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Rotational spectroscopy with an optical centrifuge Aleksey Korobenko,*a Alexander A. Milner,a John W. Hepburnb and Valery Milnera We demonstrate a new spectroscopic method for studying electronic transitions in molecules with extremely broad range of angular momentum. We employ an optical centrifuge to create narrow rotational wave packets in the ground electronic state of 16O2. Using the technique of resonance-enhanced multi-photon
Received 30th October 2013, Accepted 9th January 2014
ionization, we record the spectrum of multiple ro-vibrational transitions between X3Sg and C3Pg electronic
DOI: 10.1039/c3cp54598a
manifolds of oxygen. Direct control of rotational excitation, extending to rotational quantum numbers as high as N \ 120, enables us to interpret the complex structure of rotational spectra of C3Pg beyond
www.rsc.org/pccp
thermally accessible levels.
The dynamics and spectroscopy of highly excited states of molecules is an issue of great importance to chemical physics. Perturbative approaches do not always work at high levels of excitation, where coupling between degrees of freedom changes dramatically from what is observed at thermal energies.1 As a result, interpreting molecular spectra becomes increasingly difficult as the level of excitation grows.2 Significant geometric changes in highly excited molecules, when the level of excitation exceeds an isomerization barrier, make understanding molecular spectroscopy in these energy ranges an ongoing challenge.4,5 This challenge can become more acute in the case of spectroscopic studies of a process, where product molecules can be formed in highly excited states.6,7 To detect the low density products, resonance-enhanced multiphoton ionization (REMPI) is often employed due to its high sensitivity, spectral resolution and versatility.8,9 This means that the electronic spectroscopy of a highly rotationally excited molecule must be understood, both the assignment of resonances and their strengths. This task can be complicated by a predissociative coupling and decay behavior in the intermediate excited electronic states.10 Assuming that the molecule of interest is reasonably stable, REMPI spectra recorded at high temperatures can provide information on the properties of highly excited states, but this approach is limited both by the temperatures that the molecule can tolerate before it dissociates, and by the difficulty of unraveling the complex spectrum of a high temperature molecule, as illustrated by the work done on the spectrum of high temperature water.2 In the case of oxygen, reaching the high rotational states probed in this paper (N > 100) would require a temperature of E50 000 K. a
Department of Physics & Astronomy, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1. E-mail: [email protected] b Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1
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Rotational excitation of oxygen with strong ultra-short laser pulses is limited to N B 40 due to the rapidly increased ionization rate with growing laser intensities.3 Even if a broad thermal distribution of highly excited rotational states could be produced in a diatomic molecule such as oxygen, the triplet structure of the ground and excited states coupled with twophoton selection rules (for the C3Pg (v 0 = 2) ’’ X3Sg (v00 = 0) transition), would result in as many as 21 overlapping rotational branches, making spectroscopic assignment challenging.11 Optical centrifuge is an alternative tool for exciting molecules to extremely high rotational states by means of non-resonant laser fields.12–15 In a recent study, we have shown that the centrifuge can be used to produce and control the so-called ‘‘super rotor’’ states – coherent rotational wave packets with ultra-high angular momentum N and narrow distribution width dN { N.16 Here we utilize this unique capability of the centrifuge for the purpose of obtaining and interpreting complex REMPI spectra of oxygen super rotors (0 o N t 120). We excite oxygen to a narrow rotational wave packet whose center is accurately tuned across the broad range of well defined N values. The centrifuge excitation is then followed by a REMPI measurement. Owing to the narrow N distribution, the detected spectrum becomes significantly less congested, and identifying rotational resonances is greatly simplified. Following the original recipe by Karczmarek et al.,12 we utilize the output of an 800 nm, 35 fs (full width at half-maximum, FWHM), Ti:Sapphire regenerative amplifier. We split its spectrum in half at around the central wavelength (Fig. 1a), in a Fourier plane of a pulse shaper. Frequency chirps of equal magnitude (0.26 ps2) and opposite signs are applied to the ‘‘red’’ and ‘‘blue’’ arms of the centrifuge, as demonstrated by the cross-correlation frequency-resolved optical gating (XFROG) measurement (Fig. 1c). The latter was carried out by overlapping the centrifuge pulse with a reference Fourier-transform limited pulse on a 20 mm-thick BaB2O4 crystal. The bandwidth of the reference pulse was reduced
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Fig. 1 Optical centrifuge. (a) Broadband laser pulses from a Ti:S chirped pulse amplifier (10 mJ, 35 fs, 1 KHz repetition rate) are dispersed with a diffraction grating and split in the center of the spectrum in a Fourier plane of the focusing lens into ‘‘red’’ and ‘‘blue’’ arms, whose chirps are individually controlled by two separate ‘‘chirp boxes’’. The chirp of the ‘‘red’’ arm is reversed, while that of the ‘‘blue’’ arm is left unchanged. Movable shutter on a motorized linear stage (inset) allows precise truncation of the ‘‘blue’’ arm bandwidth. (b) Spectrum of the centrifuge pulse after shaping. Solid red (dashed black) line corresponds to the truncated (full) centrifuge. (c) Cross-correlation frequency-resolved optical gating (XFROG) spectrogram of the truncated centrifuge field, schematically shown below the XFROG plot. O is the angular frequency at which molecules are released from the centrifuge.
to about 1 nm in a separate pulse shaper to increase the spectral resolution. The spectrum of the frequency mixing signal was measured as a function of the relative time delay between the centrifuge and reference pulses. The two centrifuge arms are combined with a polarizing beam splitter cube, and polarized with an opposite sense of circular polarization. Optical interference of the two circularly polarized frequency-chirped laser fields results in a pulse with rotating linear polarization (inset to Fig. 1c). Because of the anisotropic polarizability, molecular axes line up along the axis of laser polarization, and then follow it adiabatically as the plane of polarization rotates with increasing angular frequency. Quantum-mechanically, this process corresponds to the rotational ladder climbing, executed as a series of consecutive Raman transitions between the rotational levels separated by DN = 2. Each step consists of absorbing a photon from the blue centrifuge arm and emitting a photon into the red arm. The frequency difference between the two photons (2O) grows in time following the rotational line separation. Opposite circular polarization of the two centrifuge arms ensures DMN = 2 selection rule, resulting in unidirectional rotation. Given the available spectral bandwidth, the accelerating centrifuge can reach angular frequencies on the order of 10 THz, which in the case of oxygen corresponds to the rotational quantum number N E 119. As we have demonstrated in ref. 16 truncating the spectrum of the centrifuge in a Fourier plane of the pulse shaper by a movable shutter (see inset to Fig. 1a, and field spectrum in Fig. 1b) enables accurate control of the rotational state of the centrifuged molecules. Characterizing the centrifuge field with XFROG allowed us to calibrate the final rotation speed of the
4072 | Phys. Chem. Chem. Phys., 2014, 16, 4071--4076
centrifuge, and hence the corresponding molecular angular momentum, as a function of the shutter position. REMPI detection was carried out using narrowband nanosecond probe pulses tunable from 279 nm to 288 nm (0.1 cm1 line width, 500 mJ per pulse, 50 Hz repetition rate). The probe beam was combined with a centrifuge beam (5 mJ per pulse) on a dichroic mirror (Fig. 2), and focused with a 35 mm focal length spherical aluminium mirror on a supersonically expanded molecular jet passing between the charged plates of the time-of-flight (TOF) mass spectrometer. We estimate the peak centrifuge field intensity at the focal spot around 1013 W cm2. The jet was generated by an Even-Lavie pulsed valve (25 ms opening time, 150 mm nozzle diameter) located 20 cm away from the detection region. Ion current was detected with a microchannel plate (MCP) detector. The initial rotational temperature of the sample, extracted from the REMPI spectrum taken without the centrifuge field (Fig. 3a), was about 10 K. The main result of this work is shown in Fig. 3, where the detected ion count is plotted against the probe energy (horizontal axis) and the final rotation speed O of the truncated centrifuge (vertical axis). The latter is expressed in terms of the angular momentum N of an oxygen molecule rotating with the angular frequency O, according to: O = 2pc[E(N) E(N 1)], E(N) = BN(N + 1) DN2(N + 1)2, where E is the energy of state |Ni, c is the speed of light in vacuum, B = 1.438 cm1 and D = 4.839 106 cm1.18 The validity of Dunham expansion of rotational energy to second order in
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Fig. 2 Detection setup. Centrifuge beam is combined with a tunable UV laser pulse and focused inside a vacuum chamber on a supersonically expanded oxygen jet between the charged plates of a time-of-flight (TOF) mass spectrometer. The ionization rate is measured with a multi-channel plate (MCP) detector.
N(N + 1) at extremely high values of N has been demonstrated in our previous study.16 Each peak in the two-dimensional REMPI spectrogram of Fig. 3b corresponds to a two-photon transition between a rotational level in the electronic ground state, X3Sg, and a rotational level of C3Pg. The finite horizontal width of the observed peaks stems from the predissociation line width (as in conventional
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‘‘1D REMPI’’ detection), whereas finite vertical spread reflects the narrow width of the excited rotational wave packet created by the centrifuge. The complexity of the two-photon absorption line structure in rotationally hot oxygen gas is illustrated by red and yellow lines in Fig. 3a which correspond to the hot thermal ensemble (simulated numerically) and the ensemble of centrifuged molecules (experimentally observed 2D spectrogram integrated along its vertical dimension), respectively. In sharp contrast to conventional 1D REMPI spectroscopy, controlled centrifuge spinning offers direct assignment of rotational quantum numbers to the observed REMPI peaks, as well as significantly better peak separation due to their distribution along the added second dimension. Vertical traces originating from bright resonance peaks in Fig. 3b (examples are marked with white arrows) correspond to molecules which ‘‘leaked out’’ of the weakened centrifuge potential before reaching the terminal angular frequency of the centrifuge. After escaping the centrifuge, these molecules continue their free rotation while the trap is accelerating further. The three bright vertical stripes reproduce the initial cold beam spectrum (blue line in Fig. 3a) and correspond to the molecules which were not trapped by the centrifuge. The width of the final rotational wave packets can be readily extracted as dN E 7 (FWHM), from the vertical cross sections, shown in Fig. 3c. Here, we detected rotational states with N as high as B80. Rotational line broadening above N E 60 can be attributed to the increasing Rydberg-valence interaction (governed by the Franck–Condon (FC) overlap with the continuum wavefunctions) similarly to the previously observed rotational broadening in the lower vibrational states (v0 = 0,1) of the excited potential.11
Fig. 3 2D REMPI spectrogram for a linearly polarized probe. (a) Experimental spectra of cold (10 K, blue) and centrifuged molecules (yellow), along with a simulated spectrum of a ‘‘hot’’ thermal ensemble (3000 K, red) calculated with pgopher software.17 (b) Ion signal as a function of the probe laser twophoton energy and molecular angular momentum defined by the centrifuge final rotation speed. Different areas of the 2D plot were measured with different sensitivities and probe intensities and are displayed with different color scales to compensate for the broad dynamic range of the data. (c) Vertical cross-sections of several consecutive peaks from one particular branch, shown in the inset to b. The peaks are regularly separated with a distance of DN = 2 reflecting 16O2 nuclear spin statistics.
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One can see that the peaks in Fig. 3 are grouped in regular patterns, resembling Fortrat parabolas corresponding to different rotational branches. Within a single branch, the center of each consecutive resonant peak is shifted by DN = 2 (Fig. 3c), reflecting 16 O2 nuclear spin statistics. Circularly polarized light can be used to further simplify the spectrum. As shown in Fig. 4, the signal strength of different rotational branches depends on the handedness of probe polarization. This is due to the highly non-uniform population distribution among the magnetic sub-levels in the centrifuged wave packet, with most of the population concentrated at MN C N (or MN C N).12 To identify different rotational branches, we use three sets of molecular constants (for F1,F2 and F3 spin–orbit components of the excited state) from the previous studies on thermally excited ensembles.7,19 The three components correspond to L + S = 0 (F1), 1 (F2) and 2 (F3), with L and S being the projections of the orbital and spin components of the total angular momentum on the molecular axis, respectively. These constants are listed in Table 1. For F2 and F3 components, our results are well described by the constants provided by Lewis et al.19 On the other hand, the observed F1 peaks do not agree well with the suggested numerical values (n0 = 69 366 cm1 and B0 = 1.6 cm1), as shown in Fig. 5. This can be attributed to the complexity of the broadened and highly overlapping structure of F1 lines, which makes it hard to interpret and fit the data from a thermally populated ensemble. Centrifuge spectroscopy enables
PCCP Table 1
Molecular constants used to fit the data in Fig. 4
Spin–orbit branch
v0/cm1
B0/cm1
D/cm1
3
69 375 69 445 69 550
1.585 1.648 1.685
2.5 107 1.0 105 1.3 105
P0(F1) P1(F2) 3 P2(F3) 3
us to correct the values of F1 molecular constants (Table 1) by performing the fit of the most pronounced DN = 2 branch (Fig. 5). The lowest vibrational level of C3Pg electronic state of oxygen known to exhibit well-resolved rotational structure is v = 2.11 Predissociation to the closely lying valence state 13Pg broadens the rotational spectrum of the lower vibrational states v = 0,1. This broadening is weakened in the case of v = 2 because the repulsive potential crosses the level near the node of the vibrational wavefunction, lowering the Franck–Condon overlap.11 The FC overlap, however, increases with the increasing degree of rotational excitation. At high values of N, we observe a significant line broadening which results in a completely unresolvable rotational structure at N \ 60 (see Fig. 3). At even higher centrifuge frequencies, corresponding to the extreme rotational levels with 99 o N o 125, we observe the re-appearance of narrow resonances shown in Fig. 6. Their line width drops down to a well-resolved B7 cm1, as shown in Fig. 7. Similar non-monotonic N-dependencies were previously
Fig. 4 2D REMPI spectrogram for a circularly polarized probe. Electric field vector is counter-rotating (a) and co-rotating (b) with the centrifuged molecules. The directionality of laser-induced rotation results in the sensitivity of the measured signal to the handedness of probe polarization. The results of fitting the data to the theoretical model are shown with colored lines and markers for different branches and resonances, respectively (see text for details). Branch nomenclature is the same as in ref. 11.
4074 | Phys. Chem. Chem. Phys., 2014, 16, 4071--4076
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Fig. 5 Comparison of the observed REMPI data for the perturbed F1 spin–orbit component with the calculations based on molecular constants from this work (red circles), White et al.7 (blue triangles) and Lewis et al.19 (purple squares).
observed in OD21 where they were used to analyze the repulsive state. Indeed, according to the Fermi Golden Rule, the line width is proportional to the predissociation matrix elements between the bound and the continuum eigenstates, as well as the density of states in the continuum. As shown in ref. 21 the behavior of both quantities with N can be calculated numerically and used for extracting the parameters of the repulsive state from the experimentally observed dependence on the rotational quantum number.
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Fig. 7 Observed linewidths of J 0 = N 0 1 (triangles) and J 0 = N 0 (squares) spin–orbit sublevels of C3Pg (v 0 = 1) level as functions of rotational quantum number N 0 . Inset demonstrates a fit of experimental data (solid red) to a sum of lorentzians (dashed black) in order to extract line widths. Absolute position, absolute area and the widths of two peaks were fitted for each doublet individually, with the areas ratio fixed to a value extracted from the best resolved N 0 = 115 doublet and with a doublet line separation equal to a calculated one.
Our analysis showed that, unlike the previously discussed branches of C3Pg (v 0 = 2) ’’ X3Sg (v00 = 0), the observed ultra-high narrow lines originate from the v 0 = 1 state, which displays no resolvable rotational structure at lower rotational levels, but re-appears at higher J’s. Well described by Hund’s
Fig. 6 Ultra-high rotational resonances of O2. The two panels correspond to two possible ways of fitting the observed resonant branches (apparent along white dashed lines) to the calculated Hund’s case (b) structure (labeled with markers). In panel a, the upper branch corresponds to DN = 1, and the lower one to DN = 3, resulting in Bv = 1.620 cm1 and Dv = 4.4 106 cm1. In panel b, the upper branch overlaps with DN = 2, whereas the lower one with DN = 2, yielding Bv = 1.664 cm1 and Dv = 5.7 106 cm1.
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case (b) at such high degree of rotational excitation, the observed rotational structure consists of a series of spin–orbit multiplets. Out of 9 possible DN branches, we have observed only two (dashed lines in Fig. 6). Given this limited amount of information, fitting the data by a single set of molecular constants proved difficult. Our analysis resulted in two possibilities shown in panels a and b of Fig. 6. The retrieved molecular constants are Bv = 1.620 cm1 and Dv = 4.4 106 cm1 for plot a, and Bv = 1.664 cm1 and Dv = 5.7 106 cm1 for plot b. To choose between the two possibilities, we note that in Hund’s case (a), an effective rotational constant B0 for F2 spin–orbit component is equal to the true Bv value.20 This implies that at v = 2, Bv = 1.648 cm1 (see Table 1). Since we expect Bv to decrease with v, Fig. 6b should reflect the correct branch assignment. In conclusion, we have demonstrated a new spectroscopic method for studying the rotational structure of electronic transitions in molecules. The method is based on controlled molecular spinning with an optical centrifuge. We have applied this technique to C3Pg ’’ X3Sg (v00 = 0) in O2. By varying the level of rotational excitation, we have observed rotational line broadening and narrowing associated with the dependence of predissociation rates on the molecular angular momentum. In case of v 0 = 2, resolved at lower rotational states (N t 60), we showed an agreement with previously reported molecular constants for F2 and F3 spin–orbit components and, owing to the higher resolution of the implemented method, refined those for the strongly perturbed F1 component. In case of v 0 = 1, extreme rotational excitation (N \ 100) resulted in the suppression of predissociation and enabled us to determine previously unknown rotational constants.
Acknowledgements This work has been supported by the CFI, BCKDF and NSERC, and carried out under the auspices of the Center for Research on Ultra-Cold Systems (CRUCS). We gratefully acknowledge stimulating discussions with R. Krems, V. Petrovic, M. Shapiro and E. Grant. We would also like to thank one of the reviewers of this manuscript for pointing out that the dependence of the rotational line width on N could be used for mapping out the repulsive potential responsible for the molecular predissociation. The analysis presented in Fig. 7 is a result of this valuable suggestion.
4076 | Phys. Chem. Chem. Phys., 2014, 16, 4071--4076
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References 1 J. C. Keske and B. H. Pate, Annu. Rev. Phys. Chem., 2000, 51, 323–353. 2 O. L. Polyansky, N. F. Zobov, S. Viti, J. Tennyson, P. F. Bernath and L. Wallace, Science, 1997, 277, 346–348. 3 H.-M. Frey, P. Beaud, T. Gerber, B. Mischler, P. P. Radi and A. P. Tzannis, Appl. Phys. B: Lasers Opt., 1999, 68, 735–739. 4 M. P. Jacobson, C. Jung, H. S. Taylor and R. W. Field, J. Chem. Phys., 1999, 111, 600–618. 5 J. Ma, D. Xu, H. Guo, V. Tyng and M. E. Kellman, J. Chem. Phys., 2012, 136, 014304. 6 A. S. Mullin, C. A. Michaels and G. W. Flynn, J. Chem. Phys., 1995, 102, 6032–6045. 7 M. G. White and R. J. Beuhler, J. Chem. Phys., 2004, 120, 2445–2455. 8 V. S. Letokhov, Laser photoionization spectroscopy, Academic Press, 1987. 9 M. N. R. Ashfold and J. D. Howe, Annu. Rev. Phys. Chem., 1994, 45, 57–82. 10 M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys., 1984, 84, 35–50. 11 A. Sur, C. V. Ramana, W. A. Chupka and S. D. Colson, J. Chem. Phys., 1986, 84, 69. 12 J. Karczmarek, J. Wright, P. Corkum and M. Ivanov, Phys. Rev. Lett., 1999, 82, 3420–3423. 13 D. Villeneuve, S. Aseyev, P. Dietrich, M. Spanner, M. Ivanov and P. Corkum, Phys. Rev. Lett., 2000, 85, 542–545. 14 L. Yuan, S. W. Teitelbaum, A. Robinson and A. S. Mullin, PNAS, 2011, 108, 6872–6877. 15 L. Yuan, C. Toro, M. Bell and A. S. Mullin, Faraday Discuss., 2011, 150, 101–111. 16 A. Korobenko, A. A. Milner and V. Milner, arXiv preprint arXiv:1304.0438, 2013. 17 PGOPHER, a Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.uk. 18 K. P. Huber and G. Herzberg, NIST Chemistry WebBook, NIST Standard Reference Database, National Institute of Standards and Technology, Gaithersburg MD, 2012, vol. 69. 19 B. R. Lewis, S. T. Gibson, J. S. Morrill and M. L. Ginter, J. Chem. Phys., 1999, 111, 186. 20 G. Herzberg, Molecular spectra and molecular structure, Krieger Publishing Co., Malabar, Florida, 2nd edn, 1950, vol. I. 21 J. Czarny, P. Felenbok and H. Lefebvre-Brion, J. Phys. B: At. Mol. Phys., 1971, 4, 124.
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Rotational spectroscopy with an optical centrifuge Aleksey Korobenko,*a Alexander A. Milner,a John W. Hepburnb and Valery Milnera We demonstrate a new spectroscopic method for studying electronic transitions in molecules with extremely broad range of angular momentum. We employ an optical centrifuge to create narrow rotational wave packets in the ground electronic state of 16O2. Using the technique of resonance-enhanced multi-photon
Received 30th October 2013, Accepted 9th January 2014
ionization, we record the spectrum of multiple ro-vibrational transitions between X3Sg and C3Pg electronic
DOI: 10.1039/c3cp54598a
manifolds of oxygen. Direct control of rotational excitation, extending to rotational quantum numbers as high as N \ 120, enables us to interpret the complex structure of rotational spectra of C3Pg beyond
www.rsc.org/pccp
thermally accessible levels.
The dynamics and spectroscopy of highly excited states of molecules is an issue of great importance to chemical physics. Perturbative approaches do not always work at high levels of excitation, where coupling between degrees of freedom changes dramatically from what is observed at thermal energies.1 As a result, interpreting molecular spectra becomes increasingly difficult as the level of excitation grows.2 Significant geometric changes in highly excited molecules, when the level of excitation exceeds an isomerization barrier, make understanding molecular spectroscopy in these energy ranges an ongoing challenge.4,5 This challenge can become more acute in the case of spectroscopic studies of a process, where product molecules can be formed in highly excited states.6,7 To detect the low density products, resonance-enhanced multiphoton ionization (REMPI) is often employed due to its high sensitivity, spectral resolution and versatility.8,9 This means that the electronic spectroscopy of a highly rotationally excited molecule must be understood, both the assignment of resonances and their strengths. This task can be complicated by a predissociative coupling and decay behavior in the intermediate excited electronic states.10 Assuming that the molecule of interest is reasonably stable, REMPI spectra recorded at high temperatures can provide information on the properties of highly excited states, but this approach is limited both by the temperatures that the molecule can tolerate before it dissociates, and by the difficulty of unraveling the complex spectrum of a high temperature molecule, as illustrated by the work done on the spectrum of high temperature water.2 In the case of oxygen, reaching the high rotational states probed in this paper (N > 100) would require a temperature of E50 000 K. a
Department of Physics & Astronomy, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1. E-mail: [email protected] b Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1
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Rotational excitation of oxygen with strong ultra-short laser pulses is limited to N B 40 due to the rapidly increased ionization rate with growing laser intensities.3 Even if a broad thermal distribution of highly excited rotational states could be produced in a diatomic molecule such as oxygen, the triplet structure of the ground and excited states coupled with twophoton selection rules (for the C3Pg (v 0 = 2) ’’ X3Sg (v00 = 0) transition), would result in as many as 21 overlapping rotational branches, making spectroscopic assignment challenging.11 Optical centrifuge is an alternative tool for exciting molecules to extremely high rotational states by means of non-resonant laser fields.12–15 In a recent study, we have shown that the centrifuge can be used to produce and control the so-called ‘‘super rotor’’ states – coherent rotational wave packets with ultra-high angular momentum N and narrow distribution width dN { N.16 Here we utilize this unique capability of the centrifuge for the purpose of obtaining and interpreting complex REMPI spectra of oxygen super rotors (0 o N t 120). We excite oxygen to a narrow rotational wave packet whose center is accurately tuned across the broad range of well defined N values. The centrifuge excitation is then followed by a REMPI measurement. Owing to the narrow N distribution, the detected spectrum becomes significantly less congested, and identifying rotational resonances is greatly simplified. Following the original recipe by Karczmarek et al.,12 we utilize the output of an 800 nm, 35 fs (full width at half-maximum, FWHM), Ti:Sapphire regenerative amplifier. We split its spectrum in half at around the central wavelength (Fig. 1a), in a Fourier plane of a pulse shaper. Frequency chirps of equal magnitude (0.26 ps2) and opposite signs are applied to the ‘‘red’’ and ‘‘blue’’ arms of the centrifuge, as demonstrated by the cross-correlation frequency-resolved optical gating (XFROG) measurement (Fig. 1c). The latter was carried out by overlapping the centrifuge pulse with a reference Fourier-transform limited pulse on a 20 mm-thick BaB2O4 crystal. The bandwidth of the reference pulse was reduced
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Fig. 1 Optical centrifuge. (a) Broadband laser pulses from a Ti:S chirped pulse amplifier (10 mJ, 35 fs, 1 KHz repetition rate) are dispersed with a diffraction grating and split in the center of the spectrum in a Fourier plane of the focusing lens into ‘‘red’’ and ‘‘blue’’ arms, whose chirps are individually controlled by two separate ‘‘chirp boxes’’. The chirp of the ‘‘red’’ arm is reversed, while that of the ‘‘blue’’ arm is left unchanged. Movable shutter on a motorized linear stage (inset) allows precise truncation of the ‘‘blue’’ arm bandwidth. (b) Spectrum of the centrifuge pulse after shaping. Solid red (dashed black) line corresponds to the truncated (full) centrifuge. (c) Cross-correlation frequency-resolved optical gating (XFROG) spectrogram of the truncated centrifuge field, schematically shown below the XFROG plot. O is the angular frequency at which molecules are released from the centrifuge.
to about 1 nm in a separate pulse shaper to increase the spectral resolution. The spectrum of the frequency mixing signal was measured as a function of the relative time delay between the centrifuge and reference pulses. The two centrifuge arms are combined with a polarizing beam splitter cube, and polarized with an opposite sense of circular polarization. Optical interference of the two circularly polarized frequency-chirped laser fields results in a pulse with rotating linear polarization (inset to Fig. 1c). Because of the anisotropic polarizability, molecular axes line up along the axis of laser polarization, and then follow it adiabatically as the plane of polarization rotates with increasing angular frequency. Quantum-mechanically, this process corresponds to the rotational ladder climbing, executed as a series of consecutive Raman transitions between the rotational levels separated by DN = 2. Each step consists of absorbing a photon from the blue centrifuge arm and emitting a photon into the red arm. The frequency difference between the two photons (2O) grows in time following the rotational line separation. Opposite circular polarization of the two centrifuge arms ensures DMN = 2 selection rule, resulting in unidirectional rotation. Given the available spectral bandwidth, the accelerating centrifuge can reach angular frequencies on the order of 10 THz, which in the case of oxygen corresponds to the rotational quantum number N E 119. As we have demonstrated in ref. 16 truncating the spectrum of the centrifuge in a Fourier plane of the pulse shaper by a movable shutter (see inset to Fig. 1a, and field spectrum in Fig. 1b) enables accurate control of the rotational state of the centrifuged molecules. Characterizing the centrifuge field with XFROG allowed us to calibrate the final rotation speed of the
4072 | Phys. Chem. Chem. Phys., 2014, 16, 4071--4076
centrifuge, and hence the corresponding molecular angular momentum, as a function of the shutter position. REMPI detection was carried out using narrowband nanosecond probe pulses tunable from 279 nm to 288 nm (0.1 cm1 line width, 500 mJ per pulse, 50 Hz repetition rate). The probe beam was combined with a centrifuge beam (5 mJ per pulse) on a dichroic mirror (Fig. 2), and focused with a 35 mm focal length spherical aluminium mirror on a supersonically expanded molecular jet passing between the charged plates of the time-of-flight (TOF) mass spectrometer. We estimate the peak centrifuge field intensity at the focal spot around 1013 W cm2. The jet was generated by an Even-Lavie pulsed valve (25 ms opening time, 150 mm nozzle diameter) located 20 cm away from the detection region. Ion current was detected with a microchannel plate (MCP) detector. The initial rotational temperature of the sample, extracted from the REMPI spectrum taken without the centrifuge field (Fig. 3a), was about 10 K. The main result of this work is shown in Fig. 3, where the detected ion count is plotted against the probe energy (horizontal axis) and the final rotation speed O of the truncated centrifuge (vertical axis). The latter is expressed in terms of the angular momentum N of an oxygen molecule rotating with the angular frequency O, according to: O = 2pc[E(N) E(N 1)], E(N) = BN(N + 1) DN2(N + 1)2, where E is the energy of state |Ni, c is the speed of light in vacuum, B = 1.438 cm1 and D = 4.839 106 cm1.18 The validity of Dunham expansion of rotational energy to second order in
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Fig. 2 Detection setup. Centrifuge beam is combined with a tunable UV laser pulse and focused inside a vacuum chamber on a supersonically expanded oxygen jet between the charged plates of a time-of-flight (TOF) mass spectrometer. The ionization rate is measured with a multi-channel plate (MCP) detector.
N(N + 1) at extremely high values of N has been demonstrated in our previous study.16 Each peak in the two-dimensional REMPI spectrogram of Fig. 3b corresponds to a two-photon transition between a rotational level in the electronic ground state, X3Sg, and a rotational level of C3Pg. The finite horizontal width of the observed peaks stems from the predissociation line width (as in conventional
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‘‘1D REMPI’’ detection), whereas finite vertical spread reflects the narrow width of the excited rotational wave packet created by the centrifuge. The complexity of the two-photon absorption line structure in rotationally hot oxygen gas is illustrated by red and yellow lines in Fig. 3a which correspond to the hot thermal ensemble (simulated numerically) and the ensemble of centrifuged molecules (experimentally observed 2D spectrogram integrated along its vertical dimension), respectively. In sharp contrast to conventional 1D REMPI spectroscopy, controlled centrifuge spinning offers direct assignment of rotational quantum numbers to the observed REMPI peaks, as well as significantly better peak separation due to their distribution along the added second dimension. Vertical traces originating from bright resonance peaks in Fig. 3b (examples are marked with white arrows) correspond to molecules which ‘‘leaked out’’ of the weakened centrifuge potential before reaching the terminal angular frequency of the centrifuge. After escaping the centrifuge, these molecules continue their free rotation while the trap is accelerating further. The three bright vertical stripes reproduce the initial cold beam spectrum (blue line in Fig. 3a) and correspond to the molecules which were not trapped by the centrifuge. The width of the final rotational wave packets can be readily extracted as dN E 7 (FWHM), from the vertical cross sections, shown in Fig. 3c. Here, we detected rotational states with N as high as B80. Rotational line broadening above N E 60 can be attributed to the increasing Rydberg-valence interaction (governed by the Franck–Condon (FC) overlap with the continuum wavefunctions) similarly to the previously observed rotational broadening in the lower vibrational states (v0 = 0,1) of the excited potential.11
Fig. 3 2D REMPI spectrogram for a linearly polarized probe. (a) Experimental spectra of cold (10 K, blue) and centrifuged molecules (yellow), along with a simulated spectrum of a ‘‘hot’’ thermal ensemble (3000 K, red) calculated with pgopher software.17 (b) Ion signal as a function of the probe laser twophoton energy and molecular angular momentum defined by the centrifuge final rotation speed. Different areas of the 2D plot were measured with different sensitivities and probe intensities and are displayed with different color scales to compensate for the broad dynamic range of the data. (c) Vertical cross-sections of several consecutive peaks from one particular branch, shown in the inset to b. The peaks are regularly separated with a distance of DN = 2 reflecting 16O2 nuclear spin statistics.
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One can see that the peaks in Fig. 3 are grouped in regular patterns, resembling Fortrat parabolas corresponding to different rotational branches. Within a single branch, the center of each consecutive resonant peak is shifted by DN = 2 (Fig. 3c), reflecting 16 O2 nuclear spin statistics. Circularly polarized light can be used to further simplify the spectrum. As shown in Fig. 4, the signal strength of different rotational branches depends on the handedness of probe polarization. This is due to the highly non-uniform population distribution among the magnetic sub-levels in the centrifuged wave packet, with most of the population concentrated at MN C N (or MN C N).12 To identify different rotational branches, we use three sets of molecular constants (for F1,F2 and F3 spin–orbit components of the excited state) from the previous studies on thermally excited ensembles.7,19 The three components correspond to L + S = 0 (F1), 1 (F2) and 2 (F3), with L and S being the projections of the orbital and spin components of the total angular momentum on the molecular axis, respectively. These constants are listed in Table 1. For F2 and F3 components, our results are well described by the constants provided by Lewis et al.19 On the other hand, the observed F1 peaks do not agree well with the suggested numerical values (n0 = 69 366 cm1 and B0 = 1.6 cm1), as shown in Fig. 5. This can be attributed to the complexity of the broadened and highly overlapping structure of F1 lines, which makes it hard to interpret and fit the data from a thermally populated ensemble. Centrifuge spectroscopy enables
PCCP Table 1
Molecular constants used to fit the data in Fig. 4
Spin–orbit branch
v0/cm1
B0/cm1
D/cm1
3
69 375 69 445 69 550
1.585 1.648 1.685
2.5 107 1.0 105 1.3 105
P0(F1) P1(F2) 3 P2(F3) 3
us to correct the values of F1 molecular constants (Table 1) by performing the fit of the most pronounced DN = 2 branch (Fig. 5). The lowest vibrational level of C3Pg electronic state of oxygen known to exhibit well-resolved rotational structure is v = 2.11 Predissociation to the closely lying valence state 13Pg broadens the rotational spectrum of the lower vibrational states v = 0,1. This broadening is weakened in the case of v = 2 because the repulsive potential crosses the level near the node of the vibrational wavefunction, lowering the Franck–Condon overlap.11 The FC overlap, however, increases with the increasing degree of rotational excitation. At high values of N, we observe a significant line broadening which results in a completely unresolvable rotational structure at N \ 60 (see Fig. 3). At even higher centrifuge frequencies, corresponding to the extreme rotational levels with 99 o N o 125, we observe the re-appearance of narrow resonances shown in Fig. 6. Their line width drops down to a well-resolved B7 cm1, as shown in Fig. 7. Similar non-monotonic N-dependencies were previously
Fig. 4 2D REMPI spectrogram for a circularly polarized probe. Electric field vector is counter-rotating (a) and co-rotating (b) with the centrifuged molecules. The directionality of laser-induced rotation results in the sensitivity of the measured signal to the handedness of probe polarization. The results of fitting the data to the theoretical model are shown with colored lines and markers for different branches and resonances, respectively (see text for details). Branch nomenclature is the same as in ref. 11.
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Fig. 5 Comparison of the observed REMPI data for the perturbed F1 spin–orbit component with the calculations based on molecular constants from this work (red circles), White et al.7 (blue triangles) and Lewis et al.19 (purple squares).
observed in OD21 where they were used to analyze the repulsive state. Indeed, according to the Fermi Golden Rule, the line width is proportional to the predissociation matrix elements between the bound and the continuum eigenstates, as well as the density of states in the continuum. As shown in ref. 21 the behavior of both quantities with N can be calculated numerically and used for extracting the parameters of the repulsive state from the experimentally observed dependence on the rotational quantum number.
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Fig. 7 Observed linewidths of J 0 = N 0 1 (triangles) and J 0 = N 0 (squares) spin–orbit sublevels of C3Pg (v 0 = 1) level as functions of rotational quantum number N 0 . Inset demonstrates a fit of experimental data (solid red) to a sum of lorentzians (dashed black) in order to extract line widths. Absolute position, absolute area and the widths of two peaks were fitted for each doublet individually, with the areas ratio fixed to a value extracted from the best resolved N 0 = 115 doublet and with a doublet line separation equal to a calculated one.
Our analysis showed that, unlike the previously discussed branches of C3Pg (v 0 = 2) ’’ X3Sg (v00 = 0), the observed ultra-high narrow lines originate from the v 0 = 1 state, which displays no resolvable rotational structure at lower rotational levels, but re-appears at higher J’s. Well described by Hund’s
Fig. 6 Ultra-high rotational resonances of O2. The two panels correspond to two possible ways of fitting the observed resonant branches (apparent along white dashed lines) to the calculated Hund’s case (b) structure (labeled with markers). In panel a, the upper branch corresponds to DN = 1, and the lower one to DN = 3, resulting in Bv = 1.620 cm1 and Dv = 4.4 106 cm1. In panel b, the upper branch overlaps with DN = 2, whereas the lower one with DN = 2, yielding Bv = 1.664 cm1 and Dv = 5.7 106 cm1.
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case (b) at such high degree of rotational excitation, the observed rotational structure consists of a series of spin–orbit multiplets. Out of 9 possible DN branches, we have observed only two (dashed lines in Fig. 6). Given this limited amount of information, fitting the data by a single set of molecular constants proved difficult. Our analysis resulted in two possibilities shown in panels a and b of Fig. 6. The retrieved molecular constants are Bv = 1.620 cm1 and Dv = 4.4 106 cm1 for plot a, and Bv = 1.664 cm1 and Dv = 5.7 106 cm1 for plot b. To choose between the two possibilities, we note that in Hund’s case (a), an effective rotational constant B0 for F2 spin–orbit component is equal to the true Bv value.20 This implies that at v = 2, Bv = 1.648 cm1 (see Table 1). Since we expect Bv to decrease with v, Fig. 6b should reflect the correct branch assignment. In conclusion, we have demonstrated a new spectroscopic method for studying the rotational structure of electronic transitions in molecules. The method is based on controlled molecular spinning with an optical centrifuge. We have applied this technique to C3Pg ’’ X3Sg (v00 = 0) in O2. By varying the level of rotational excitation, we have observed rotational line broadening and narrowing associated with the dependence of predissociation rates on the molecular angular momentum. In case of v 0 = 2, resolved at lower rotational states (N t 60), we showed an agreement with previously reported molecular constants for F2 and F3 spin–orbit components and, owing to the higher resolution of the implemented method, refined those for the strongly perturbed F1 component. In case of v 0 = 1, extreme rotational excitation (N \ 100) resulted in the suppression of predissociation and enabled us to determine previously unknown rotational constants.
Acknowledgements This work has been supported by the CFI, BCKDF and NSERC, and carried out under the auspices of the Center for Research on Ultra-Cold Systems (CRUCS). We gratefully acknowledge stimulating discussions with R. Krems, V. Petrovic, M. Shapiro and E. Grant. We would also like to thank one of the reviewers of this manuscript for pointing out that the dependence of the rotational line width on N could be used for mapping out the repulsive potential responsible for the molecular predissociation. The analysis presented in Fig. 7 is a result of this valuable suggestion.
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