiode (upper red trace) and with the autobalancing detector (lower blue trace) and (b) the magnitude of their Fourier transform with a resolution of 380 MHz. The cavity was filled with 5 ppm of acetylene in 150 Torr of nitrogen, the optical power detected on each photodiode of the autobalancing detector was $100\mu \mathrm{W}$. The noise is reduced by a factor of 600 by the autobalancing detector at the frequency of the interferogram (180 kHz, corresponding to $6520{\mathrm{cm}}^{-1}$), as is demonstrated in (c), where a zoom of (b) is shown.

Figure 3

(a) Single element sensitivity in a normalized spectrum as a function of optical power incident on one photodetector at a resolution of 380 MHz (red triangular markers) and 2.3 GHz (blue square markers). Each data point is an average of 10 and 30 measurements, respectively, and the error bars are one standard error. The red and blue lines represent the corresponding shot noise limit, which is $6^{1/2}$ times lower at a resolution of 2.3 GHz because of the 6 times lower number of resolved spectral elements. (b) The Allan Deviation of a single element on the baseline between acetylene absorption lines in a spectrum measured at a resolution of 380 MHz and $100\mu \mathrm{W}$ of power, such as shown in Fig. 4a. The linear fit has a ${\tau }^{-1/2}$ dependence characteristic for white noise up to 400 s.

Figure 4

Normalized experimental (blue) and theoretical (red and green, inverted for clarity) spectra of 2 ppm of acetylene in (a)–(c) 150 Torr of ${\mathrm{N}}_2$ measured in 6 s with 380 MHz resolution and in (d) 630 Torr of ${\mathrm{N}}_2$ measured in 1 s with 2.3 GHz resolution. (b) and (c) show zooms of two parts of the spectrum shown in (a). (b) The slightly dispersive shape of the experimental absorption lines (blue), reproduced well in the model spectrum (green, inverted), is caused by the fact that the comb lines are offset from their respective cavity modes at wavelengths away from the laser locking points (chosen at 1528 and 1535 nm in this case). (c) At the locking points and in their vicinity, the comb lines are on resonance with the cavity modes and the absorption lines lack the dispersive part. The signal-to-noise ratio is lower in (b) than in (c) because of the lower comb power at these wavelengths.