1. Introduction

So far, atoms have been the natural playground for the observation and precise measurement of tiny physical effects. From a theoretical point of view, the intrinsic simplicity of atomic systems enables reliable modelling. Experimentally most atomic transitions lie the in the visible/UV, where tunable coherent sources are easily available. Moreover, frequency stabilization and sub-Hertz narrowing of such lasers has been achieved[1] mainly thanks to high-finesse Fabry-Perot cavities even exceeding the one-million value[2]. In the last decade a revolutionary metrological tool, the optical frequency-comb synthesizer (OFCS), has become available. It is a clockwork based on a mode-locked fs laser (eventually combined with a strongly nonlinear optical fiber) providing a single-step link between the optical and microwave regions[3, 4, 5]. The appearance of the OFCS has added a Cs-traceable frequency scale to measurements throughout the entire visible range and, more recently, up to about 2.5 µm wavelength[6]. But the strongest transitions for most of simple molecules, belonging to the so-called fingerprint region, lie at wavelengths longer than 2.5 µm and may have natural linewidths of a few tens of Hz. Difference-frequency-generation (DFG) from near-IR continuous-wave (CW) lasers in nonlinear crystals has proven to be a low-noise[7], well suited tool for high-resolution[8] and high-sensitivity[9] molecular spectroscopy in the mid-IR. Sub-Doppler spectra with absolute frequency scales have been observed[10] using such a DFG, linked to an OFCS. OFCS transfer to the mid-IR region has also been demonstrated by using optical parametric oscillators (OPO)[11], or by direct non-linear down-conversion of the OFCS, both with a DFG process[12] and with an OPO[13]. The technology of periodic poling[14, 15], i.e. the use of crystals having ferroelectric domains with a periodically inverted polarity to achieve quasi-phase-matching of the waves involved in the nonlinear process, has largely increased the DFG efficiency boosting the power of single-pass DFG mid-IR radiation in bulk crystals up to the mW range[16]. However, setting up a widely tunable source with a linewidth narrower than the natural width of molecular transitions, has proven to be very challenging, to date. In principle quantum cascade lasers (QCLs)[17] can achieve such performance when operated with an external-cavity geometry, which can provide a relative tunability around the center wavelength even exceeding 20%[18]. In addition, QCLs are expected to have a very narrow intrinsic linewidth (due to the negligible linewidth enhancement factor α)[19], though technical noise has prevented to observe this limiting value, so far. The availability of a highly precise and sensitive probe, able to encompass wide IR regions, is the key to access the strongest ro-vibrational transitions for most of simple molecules. Such a tool could provide new insights in elusive quantum-mechanical effects encoded in molecules[20, 21, 22, 23, 24, 25, 26, 27] and open new perspectives for all applied fields relying on trace molecule detection. In this work we demonstrate operation of a widely tunable, ultra-stable, Cs-traceable coherent source in the mid IR, that combines high-efficiency DFG with an OFCS. Linewidth narrowing is achieved by using the OFCS as a transfer oscillator in a phase-lock scheme. Such a source could be a suitable probe for coherent control and metrology of ultracold molecular ensembles[28].

2. Experimental set-up

Our OFCS-referenced DFG source can generate 300-80 µWidler radiation at any wavelength between 3950 and 4570 nm. The significant variation in generated power is due to the 1/λ ² _i dependence of the nonlinear efficiency on the idler wavelength λ_i and to the absorption losses in LiNbO₃, that finally set the long-wavelength edge[7]. Instead, tunability at shorter wavelengths can be easily extended by a proper choice of fiber lasers/amplifiers and/or different semiconductor lasers. A schematic of the DFG source is shown in Fig. 1. A 50-mm-long periodically-poled LiNbO₃ (PPLN) crystal mixes about 100 mW pump radiation from an external-cavity diode laser (ECDL) with about 3.4Wsignal radiation from a Yb-fiber-amplified Nd:YAG laser at 1064 nm. The ECDL has a feedback diffraction grating moved by a piezo-electric transducer (PZT) and is tunable between 838 and 863 nm. In order to control the phase/frequency of the generated IR radiation against our fs Ti:sapphire OFCS, which covers an octave in the visible/near-IR region (500-1100 nm), we follow an electronic scheme based on direct digital synthesis (DDS)[29]. Both pump and signal frequencies are beaten with the closest tooth of the OFCS (the corresponding integer orders N_p and N_s are measured by a wave-meter) and the respective RF beat notes Δν_pc and Δν_sc satisfy the following equations:

 

Fig. 1. OFCS-referenced DFG IR source. OFCS is used as a transfer oscillator to phase-lock the ECDL directly to the Nd:YAG. DM, dichroic mirror; Ge, germanium filter. See text for other acronyms.

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where ν_r≈1 GHz is the repetition rate and ν_o is the OFCS carrier-envelope-offset (CEO), which is canceled from these beat notes by standard RF mixing. A low bandwidth (≈10 Hz) phase-locked-loop (PLL) is used to remove the frequency drift of the Nd:YAG laser. A DDS circuit multiplies the Δν_sc+ν_o frequency by a factor N_p/N_s. A second PLL circuit with a wide bandwidth (≈2 MHz) locks the Δν_pc +ν_o frequency to the DDS output by sending feedback corrections to the ECDL current and PZT voltage. The pump frequency is then ν_p=(N_p/N_s)νs, without any contribution from the OFCS parameters ν_o and ν_r (at least at frequencies >10 Hz). As a consequence, the absolute frequency ν_i of the generated idler radiation is given by the following equation:

The idler linewidth δν_i can be expressed in terms of the signal linewidth δν_s, as follows:

where, for all frequencies below 10 Hz, δν_s traces the linewidth of the comb tooth around 1064 nm while, for all frequencies above 10 Hz, δν_s coincides with the free-running Nd:YAG laser fluctuations. The accuracy of ν_i is only limited by the reference oscillator of our OFCS, which is a Rb/GPS-disciplined 10-MHz quartz with a stability of 6·10^-13 at 1 s and a minimum accuracy of 2·10^-12. Moreover, continuous scans of ν_i up to 2 GHz can be performed by sweeping νr, with a full coverage without gaps between 3950 and 4570 nm. We would like to point out that such a scheme is used for the first time to phase-lock two laser sources which are 70 THz apart, achieving a DFG radiation with a frequency not only accurate against the Cs primary standard, but also stable (narrow linewidth). Such approach can be easily generalized to larger frequency separations, at least in the OFCS operation range. From the previous discussion emerges that the attainable stability is ruled only by the signal laser. Of course, several approaches can be implemented to further enhance the signal frequency stability, e.g. by narrowing it onto Fabry–Perot cavities[30, 31].

3. Frequency stability and absorption sensitivity characterization

In order to test the frequency stability of this source and the achievable absorption sensitivity, we built a 1-m-long high-finesse cavity with maximum reflectivity at 4500 nm. The ZnSe plano-concave mirrors have a high-reflection coating on their concave surface (6 m radius of curvature) and an anti-reflection coating on the plane surface. Each mirror was measured to have 270 ppm losses (100 ppm absorption and 170 ppm transmission), corresponding to a finesse F≈11500. The transmitted power through the resonant cavity was about 35% of the incident one and the achieved mode-matching was 86%. The mirror holders are separated by a three-bar Invar structure which guarantees a good passive thermal stability. The whole structure lays inside a vacuum chamber with a cantilever system damping mechanical vibrations in all directions. The vacuum conditions prevent frequency fluctuations due to pressure changes. A three PZT system is mounted on one mirror for fine cavity tuning. In order to use this cavity as frequency noise discriminator of the IR source, we have characterized its passive frequency stability. The cavity drift of about 1 kHz/s was measured from the linewidth of the cavity transmission averaged over long time scales (about 500 s) when illuminated with the OFCS-locked DFG source, which has negligible drift in this time interval. At 100 Hz, the frequency noise induced by the PZT-driven electronics was measured to be one order of magnitude lower than the one of the IR source, and it decreases with a 1/f behavior up to 30 kHz. A resonance frequency of about 19 Hz and a damping time of about 5 s for the cantilever damped vibration system were measured by using an accelerometer. In Fig. 2 (a), we assigned the 19 Hz peak to the residual vibrational cavity noise at the cantilever resonance. Due to the narrow linewidth of this resonance, the noise amplitude falls by 15 dB at 20 Hz. For frequencies higher than 20 Hz, the vibrations are damped following a 1/f² law in units of $\mathrm{Hz}⁄\sqrt{\mathit{Hz}}$, as inferred by the solution of the differential equation for a damped harmonic oscillator forced by external vibration-induced white noise.

 

Fig. 2. (a) Frequency noise spectral density recorded with a FFT spectrum analyzer. Three spectra with different frequency spans (2 kHz, 10 kHz, 1 MHz) are stuck together and plotted in the same graph (RBW=3·10^-3×span). (b) Typical single-shot cavity ring-down signal. The experimental data points, the exponential fit curve and the residuals are shown.

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To characterize the frequency noise of our source, we tuned the cavity length at a transmission corresponding to half of the peak value and used the slope of the fringe side as a frequency-to-amplitude converter. The frequency noise spectral density recorded with a FFT spectrum analyzer is shown in Fig. 2 (a). The red lines highlight different behaviours of the spectrum: 1/f technical noise (ν<2 kHz), white noise (ν>2 kHz), cavity-cut-off region (ν>10 kHz), detector-cut-off region (ν>400 kHz). Following the above discussion about the cavity frequency stability, we can consider negligible the cavity contribution to this noise in the spectral range shown in the figure. From the power spectral density in the white-noise region we can infer an IR intrinsic linewidth[32] of about 10 Hz, while the time-integrated linewidth over 1 ms is about 1 kHz. In order to evaluate the signal-to-idler frequency noise transfer, we also applied a 8 kHz frequency modulation onto the Nd:YAG laser radiation, with known amplitudes A_mod. In the frequency-to-amplitude cavity converted spectrum at 4500 nm, the peak at 8 kHz is observed with amplitudes of about (N_p/N_s-1)A_mod, in agreement with Eq. 3, confirming the negligible cavity contribution to the measured noise spectral density.

To measure the absorption sensitivity, we performed CW cavity ring-down (CRD) spectroscopy[33] with the empty cavity (pressure<10^-5 mbar). The IR radiation is switched off in ≈200 ns by deflecting the pump beam with an acousto-optic modulator (AOM) in double-pass configuration. Fig. 2 (b) shows a single-shot CRD event, the exponential fit and the corresponding residuals. The standard error over 1/τ achieved in a measurement time T=100 µs (4·10^-5 µs^-1) yields an absorption sensitivity of 1.3·10^-11 cm^-1Hz-^1/2. The shot-noise-limited minimum detectable absorption is expressed by the following equation[34]:

where L=100 cm is the cavity length, B=1/(2πT) is the detection bandwidth, η≈2.5 A/W is the detector responsivity, P≈6 µW is the detected optical power. The calculated value α_min=8.0·10^-12 cm^-1Hz-^1/2 is then very close to the experimental one. Actually, the achievable sensitivity over longer timescales is even two orders of magnitude worse than expected. We ascribe that discrepancy to shot-to shot geometry-dependent variations of τ, optical fringes, finite extinction ratio of the light modulator, similarly to what was observed by other groups performing CRD.

4. Conclusions

In conclusion, we have developed a mid-IR coherent source whose frequency is tunable over 600 nm around 4250 nm, having a 10-Hz intrinsic linewidth, a short-term absorption sensitivity down to 10^-11 cm^-1Hz-^1/2 and an accuracy better than 2·10^-12, limited by the OFCS clock. It should be noted that the low wavelength limit is only determined by the tunability of the pump/signal sources, while the transparency range of the nonlinear crystal sets the upper one. This new source can be a key tool to search for physical “secrets” still well kept in molecules, such as the evidence of parity violation (e.g. by looking for energy differences between enantiomers) or tiny variation of fundamental constants of nature, like the electron-to-proton mass ratio m_e/m_p (e.g. looking for variations in the rotational/vibrational energy ratio). In addition, novel spectroscopic instrumentation, based on such radiation source, can be built for highly sensitive and precise molecular detection with application to key fields, like homeland security, environmental and geochemical monitoring or biomedicine.