1. Inroduction

Since the advent of ultrafast lasers, coherent and quantum control of molecular rotations has been an active field of research, providing researchers with a versatile tool to obtain spectroscopic information from gas-phase molecules [1–3]. Although the corresponding applications seem to be unrelated and scattered across various subfields of physics [4], they are all based on the same physical framework. Non-resonant parity-preserving interaction between intense laser pulses and molecular polarizability anisotropy aligns the molecular axes with the laser polarization by exerting an external torque. If the interaction is adiabatic, i.e. the pulse duration is equal to or longer than the periods of rotational transitions, the rotation is hindered and pendular states can be formed [5]. On the other hand, if the pulse duration is much shorter than the rotational transition periods, the alignment is nonadiabatic, i.e. the excitation is impulsive. Theoretical calculations in Ref. [6] show that for fully non-adiabatic alignment, the excitation pulse needs to be at least ten times shorter than a specific rotational transition period. If non-adiabatic alignment conditions are met, a quantum wavepacket of coherently excited rotational Raman transitions is created. In fact, non-adiabatic excitation of rotational wavepackets has been historically used for time-domain rotational coherence spectroscopy, mainly for high precision measurements of geometric properties of molecules [7]. Directly after the interaction with the laser pulse has ceased, the aligned molecules continue rotating freely and should ultimately dephase into an isotropic angular distribution. However, since the angular momentum and energy levels are quantized with ${E_{JM}} = hBcJ(J + 1)$, the wavepacket evolves coherently with a rephasing period of ${T_{rev}} = 1/(2Bc)$, where T_rev is the so called “rotational revival period”, B is the molecular rotational constant, c is the speed of light, J is the rotational quantum number, M is the magnetic quantum number, and h is Planck’s constant. The degree of alignment depends on the pulse shape, duration, and intensity, as well as polarizability anisotropy of the targeted molecules [6], and it is quantified with:

Several experimental techniques have been utilized to study molecular alignment, for example Coulomb explosion imaging for low density gases [9], alignment-induced transient birefringence with weak pulse probing [10], and non-resonant degenerate four-wave mixing (DFWM) [11]. Spatial alignment of molecules enables manipulation and control of the quantum mechanical rotations of the molecules. The schemes for coherent control and their purposes are diverse; from innovative applications such as quantum computing [12] to practical solutions for overcoming challenges of non-adiabatic alignment. One of the main challenges is the risk of ionization owing to strong-field interactions with the molecules. High energy rotational transitions demand higher field strength in order to align with the laser pulse polarization. Therefore, ionization can be a complication for all of the aforementioned experimental approaches, since the imposed upper limit of the laser intensity might not be high enough to achieve a high degree of alignment, especially for hot thermal ensembles [6]. A commonly practiced solution to minimize the ionization probability has been the utilization of a pulse train, spectrally modulated in some cases, and split from a single strong pulse for multiple excitation [13–15]. However, it has been shown in several studies that applying a train of pulses limits the non-adiabatic excitation to relatively low energy rotational transitions due to the Anderson localization effect and centrifugal distortion (see for example [16]).

Multiple excitation is one of several approaches to coherent control of molecular rotation. An optical centrifuge is another type of coherent control method used for excitation of high energy rotational transitions, circumventing the localization effect [17,18]. In this type of quantum control, circular polarizers, extra multipath amplifiers, and pulse shapers are used on fs pulses to create strong ps-excitation pulses able to accelerate the rotating molecules to J levels beyond what can be reached by thermal excitation (∼50000 K). However, one of the most common coherent control approaches, and the focus of this paper, is utilization of a second excitation pulse (control pulse), to manipulate the initially generated wavepacket. If the control pulse (or two pulses in case of DFWM) is identical to the first excitation pulse and exactly in phase with the wavepacket, i.e. if it arrives at an integer multiple of T_rev after the first excitation, the alignment is enhanced and the signal is amplified [13]. On the other hand, if the control pulse is out of phase with the wavepacket, i.e. it arrives at odd integers of 1/2 T_rev, destructive interference destroys the molecular alignment and annihilates, i.e. dumps, the corresponding signal [19,20]. Moreover, a delay of odd integers of 1/4 T_rev between the excitation pulses has been shown to have applications in isomer-selective control of homonuclear diatomics [21].

Although there have been successful reports of coherent control performed at room temperature and near atmospheric pressure, most of the techniques have generated more promising results for cold ensembles, with a Boltzmann population distribution over low J levels, avoiding the centrifugal distortion effect and ionization. Moreover, a coherent rotational wavepacket generated from a thermal ensemble at near room temperature and atmospheric pressure decays in the order of 100 ps. In the case of an optical centrifuge with weak-field polarization probing, the decay of the “super-rotors” extends to several 100 ps owing to the long mean free time of the molecules relative to the period of rotational transitions at near- or sub-atmospheric pressures [17]. However, to the best of our knowledge, detection in all of the aforementioned experiments has been temporal via time-consuming successive probing over multiple delays with ultrashort laser pulses in stable and homogeneous environments. Clearly, time-domain interrogation limits the available spectroscopic applications. Nevertheless, if the entire temporal decay is extracted, presumably with hours of data collection, the corresponding spectrum may be retrieved through Fourier transformation [21].

In this paper, we present a novel method to control the shape of spectra using two-beam hybrid fs/ns coherent anti-Stokes Raman scattering (RCARS). The method provides for simultaneous detection of the signal in both temporal and spectral domains within a single-shot acquisition, employing significantly lower excitation pulse energies in comparison to conventional coherent control approaches. Specifically, single-shot detection in the frequency domain enables instantaneous measurement in non-stationary and unpredictable environments such as turbulent reacting flows. Moreover, using low energy excitation allows application of coherent control at various pressures and temperatures by eliminating the risk of multiphoton ionization [22–24]. There is also no need for pulse shapers and spectral modulation, since the attenuated transform-limited fs pulses can be used directly for excitation. In experiments such as controlling molecular super-rotors [25], even for very fast spinning molecules present at low pressures, the method would allow detection of the entire coherence decay within a single-shot acquisition using a long ns probe field. Furthermore, the method enables utilization of coherent control in typical RCARS spectroscopic applications, such as accurate thermometry and species detection, including concentration measurements in reacting flows [26,27]. We use a selective excitation approach as an illustrative example to demonstrate the exceptional versatility and capacity of the technique.

2. Experimental

Rotational CARS is a non-linear and non-degenerate four-wave-mixing optical technique, where three laser fields, namely pump (ω₁), Stokes (ω₂), and probe (ω₃), interact with the molecular third order susceptibility χ⁽³⁾. As a result of this interaction a forth field (ω₄) (i.e. the CARS signal) is generated. The CARS signal exhibits laser-like features with high directionality, obeying the phase matching condition and conservation of momentum, suitable for measurements with high background luminosity [26]. The signal is significantly enhanced if |ω₁ – ω₂| is equal to an allowed Raman transition frequency, i.e. ΔJ = 2 for linear molecules (Fig. 1(a)). The experimental setup for this method is schematically depicted in Fig. 1(b). The source of the excitation pulses was a Ti:Sapphire laser system (Coherent, Hidra-50) providing transform-limited 125 fs pulses at 800 nm with 10 Hz repetition rate. The fs pulse was divided into two pulses of equal energy by a beam splitter, one of which is the first excitation (pump) pulse and the other the second excitation (control) pulse. A motorized optical delay line adjusted the time delay between the pump and control pulses. The probe was provided by a single-mode Nd:YAG laser (Quantel YG:981E) at 532 nm and pulse repetition rate of 10 Hz and duration of ∼15 ns. The spectral full width at half maximum (FWHM) of the probe beam was 0.003 cm⁻¹. The probe and the excitation pulses were focused into a rectangular cross-section gas sample cell through small, open slots on opposite sides (see e.g. [23,24,32]). Air does not enter the cell, however, because it has two similarly-slotted Ar-filled cells mounted on the optical input and output sides of the sample cell. The energy of the fs pulses was 40 µJ (in each pulse) and the ns pulse energy was 30 mJ. The angle between the probe and excitation beams was 5° following the phase-matching condition and polarizations presented in Ref. [28]. The signal was collimated and then separated from the probe by a linear polarizer and a short-pass filter, after which it was focused onto the entrance slit of a 1-meter Czerny–Turner spectrograph. A holographic grating with 2400 grooves/mm dispersed the signal before it was imaged at the slit of the streak camera (Optronis, Optoscope). The laser pulses and the streak camera were synchronized using pulse/delay generators resulting in 45 ps temporal jitter (root mean square) calculated from 300 single shots. The temporal resolution of the detection system in each shot was 23 ps and the spectral resolution was 2.22 cm⁻¹.

 

Fig. 1. (a) Energy diagram of RCARS, and (b) schematic of the experimental setup; VA- variable attenuator, HW- half-wave plate, BS- beam splitter, ODL- optical delay line, BD- beam dump, P- polarizer, L1, L2, and L3- lenses (f = 150 mm, 300 mm, and 750 mm, respectively), A- analyzer, SP- short-pass filter (Semrock, Razor edge, 561 nm), SC- streak camera.

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3. Results and discussion

Figure 2 shows single-excitation RCARS spectrograms of nitrogen (N₂), oxygen (O₂), air, and methane (CH₄), recorded at atmospheric pressure and room temperature and averaged over 300 single shots. As can be seen from the figure, the entire decays of the dispersed coherences are recorded up to ∼300 ps, limited by the dynamic range of the streak camera.

 

Fig. 2. Experimental RCARS spectrograms of nitrogen (N₂), oxygen (O₂), air, and methane (CH₄), averaged over 300 single shots and recorded at room temperature and atmospheric pressure. The apparent stripes in the CH₄ spectrogram are due imperfections in the detection system.

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Since CH₄ is a spherical top and thus not rotationally Raman active, its purely non-resonant signal reflects both the temporal resolution of the detection system and the effective spectral bandwidth of the excitation pulses. The latter is especially important since all the spectrograms are compensated spectrally with this measured effective band shape. Time zero is chosen as the point where the CH₄ signal peaks. The rotational revival periods of N₂ and O₂ are 8.38 ps and 11.60 ps, respectively. Thus, the periodic signature of the rotational recurrences on the resonances is obscured by the limited temporal resolution of our detection system and can therefore not be observed in Fig. 2. However, the manifestation of the rotational revivals on the coherences derived by fs/ps RCARS has been observed and reported using an asymmetric ps-probe pulse [29]. An explanation for this manifestation is presented in Fig. 3. The imaginary part of the numerically calculated Raman response of N₂ to the first excitation pulse at room temperature and atmospheric pressure is depicted in Fig. 3 as the blue curve. The response to the control pulse at half of the T_rev of N₂, i.e. at 4.19 ps, is also displayed as the red curve. The interference of the two generated coherences, as expected, is destructive, hence eliminating the induced alignment (black dotted curve).

 

Fig. 3. Imaginary part of the Raman molecular response of N₂ with one pulse excitation at t = 0 (blue curve), and t = 4.19 ps (red curve), and the interference of the two responses (black dotted curve)

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Since, according to the calculations in Ref. [6] for transitions higher than J = 3, excitation with 125 fs pulse duration may not be entirely impulsive, the molecular response in Fig. 3 is convolved temporally with the cross sections of the perfectly overlapping field envelops of ω₁ and ω₂, i.e. E²(t), with E being completely Gaussian and having a FWHM of 125 fs. Figure 4 depicts the corresponding experimental RCARS spectra related to Fig. 3, all integrated temporally after t = 25 ps in order to avoid the non-resonant contribution. All curves are normalized with respect to the largest spectral peak. Although there has been successful demonstration of heterodyne CARS measurements [30], the majority of the RCARS experiments are performed in homodyne fashion, recording the square of the signal polarization |P²| at the CCD chip instead of the polarization itself. Therefore, as can be seen in the figure, even though having different phases, the recorded RCARS signals of N₂ with both excitation pulses are almost identical. It is worth noting that the Fourier transform of the two signals presented in Fig. 4 does not result in retrieving the corresponding temporal response, emphasizing the benefits of simultaneous access to the temporal domain via detection with the streak camera.

 

Fig. 4. Time integrated experimental RCARS signal of N₂ with single excitation at t = 0 (blue curve), and t = 4.19 ps (green dots), and destructive interference of the two signals with double pulse excitation (thick red curve). A theoretically calculated spectrum of the interference is shown with the black curve. The spectra are recorded at room temperature and atmospheric pressure and averaged over 300 single shots and integrated after t = 25 ps.

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The red curve in Fig. 4 is the experimental result for destructive interference of the two N₂ signals excited at t = 0 and t = 4.19 ps. As predicted numerically in Fig. 3, the initially created rotational wavepacket is annihilated (“dumped”) by the control pulse, resulting in an attenuation of a factor of ∼40. Furthermore, there is excellent agreement between the experimental data and the theoretical calculation. The theoretical model follows closely the one described in Ref. [31], which has been successfully utilized for single-shot thermometry in the gas phase [23,32]. There are a few modifications to the model from Ref. [23]; the second molecular response at the delay of τ is included and RCARS calculations of O₂ are added. For the latter, the approach reported in Ref. [33] is employed by considering the triplet rotational states rather than a simplified singlet assumption. Although efforts have been made to quantify the collisional Raman line broadening of O₂, as described in [34,35], a modified exponential energy gap model (MEG) is applied for this proof of concept, assuming the same collisional dephasing rates for the triplet states [36].

Pure rotational Raman resonances are located within a spectral range covering merely a few hundreds of wavenumbers for essentially all molecular gases [37]. Broadband Raman excitation thus allows detection of multiple species within a single-shot acquisition, which is considered one of the major assets of RCARS for diagnostics [26]. However, this inherent capacity can only be utilized as long as the RCARS spectrum of all the species involved can be accurately modelled, which requires valid molecular constants, including collisional broadening coefficients. There is also a limitation dictated by the relative molecular concentrations in the gas mixture; the spectral lines of a molecular species present in very low concentrations will be concealed by the much stronger lines associated with species present in high concentrations. Our method of selective excitation offers effective solutions to both of these common spectroscopic issues. In the following, we provide examples of how this method of coherent control can resolve the aforementioned challenges.

Figure 5(a) depicts the temporal integration of a selectively excited O₂ spectrogram averaged over 300 single shots, one of which is presented in Fig. 5(b). While the first excitation pulse generated the rotational coherences of N₂ and O₂ molecules present in air, the second pulse sent at 1/2 T_rev of N₂, has efficiently removed (“dumped”) the N₂ coherences, leaving only perturbed O₂ lines in the spectrum. This can be confirmed by comparing the air and pure O₂ RCARS perturbed spectra, indicated with red and blue curves in Fig. 5(a). Both spectra, which are nearly identical, were prepared by sending the control pulse at the N₂ dumping delay time of 4.19 ps. Comparing the unperturbed O₂ spectrum with one-pulse excitation, shown as the dotted blue curve in Fig. 5(a), and the perturbed O₂ spectrum indicated with the solid blue curve, reveals that the O₂ coherences are significantly altered by the control pulse. This coherence disturbance is theoretically predicted by our model and is shown as the black dashed curve in Fig. 5(a), which overlaps the experimental data quite well. Figure 5(b) contains a spectrum of selectively excited O₂ rotational coherences in air recorded within a single- shot acquisition and compared with the theoretical prediction. The high signal-to-noise ratio demonstrates excellent potential to apply the method for instantaneous measurement in non-stationary environments. Indeed, for one pulse excitation of a species present at lower concentrations, the corresponding lines might be masked by the lines of the dominant species, depending on the spectral resolution. This is usually the case for species detection in reactive flow fields, where N₂ as an inert gas dominates the probe volume and masks the lines of other species in lower concentrations such as O₂, CO, CO₂, NO, or NO₂.

 

Fig. 5. (a) Spectra resulting from temporal integration of averaged experimentally recorded RCARS spectrograms with double pulse excitation of air (red curve) and pure O₂ (blue curve) with t = 4.19 ps delay between the pulses. The theoretical prediction is indicated with black dashed curve. For comparison, an unperturbed O₂ spectrum with one pulse excitation is shown with the dotted blue curve, which is integrated temporally from O₂ spectrogram in Fig. 2. (b) Rotational CARS spectrum of air with double pulse excitation recorded in a single-shot acquisition (red curve), together with theoretical prediction of the signal plotted with black dashed curve. The spectra are recorded at room temperature and atmospheric pressure and integrated after t = 25 ps, and averaged in (a) over 300 single shots

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Figure 6 demonstrates an application of RCARS-coherent control for detection of species with relatively low concentration in gas mixtures. A temporally integrated, one-pulse-excitation RCARS spectrum of a binary mixture, containing 93% of N₂ and 7% of O₂, is shown by the red curve in Fig. 6. The spectral resolution is not sufficient to isolate the weak O₂ lines from the strong N₂ lines, resulting in a spectrum where essentially all O₂ lines are completely masked by the N₂ lines. However, after successfully dumping the N₂ coherences, by applying the control pulse, the perturbed spectrum of pure O₂ appears (blue curve), which very closely follows the theoretical prediction indicated with the black dotted curve. Interestingly, the O₂ spectra in Fig. 5(a) and Fig. 6 are virtually identical, differing only in intensity. Hence, this method convincingly demonstrates the potential for minor species detection, and it suggests quantification with higher accuracy. It is worth mentioning that the proposed coherent control method, if used for spectroscopic purposes without any need to study the dynamics of the coherences, can also be done with single-shot ps probing at a specific delay, preferably after the non-resonant trace leaves the signal, together with use of a conventional CCD camera instead of the streak camera for spectral detection.

 

Fig. 6. Experimental RCARS signal of a binary mixture of 93% N₂ and 7% O₂ with one pulse excitation (red curve), and double pulse excitation (blue curve). The theoretically calculated spectrum of the latter is shown with the black dotted curve. The spectra are recorded at room temperature and atmospheric pressure and averaged over 300 single shots and integrated after t = 25 ps.

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An interesting aspect associated with the use of a streak camera for detection is presented in Fig. 7. The two purely non-resonant signals of CH₄, generated in quick succession by the two excitation pulses, create optical beats on the CCD chip of the streak camera, from which the time delay between the excitation pulses can be measured very accurately. This type of optical beating can also appear in the time domain, when two or more spectral lines have frequency differences smaller than the spectral resolution (see for example spectrogram of air in Fig. 2 around 84 cm⁻¹). Figure 7(a) shows an averaged RCARS spectrogram of CH₄ generated by two excitation pulses with the relative delay resulting in the data presented in Fig. 4. The blue curve in Fig. 7(b) is the temporal integration of the spectrogram in Fig. 7(a). A first-order sinusoidal function, $I = A\sin ({\omega _{fit}}K)$ was chosen to find the best fit to the blue curve, where K is the wavenumber and A is a dimensionless amplitude. The best fit is shown as the dashed black curve, with a derived frequency of ω_fit = 0.7901 rad·cm, corresponding to a temporal period of T_fit = 4.1945 ps. This result is strikingly close to t = 4.1914 ps, which is our theoretical calculation for 1/2 T_rev of N₂ based on the molecular constants presented in Ref. [38] considering all the rotation-vibration interaction coefficients.

 

Fig. 7. (a) Optical beats recorded with the streak camera. The beats are created by two non-resonant signals of CH₄ generated with a certain time delay arriving at different times on the CCD chip, and (b) time integrated version of (a) shown by the blue curve. The best sinusoidal fit is shown with the black dashed curve.

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4. Conclusion

In conclusion, quantum control of molecular rotation with hybrid fs/ns RCARS enables completely new, quantified spectroscopic applications in gas-phase diagnostics, such as selective species detection and thermometry with possibly higher accuracy for measurements at low concentrations. Moreover, low excitation-pulse energy significantly reduces the multiphoton-ionization risk, hence opening up for applications at various temperatures and pressures. In this method, an ultrashort fs pulse aligns the ensemble of molecules involved in a non-degenerate four-wave-mixing process. Consequently, selective signal amplification is possible by sending a control (subsequent) pulse at a delay corresponding to the molecular revival period of a specific species after the first prompt excitation. Moreover, as presented in this paper, a control pulse at half of the revival period of a species can efficiently annihilate the corresponding induced alignment, resulting in selective excitation and alignment of other species in the mixture. Subsequently, the selectively aligned molecules can be ionized and separated from the mixture [39]. Furthermore, selectively removing rotational coherences has the potential for detection of minor species present in the probe volume. Rotational coherent wavepackets have lifetimes limited mainly by collisional dephasing. These lifetimes are on the order of few ps to hundreds of ps depending on pressure and the frequencies of the rotations. Therefore, probing with a long ns pulse allows detection of the entire decay within a single-shot acquisition, avoiding slow measurement series with delayed fs probing. Moreover, simultaneously resolving the signal in temporal and spectral domains within a single-shot acquisition enables spectroscopic applications in non-stationary environments as well as studying the dynamics of molecules undergoing the quantum control processes.

Nitrogen and oxygen were chosen as examples in the present work and our experimental data are accurately predicted by theoretical calculations. This method motivates further investigations in utilizing CARS, in order to control the molecular rotation for various purposes such as excitation of super-rotors, and selective species excitation/annihilation/amplification in realistic and practical environments with a significantly faster and less complex experimental approach. The method also has possible applications in molecular dynamics studies, species separation with laser fields, as well as spectroscopic laser diagnostics in reactive flows such as low-density species detection and accurate thermometry.