A phase-stable dual-comb interferometer

ARTICLE DOI: 10.1038/s41467-018-05509-6 OPEN A phase-stable dual-comb interferometer 1234567890():,; Zaijun Chen1,2, Ming Yan1,2, Theodor W. Hänsch1,2 & Nathalie Picqué1,2 Laser frequency combs emit a spectrum with hundreds of thousands of evenly spaced phasecoherent narrow lines. A comb-enabled instrument, the dual-comb interferometer, exploits interference between two frequency combs and attracts considerable interest in precision spectroscopy and sensing, distance metrology, tomography, telecommunications, etc. Mutual coherence between the two combs over the measurement time is a pre-requisite to interferometry, although it is instrumentally challenging. At best, the mutual coherence reaches about 1 s. Computer-based phase-correction techniques, which often lead to artifacts and worsened precision, must be implemented for longer averaging times. Here with feedforward relative stabilization of the carrier-envelope offset frequencies, we experimentally realize a mutual coherence over times approaching 2000 s, more than three orders of magnitude longer than that of state-of-the-art dual-comb systems. An illustration is given with near-infrared Fourier transform molecular spectroscopy with two combs of slightly different repetition frequencies. Our technique without phase correction can be implemented with any frequency comb generator including microresonators or semiconductor lasers. 1 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany. 2 Ludwig-Maximilians-Universität München, Fakultät für Physik, Schellingstr. 4/III, 80799 München, Germany. Correspondence and requests for materials should be addressed to N.P. (email: ) NATURE COMMUNICATIONS | (2018)9:3035 | DOI: 10.1038/s41467-018-05509-6 | www.nature.com/naturecommunications 1 ARTICLE T NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05509-6 he performance of laser frequency combs1 has been constantly perfected to meet scientific challenges such as optical-clock comparisons2 or low-noise microwave generation3. For about a decade, novel applications involving timedomain interference between the two frequency combs have emerged and hold promise for enhancing the precision of interferometric measurements, as encountered in spectroscopy and sensing4–7, distance metrology8, tomography9, telecommunications10, etc. With a dual-comb system, a type of two-beam interferometer, the phase difference is in most of the implementations automatically and periodically scanned by means of two asynchronous trains of pulses. Although such systems have a potential for precisions directly set by atomic clocks, they still fail in many aspects to compete with mechanical interferometers. Unfortunately, it is still challenging to control the relative timing and phase fluctuations between the two combs and therefore to keep them coherent over extended measurement times. Conversely, the precise control of the phase difference in a two-beam interferometer involving a moveable mirror has indeed been perfected over decades and the mutual coherence between the two arms of the interferometer can be maintained over tens of hours11 in standard laboratory environments. The most powerful approach for establishing mutual coherence between two frequency combs has been to lock, with fast intracavity actuators, each comb to the same pair of cavity-stabilized continuous-wave lasers with hertz-level linewidth. In this way, mutual coherence times of the order of 1 s, determined by the linewidth of the continuous-wave lasers, have been achieved and linear-phase correction enhances the effective averaging times to tens of minutes7. Alternatively, schemes correcting the relative fluctuations with analog electronics6, digital processing12, or computer algorithms13 permit measurements, even with freerunning lasers. Another current trend is to design systems with built-in passive mutual coherence5,14. None of these solutions reaches the overall performance of the cavity-locked systems. Although already technically involved, mutual coherence times of about 1 s represent a strong limitation: numerical phase correction is required to reach the averaging times of several tens or hundreds of minutes. Phase-correction techniques have been widely documented in the context of Michelson-based Fourier transform spectroscopy15 and are straightforwardly transposable to dual-comb spectroscopy. Unfortunately, such techniques are complex and may generate computational errors and artifacts in the spectra16,17. Moreover, implementing them is not always feasible: emission spectra composed of scarce lines, as encountered in coherent Raman18 or two-photon excitation19 dual-comb spectroscopy, are known to be particularly challenging to phase correct20. In Michelson-based Fourier transform spectroscopy, a proper interferometer design, such as that of the Connes-type interferometers21,22, makes phase correction superfluous. Connes-type interferometers have been widely recognized by the molecular-spectroscopy community as instruments of superior performance for high-resolution Doppler-limited spectroscopy. With the increasing number of foreseen applications for highly precise dual-comb systems, for instance to spectroscopic measurements of very weak lines, to Doppler-free broadband spectroscopy19, to precise measurements of refractive indices23, or to distance monitoring24 between formations of spacecrafts, breaking the barrier of 1 s for the interferometer coherence times and enabling dual-comb spectroscopy without phase correction is crucial. Excellent performance has already been reported with all types of spectrometers for direct frequency comb spectroscopy, including Michelson-based Fourier transform spectrometers25–27 and dispersive spectrometers28. Dual-comb spectroscopy has the distinguishing advantage, though, that the resolution only derives from the measurement time, rather than from geometry (e.g., the 2 path difference excursion in a Michelson interferometer or the grating length in a dispersive spectrograph). Therefore—in principle—the resolution in a single non-interleaved dual-comb spectrum is fundamentally limited by the comb line spacing only, rather than by the instrumental resolution of a spectrometer. This implies that the coherence time of the dual-comb interferometer is sufficiently long to resolve the individual comb lines. Extended mutual coherence times will for instance enable the measurement of broadband spectra with combs of narrow line spacing (<1 MHz) in a single continuous measurement. Such an accomplishment will accelerate the development of Doppler-free multiplex spectroscopy19 and will open up exciting prospects for precision spectroscopy and metrology over broad spectral spans. In this article, we introduce a new concept for maintaining the coherence in a dual-comb system. Using feed-forward control of the relative carrier-envelope offset frequency of the lasers, we experimentally demonstrate a mutual coher (...truncated)