1. INTRODUCTION

The advent of the mode-locked Ti:sapphire laser in the early 1990s [1] made ultrafast pump–probe experiments accessible to a broad range of scientists. This was due largely to the Ti:sapphire laser’s robustness compared to the dye lasers it replaced, but another aspect of the Ti:sapphire laser that made many experiments possible was its low-noise performance. With quiet and stable ultrafast lasers, one could record small pump-induced changes in the optical properties of a sample, which is critical when the sample is either dilute or must be excited weakly to probe the desired physics [2–6]. Both scenarios are common, and today sensitive ultrafast methods are widely applied to many problems in chemistry, physics, biology, and materials science.

Despite this enormous progress, there remain many samples for which ultrafast optical spectroscopy is still prohibitively difficult. Most directly related to the current work are the “designer” gas-phase molecules and molecular clusters that can be produced in a supersonic expansion. While a wealth of information has been gained from measuring the static spectra of these systems using a variety of methods [7–10], studies recording dynamics are much more limited. With optical spectroscopy seemingly hopeless, ultrafast experimenters instead record signals from these dilute samples by ionizing the molecules with UV pulses or strong fields and detecting the resulting ions and electrons [11,12]. This is indeed extremely sensitive due to the capabilities of single particle detection and background-free signals. However, ionization projects the molecular state of interest onto a very different manifold of final states than optical measurements, and this can make the comparison of experimental data from gas phase and condensed phase highly nontrivial [13,14]. Furthermore, while dynamics of electronically excited states can be probed by ionization, there exists no ionization-based method for probing purely vibrational dynamics that is analogous to the powerful tools of ultrafast IR spectroscopy [15].

For linear spectroscopy, optical cavities are used in many different contexts for enhancing the strength of weak optical signals from gas-phase samples and performing ultrasensitive measurements [16]. The intracavity light passes through the sample many times, and the signal is increased by a factor proportional to the cavity finesse. Using an optical frequency comb as “a million stable lasers at once” [17], several groups have employed the cavity enhancement of frequency combs for performing spectroscopy that is simultaneously sensitive, broadband, and high-resolution [18–20]. These techniques, called “cavity-enhanced direct frequency comb spectroscopy” (CE-DFCS), have now been applied to rapid trace-gas detection [21,22], breath analysis [21,23], and microsecond time-resolved kinetics [24]. However, this previous spectroscopy work has largely neglected the pulsed nature of the intracavity comb, and the fact that these pulses can be used for the sensitive detection of ultrafast time-resolved signals [25,26]. Indeed, as we show here, the gains for nonlinear spectroscopy can actually be larger, since both pump and probe pulses can be resonantly enhanced.

In this article, we describe the use of cavity-enhanced frequency combs for performing optical measurements that are simultaneously ultrasensitive and ultrafast. We report transient absorption measurements with a 120 fs time resolution and a noise level as low as $\mathrm{\Delta }\mathrm{OD}=2\times {10}^{-10}$. To our knowledge, this represents an improvement of more than 5000 over previous transient absorption results [2], and a 100-fold improvement over previous high-performance time-resolved reflectivity measurements [3]. Importantly, by also resonantly enhancing the pump pulses to high average power ($\sim 50\mathrm{W}$), there is no compromise between the $\mathrm{\Delta }\mathrm{OD}$ detection limit and the fraction of molecules that can be excited, so that the large sensitivity improvement translates directly into the usable molecular concentration. This work extends ultrafast optical spectroscopy to molecular beams, and also can be adapted to other applications where higher sensitivity is needed [5,27]. Here we perform transient-absorption spectroscopy, but the general principles can be applied to other nonlinear spectroscopies. For example, 2D spectroscopy can be implemented in a straightforward fashion using phase-cycling methods [28].

2. PRINCIPLE OF ULTRAFAST SIGNAL ENHANCEMENT

It may seem contradictory that a high-finesse optical cavity with a long coherence time can enhance ultrafast signals, which decohere rapidly, but the fundamental mechanism for ultrafast signal enhancement is the same as in CE-DFCS and other cavity-enhanced spectroscopies. In CE-DFCS, an intracavity pulse traverses a sample of molecules, identical each round trip in the limit of weak excitation, many times. The signal is enhanced by ${\mathcal{F}}_{\mathrm{probe}}/\pi$ for the case of an impedance-matched ring cavity, where ${\mathcal{F}}_{\mathrm{probe}}$ is the cavity finesse [16]. In cavity-enhanced transient absorption spectroscopy (CE-TAS), the probe pulse also traverses a sample of molecules many times, but now we prepare this sample in an excited state using a pump pulse. This excitation, done at a repetition rate equal to the cavity’s free spectral range, is identical every round trip, so from the point of view of the probe pulse absorption, there is no difference between CE-DFCS and CE-TAS, and the resulting signal enhancement is the same. Time resolution comes from the time dependence of the excited state of the molecules, as in a normal pump–probe experiment, and the time-resolved signal is recorded by simply varying the pump–probe delay with an external translation stage.

Viewed in the frequency domain, CE-TAS uses both the intracavity comb’s spectral amplitude and its spectral phase, which encodes the pulse shape and delay, whereas CE-DFCS uses only the amplitude. The recorded transient absorption signal can be viewed as a third-order wave-mixing process between the pump and probe pulses and thus depends on the spectral phase [15]. The fractional change in the probe light intensity ($\mathrm{\Delta }I/I$) scales as the product of the pump power and the probe cavity finesse. Resonant enhancement of the pump pulses, with a separate cavity of finesse ${\mathcal{F}}_{\mathrm{pump}}$, can provide passive amplification of the pump power, so in principle the signal scales as ${\mathcal{F}}_{\mathrm{pump}}{\mathcal{F}}_{\mathrm{probe}}$. However, in practice the pump power cannot be arbitrarily increased, because it is desirable to perform the experiment in the perturbative limit to avoid multiphoton excitation of the sample by the pump pulse alone. A good rule of thumb for transient absorption spectroscopy is approximately 1% excitation [29].

A diagram of the CE-TAS setup is shown in Fig. 1. The foci of two femtosecond enhancement cavities (fsECs) cross at an angle of $\sim 20\mathrm{mrad}$ above a nozzle where sample molecules are introduced in a supersonic expansion. Pump and probe pulses traverse the sample in the same direction to avoid broadening of the temporal resolution due to the transit time through the sample. High-frequency modulation/demodulation techniques can still be employed for signal recovery without penalty as long as the modulation frequency is substantially lower than the cavity linewidths, but two complications arise in detecting the signal on the intracavity probe light. The first is that while the probe cavity enhances the signal, it also increases the amplitude noise on the transmitted light, since the probe cavity turns the laser’s frequency noise into amplitude noise. This is commonly encountered in cavity-enhanced spectroscopy [16]. The second is that the supersonic expansion flow speed is not fast enough to replenish the sample within one cavity round trip, so that the sample is reused for approximately 3–10 pump–probe sequences, and the probe pulse measures not only femtosecond signals from the excited population immediately preceding it but also nanosecond signals from several preceding pump pulses. This problem is unique to CE-TAS. Coherent molecular motion can be suppressed on nanosecond time scales by collisions with carrier gas [30] or the natural decay of the excited state (the likely case for most molecules of interest in ultrafast spectroscopy), but still a large ground-state bleach signal is expected to persist.

 

Fig. 1. Schematic of the CE-TAS system. Ultrafast transient absorption experiments are performed in a molecular beam at the common focus of two optical resonators, one for the pump pulses and another for the probe pulses. Delayed counterpropagating reference pulses are used for common-mode noise subtraction. The beams are color coded for clarity, but are all the same wavelength in the current experiment. More details are given in the main text.

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We solve both of these problems by coupling a counterpropagating reference pulse train to the probe cavity and recording the difference between probe and reference pulses in an autobalanced detection scheme. The pulse sequence at the molecular sample is illustrated in Fig. 2(a). The probe and reference pulses share common-mode noise, but different signals. The probe pulse arrives shortly after the pump and records the femtosecond signal of interest, while the reference pulse arrives 6 ns later and samples the persistent bleach signal. Counterpropagation allows the reference beam to be easily separated from the probe beam in the ring cavity geometry and also reduces the concern for any parasitic coherent excitation it might produce, since this is effectively smeared out in time. Noise reduction is shown in Fig. 2(b), where subtraction of the reference pulse reduces the relative intensity noise (RIN) on the intracavity light by more than 40 dB at the modulation frequency, allowing small signals to be recovered.

 

Fig. 2. Noise subtraction. (a) Pulse sequence at the molecular sample. The probe and reference share common mode noise but sample different molecular signals. (b) Intracavity relative intensity noise (RIN) spectrum with and without subtraction of the reference pulse train. More than 40 dB of RIN can be suppressed. With the introduction of sample molecules, the signal at the pump modulation frequency of 3.2 kHz is observed.

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3. TWO-CAVITY OPERATION

Experiments are performed with a home-built 87 MHz Yb:fiber laser system consisting of a passively mode-locked fiber oscillator, a pulse stretcher, a fiber amplifier, and a pulse compressor. The oscillator is similar to the one presented in Ref. [31]. The oscillator’s net cavity group delay dispersion (GDD) is tuned to near-zero GDD, but is slightly anomalous, giving the quietist operation with a roughly 30 kHz free-running comb-tooth linewidth. Linear chirped-pulse amplification up to 9 W average power is done in a similar fashion to Schibli et al. [32]. This is ample power for generating a wide range of wavelengths, but in the present demonstration, both pump and probe combs at 529 nm are produced via simple second-harmonic generation in a beta-barium borate (BBO) crystal.

The probe cavity is a nearly impedance-matched four-mirror bow-tie ring cavity with two 50 cm radius of curvature concave mirrors for a finesse of ${\mathcal{F}}_{\mathrm{probe}}=370$ and an absorption enhancement factor of approximately 120. We measure the probe cavity finesse using a ringdown technique, as described in [23]. The intracavity focus is calculated to be 70 μm FWHM. We use a two-point Pound–Drever–Hall locking scheme to lock the comb to the cavity, as described in [33]. A tight locking of the center of the frequency comb to the probe cavity is achieved using an electro-optic modulator (EOM) inside the Yb:fiber oscillator cavity. A slower feedback loop moves a diffraction grating inside the oscillator to adjust the laser’s carrier-envelope offset frequency ($f_0$) to match that of the probe cavity, which is determined by the dispersion of the probe cavity optics [34].

The pump cavity is a four-mirror bow-tie ring cavity with a 110 μm focus formed by 75 cm radius of curvature mirrors. The pump cavity is strongly overcoupled [35], with the loss dominated by the 3% transmission of the input coupler. Since we have two cavities but the laser has only one $f_0$, determined by the lock to the probe cavity, we adjust the $f_0$ of the pump cavity to match that of the probe. This is achieved by inserting an $\sim 150\mathrm{\mu m}$ fused silica microscope cover slip at Brewster’s angle inside the pump cavity. Different cover slips were tried until one with the correct thickness was found. The pump cavity is locked to the comb using a fast piezoelectric transducer (PZT) [36] and “side-of-line” lock where the cavity’s transmitted power is used as the error signal. The pump power is then modulated at 3.2 kHz by adjusting the lock point and providing a feed-forward signal to the PZT in concert. Calculations indicate that for the low finesse ($\sim 200$) employed here, when the pump cavity’s $f_0$ is the same as the laser’s, changes in the intracavity pulse shape and delay are negligible as the intracavity pump power is modulated in this way. We have experimentally verified this by recording signals with different modulation depths and DC offsets to the lock point, confirming that the observed signal scales simply as the product of the intracavity power and the modulation depth without changing shape.

Both pump and probe cavities are mounted on an optical platform housed in a 60 cm by 120 cm rectangular vacuum chamber. The geometrical parameters of the pump and probe cavities (e.g., focal lengths, spot sizes) were chosen considering ease of alignment, interaction length in the sample, and the constraint that the cavities fit in this chamber. Overlap of pump and probe beams at the sample is obtained by aligning both cavity modes through a 100 μm diameter pinhole placed near the plane of the nozzle. This alignment cannot be optimized in situ with the current mechanical design, but this could be accomplished by motorizing the pump cavity mirrors. The pump beam polarization is rotated by inserting a wave plate in the pump beam and reorienting the intracavity cover slip.

4. TRANSIENT ABSORPTION MEASUREMENTS

For this demonstration, we chose to study gas-phase molecular iodine (${\mathrm{I}}_2$) excited to the $B{}^3{\mathrm{\Pi }}_{0_u^{+}}$ state. The $B$ state of ${\mathrm{I}}_2$ has been extensively studied using both time-resolved and static spectroscopy [30,39,40], and thus is a good candidate for testing this new technique. Excitation to the bound $B$-state potential energy surface launches a vibrational wave packet. In our experiment with pump and probe at the same wavelength, we expect to observe a bleach of the ground state absorption along with stimulated emission occurring when the wave packet returns to the Franck–Condon region, as shown in Fig. 3(b).

 

Fig. 3. Transient absorption data. (a) Measurements of a molecular wave packet in the $B{}^3{\mathrm{\Pi }}_{0_u^{+}}$ state of ${\mathrm{I}}_2$. Stimulated emission occurs when the molecule returns to the Franck–Condon region. Three vibrational states near $v=33$ on the $B$ state surface are predominantly excited, giving rise to the observed vibrational beating pattern. Rotational motion causes a rapid decay of the polarization anisotropy. The perpendicular polarization data were taken under different conditions for the pump cavity and have been multiplied by 3.2. (b) Potential energy curves [37,38] of ${\mathrm{I}}_2$ with arrows illustrating the pump and probe processes. (c) If the partial pressure of ${\mathrm{I}}_2$ in the vacuum chamber gets too high, an artifact of the CE-TAS scheme is visible before time zero due to distortion of the intracavity pulses. This artifact is effectively eliminated by reducing the gas flow. (d) The intracavity light spectrum is also visibly distorted when the artifact appears.

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To introduce the ${\mathrm{I}}_2$ sample, He or Ar carrier gas is passed through a room-temperature Teflon pickup cell containing glass wool coated in solid iodine powder and then expanded into vacuum through a 700 μm diameter nozzle. To decrease the amount of ${\mathrm{I}}_2$ in the experiment, we merge this flow with a separate stream of pure carrier gas that bypasses the pickup cell, diluting the ${\mathrm{I}}_2$ concentration. All components in the gas-handling system downstream of the pickup cell, including the nozzle, are made of Teflon to prevent undesired chemistry. The stagnation pressure is varied between 200 and 760 Torr, and the laser beams cross approximately 1 mm above the nozzle. The molecular beam is directed into a Roots pumping system while the chamber pressure is maintained below 7 mTorr by a turbomolecular pump and dry-ice-cooled cold trap.

Data are recorded by scanning the external delay stage and recording the subtracted signal (probe – reference) with a lock-in amplifier. Typical pump–probe traces from a He-seeded expansion for both parallel and perpendicular polarizations are shown in Fig. 3(a). Coherent oscillations of the $B$-state wave packet are observed on top of a ground state bleach signal. The observed oscillation frequency, vibrational beat pattern, and rotational dephasing [41,42] are in accordance with what is expected based on the known spectroscopy of iodine [30,40] and our laser spectrum. The right y-axis shows the fractional change in the transmitted light intensity ($\mathrm{\Delta }I/I$) determined from the DC photocurrent at the detector and the calibrated lock-in gain. The left y-axis shows the change in the molecular ensemble’s optical density ($\mathrm{\Delta }\mathrm{OD}$), calculated from $\mathrm{\Delta }I/I$ and the measured cavity finesse via

Systematic uncertainty regarding these quantities is estimated to contribute less than 20% error to the y-axis calibration. Diffraction effects due to spatial inhomogeneity in the excited sample (e.g., from pump misalignment) would only increase the signal enhancement factor [43]. For long delay scans, CE-TAS enjoys the practical convenience that pump/probe overlap is determined solely by the spatial modes of the pump and probe fsECs, and is therefore insensitive to the translation stage position or alignment. If high-pressure argon is used as the carrier gas, a large coherent transient with a FWHM of 120 fs is observed before the oscillatory signal, and this is used to determine the zero of the delay axis and estimate the temporal resolution. We have verified that the raw signal ($\mathrm{\Delta }I$) is linear in the pump and probe/reference powers by varying these over 1 order of magnitude and a factor of 2, respectively. At the highest pump powers employed ($\sim 50\mathrm{W}$), we estimate that the pump pulse excites a few percent of the ${\mathrm{I}}_2$ molecules.

An additional concern with the CE-TAS scheme arises from the potential distortion of the intracavity pulse shape due to absorption from background gas in the vacuum chamber. This is particularly true for a molecule like ${\mathrm{I}}_2$, with sharp spectral features that can cause the probe pulse to develop a wake. Indeed, when flowing large amounts of ${\mathrm{I}}_2$ gas, we observe a small oscillatory signal before time zero due to this wake. The appearance of this signal coincides with the onset of ${\mathrm{I}}_2$ absorption lines becoming barely visible in the intracavity light optical spectrum [Fig. 3(d)]. This artifact becomes negligible when the ${\mathrm{I}}_2$ flow is reduced, as shown in Fig. 3(c). As in other forms of cavity-enhanced spectroscopy, the total absorption of the analyte should be kept small with respect to the cavity mirror losses to avoid distortions of the signal.

We examined the noise performance of CE-TAS by reducing the ${\mathrm{I}}_2$ flow as low as we stably could with our current gas-handling system and recording 60 consecutive scans over a 1 h period. In each scan, the data are taken for 0.5 s per delay point with perpendicular polarizations and a 50 fs step size, for a total accumulation of 30 s per point. Figure 4(a) shows every 10th scan along with the average of the complete data set. The error bars in Fig. 4(a) are the uncertainty in the mean, calculated simply as the standard deviation of the 60 consecutive measurements divided by $\sqrt{60}$. The error bars have a mean size of $\mathrm{\Delta }\mathrm{OD}=2.0\times {10}^{-10}$ averaged over all delays, with a standard deviation of $2\times {10}^{-11}$. This noise level is consistent with the RIN data of Fig. 2 and the measurement time of 30 s/point when the 3 dB difference of phase-sensitive lock-in detection is accounted for, suggesting that even over 1 h data acquisition times, the measurement is dominated by white noise processes. White noise performance is also supported by an Allan deviation analysis, shown in Fig. 4(b). We thus report the sensitivity as $\mathrm{\Delta }\mathrm{OD}=1\times {10}^{-9}/\sqrt{\mathrm{Hz}}$, and our demonstrated detection limit in a practical transient absorption experiment, where averaging time must be distributed over many pump–probe delays, as $\mathrm{\Delta }\mathrm{OD}=2\times {10}^{-10}$.

 

Fig. 4. Noise performance of CE-TAS. (a) Transient absorption measurements taken with reduced gas flow and perpendicular polarizations. The red dots represent the average of 60 consecutive scans taken over a 1 h period. The black curves show every 10th scan from the data set. Inset: Zoom-in around 0.8 ps delay. Error bars represent the uncertainty in the mean. (b) The green squares show the average of the Allan deviations obtained independently for each delay point. Error bars here are the standard deviation (not the uncertainty in the mean) of this ensemble, to represent the spread in the data. The blue diamond is the average of the error bars of (a), along with their standard deviation. The gray line has a slope of $-1/2$ on the log–log plot, the expected slope for white noise performance.

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5. DISCUSSION

The ability to average for long times, due to high-frequency modulation/demodulation and the noise-canceling scheme unique to CE-TAS, is remarkable when compared to the performance of other cavity-enhanced spectroscopies, which often reach a flicker noise floor within a few minutes. Still, the current measurement remains technical noise limited. Based on previous work in suppressing noise in CE-DFCS [33,44], achieving shot-noise-limited detection should be possible, which would reduce the detection limit of the current system by 1 order of magnitude. Furthermore, the current probe cavity finesse of 370 is quite modest for cavity-enhanced spectroscopy, and this can also be improved along with the time-resolution and probe pulse bandwidths that can be achieved [45,46]. There will likely be trade-offs between the cavity finesse and the bandwidth and tunability of the probe light due to cavity-mirror dispersion [34]. The methods can be extended to the UV and IR [47], the probe light can be spectrally resolved as in conventional transient absorption spectroscopy, and multidimensional spectroscopy can be performed via phase cycling methods [28].

Even with the current performance, CE-TAS easily extends all-optical ultrafast spectroscopy to a vast array of interesting systems that can only be produced in supersonic expansions. Assuming that pump-induced changes in the absorption are on the same order of magnitude as the ground state absorption, exciting 2% of the molecules, one can study samples with an optical density as small as ${10}^{-8}$. For ${\mathrm{I}}_2$, with an absorption cross section of $3\times {10}^{-18}{\mathrm{cm}}^2$ [48], this translates to a column density less than ${10}^{10}\mathrm{molecules}/{\mathrm{cm}}^2$ . As an example system of interest, consider small gas-phase water clusters ${({\mathrm{H}}_2\mathrm{O})}_n$, which can be produced via molecular beam methods with column densities and optical densities larger than our detection limit [10]. Linear spectroscopy has been performed on these systems using cavity ringdown methods and action spectroscopy [10,49], but the small clusters are expected to dissociate in tens of picoseconds upon vibrational excitation [50], necessitating ultrafast techniques to record fleeting vibrational coherences. The application of ultrafast IR spectroscopy to small water clusters, where one can assemble the liquid “one molecule at a time” [51], could allow systematic studies of the dynamics of hydrogen bond networks with unprecedented detail. Reducing the detection limit further, as discussed above, and increasing the interaction length could potentially allow for measurements on trapped mass-selected ion clusters [52,53], where an even higher degree of control over cluster composition and temperature is attainable.

CE-TAS with only a probe cavity could also benefit other optical measurements. For example, correlated electron systems in condensed matter at low temperatures [5,6] must be excited very weakly to avoid undesired thermal effects, and this has limited efforts to study the dynamics of complex materials [27]. It is, in principle, possible to incorporate a solid sample into the probe cavity either as a component of a mirror coating or as a wafer at Brewster’s angle to perform ultrasensitive time-resolved measurements on solids as well.