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excitation amplitude for the nth pulse. Thus, |bN|2 is a periodic function of both the pulse delay T and the phase difference 9. The resonance frequency w0 is encoded not just in the amplitude an, as with conventional spectroscopy, but also in the phase of the oscillating population signal. The first pulse creates an atomic superposition with a well-defined initial phase. The maxima of the excited-state population occur when subsequent laser pulses arrive in phase with this superposition. If the time delay and the pulse-to-pulse phase shift are known, the exact transition frequency can be derived from the position of these maxima. The more pulses are used, the narrower the resulting interference fringes. Therefore, multiple-level contributions can be resolved by the use of a sufficient number of pulses.

This method to measure the transition frequency is largely insensitive to the laser pulse spectral shape, which only influences the global signal amplitude. Therefore, spectral distortions of the laser pulses due to amplification or harmonic generation have little influence on the measurement, provided the distortion is identical from pulse to pulse. In contrast, traditional single-pulse spectroscopy is strongly affected by chirp (20, 21). However, the periodicity of the signal with respect to T leads to an inherent ambiguity in the determination of the transition frequency. This ambiguity can be resolved if a previous measurement with an accuracy much better than the repetition frequency exists; otherwise, the measurement can be repeated with different repetition rates, as shown below.

The frequency comb used in our experiment is based on a mode-locked Ti:sapphire oscillator. It emits 7-nJ pulses with a bandwidth (full width at half maximum) of ~90 nm, centered at 800 nm, and with an adjustable repetition rate between 60.9 and 79 MHz. For frequency accuracy, both the repetition rate and the phase of the pulses are locked to a Global Positioning System-disciplined Rb atomic clock (1, 2, 22, 23). An electro-optic modulator (EOM) is used to select up to three consecutive pulses from the mode-locked pulse train. These pulses are amplified in a six-pass Ti:sapphire nonsaturating amplifier to an energy of about 15 |jJ per pulse (24). Spectral filtering is applied in the amplifier to limit the bandwidth of the amplified pulses to <0.5 nm. This filtering reduces the complexity of the signal, as only a single transition will be excited (see below). The amplification process gives rise to a small phase shift (~100 to 200 mrad) between the pulses, which is measured with a 1o accuracy of 25 mrad (<1/250 of an optical cycle). These measurements are performed by placing the amplifier in one arm of a Mach-Zehnder interferometer and recording spatial interferograms on a chargecoupled device (CCD) camera, from which this phase shift can be extracted (25).

To demonstrate the potential of high-frequency quantum interference metrology, we selected the 4p6 y 4p55p[1/2]0 two-photon transition in krypton at a frequency of w0/2p = 2821 THz. Because both the ground state and the excited state of this transition are J = 0 states, the atoms can be considered two-level systems. The required wavelength of 212.55 nm for the two-photon krypton resonance was obtained by fourth-harmonic generation of the amplifier output at 850.2 nm through sequential frequency doubling in two beta-barium borate (BBO) crystals. The resultant 212.55-nm pulses (1.6 mJ) were focused in a highly collimated atomic beam of krypton (Fig. 2). The excited-state population was probed by a delayed 532-nm ionization pulse (1.5 mJ, 100 ps) from a Nd:yttrium-aluminum-garnet laser-amplifier system, and the experiment was repeated at 1 kHz.

The isotope shift and the absolute transition measurements described below can be influenced by a possible systematic Doppler shift as a result of nonperpendicular excitation. Therefore, all measurements were

Fig. 1. The principle of quantum interference metrology. An atom in the ground state |g) is resonantly excited by a broadband laser pulse. This pulse creates a coherent superposition of the ground state and the excited state, with an initial phase difference between the states determined by the laser pulse. After the initial excitation, the superposition will evolve freely with a phase velocity w0 = (Ee -E )/1, where Ee - Eg is the energy difference between the states and I is Planck's constant divided by 2p. After a time T, a second pulse with a controlled phase illuminates the atom, interfering with the atomic superposition. Depending on the phase and the time delay T, the total |g) y |e) excitation probability can be either enhanced (case A, red pulse) or suppressed (case B, blue pulse). By measuring the amplitude of the superposition (i.e., the population of the excited state) after the second pulse (with, e.g., an ionizing laser pulse), the energy difference between the states can be deduced.

Fig. 2. Schematic of the experimental setup. The ultraviolet pulses (beam diameter 1 mm) are focused with an f = 30 cm lens in a collimated 0.3-mm-wide krypton beam (double skimmer arrangement, Doppler width <10 MHz) from both sides, crossing the beam perpendicularly. Measurements are performed with light from one side at a time. After the ultraviolet excitation, a delayed 532-nm pulse is used for ionization, and the resulting krypton ions are accelerated into a 60-cm time-of-flight mass spectrometer (TOF) by a pulsed electric field. Here the isotopes are separated in time (see inset) and counted with a channeltron detector.

Fig. 2. Schematic of the experimental setup. The ultraviolet pulses (beam diameter 1 mm) are focused with an f = 30 cm lens in a collimated 0.3-mm-wide krypton beam (double skimmer arrangement, Doppler width <10 MHz) from both sides, crossing the beam perpendicularly. Measurements are performed with light from one side at a time. After the ultraviolet excitation, a delayed 532-nm pulse is used for ionization, and the resulting krypton ions are accelerated into a 60-cm time-of-flight mass spectrometer (TOF) by a pulsed electric field. Here the isotopes are separated in time (see inset) and counted with a channeltron detector.

performed from two opposite sides, with the average taken to determine the Doppler-free signal (26).

The data depend on the number of phase-locked pulses used to excite the transition (Fig. 3A). The pulse delay T was scanned by changing the comb laser repetition frequency, which is near 75 MHz. With a single pulse, the excitation probability is constant. With two pulses, a clear cosine oscillation is observed, with a contrast reaching 93%.

Three-pulse excitation gives the pulse-like structure predicted by Eq. 1 (N = 3) as well as an expected narrowing by 3/2 relative to two-pulse excitation. The solid lines are fits using Eq. 1, including an additional amplitude scaling factor to account for signal strength variations between the traces. In the three-pulse case, we took into account that the amplitude contribution of the pulses is not exactly equal because of spontaneous emission of the 5p state (lifetime 23 ns) and

Fig. 3. Demonstration of quantum interference metrology. (A) 84Kr signal as a function of the repetition rate of the comb laser for one (blue), two (red), and three (green) pulses 13.3 ns apart. The solid lines are fits to the theory (see text). (B) Measurement of the quantum interference signal for various phase differences between two excitation pulses, with the pulse-to-pulse phase shift (as seen by the atom) set to 0 (green), p/2 (blue), p (black), and 3p/2 (red), respectively. (C) Measurement of the isotope shift between 84Kr (blue trace) and 86Kr (orange trace). The isotope shift can be determined from the phase shift between these two simultaneously recorded scans. The counter gate time is 10 s for each data point.

Fig. 3. Demonstration of quantum interference metrology. (A) 84Kr signal as a function of the repetition rate of the comb laser for one (blue), two (red), and three (green) pulses 13.3 ns apart. The solid lines are fits to the theory (see text). (B) Measurement of the quantum interference signal for various phase differences between two excitation pulses, with the pulse-to-pulse phase shift (as seen by the atom) set to 0 (green), p/2 (blue), p (black), and 3p/2 (red), respectively. (C) Measurement of the isotope shift between 84Kr (blue trace) and 86Kr (orange trace). The isotope shift can be determined from the phase shift between these two simultaneously recorded scans. The counter gate time is 10 s for each data point.

Fig. 4. Absolute calibration of the 4p6 y 4p55p[1/2]0 transition in krypton is performed by finding the coincidence of three separate measurement series with repetition rates of 60.9 MHz (green), 68.6 MHz (red), and 75.0 MHz (blue). The orange bars (logarithmic scale) show the normalized statistical probability per mode for each measured mode position, revealing the location of the most probable coincidence.

differences in energy between the three pulses (27). For all other measurements, we used two-pulse excitation, as this minimizes the complexity of the experiment without sacrificing accuracy in this two-level case. The first of these measurements concerns the dependence on the pulse-to-pulse (carrier envelope) phase shift 8CE (Fig. 3B), which is in complete agreement with expectations: The interference signal moves by one fringe when 8ce of the comb laser is scanned through one-eighth of a cycle (due to the frequency conversion and two-photon transition).

Isotope shifts can be measured straightforwardly. The broad spectrum of the pulses places a frequency ruler on all isotopes simultaneously, so that spectra of 80Kr through 86Kr could be acquired at the same time (Fig. 3C). The measurements of Kaufman (28) were used for identification of the proper comb line for each isotope. The resulting shifts (84Kr - -^Kr), based on at least six measurements per isotope, are 302.02 ± 0.28 MHz (80Kr), 152.41 ± 0.15 MHz (82Kr), 98.54 ± 0.17 MHz (83Kr), and -135.99 ± 0.17 MHz (86Kr). The stated uncertainties (1o) are smaller than the 6MHz uncertainty reported by Kaufman (28) by a factor of 20 to 40.

In the measurement of the absolute transition frequency, an additional issue is the determination of the mode that corresponds to the true position of the resonance. The most accurate measurement to date (29) has an uncertainty of 45 MHz, which is not sufficient to assign the mode with confidence. Therefore, measurements were repeated at repetition rates near 60.9 MHz, 68.6 MHz, and 75.0 MHz to find the point at which the measurements coincide (four to nine measurements were performed at each repetition rate). After correction of the data for the phase shifts and systematic effects (30), there were three sets of possible positions for the 5p resonance transition (Fig. 4). The measurements have one clear coincidence (with an estimated probability of 98%, based on a statistical uncertainty of 2.5 MHz for each data point) near the literature value. Combining the three sets leads to an absolute frequency of 2,820,833,097.7 MHz with a 1o uncertainty of 3.5 MHz (statistical and systematic errors combined), which is an order of magnitude smaller than the previous determination using single nanosecond laser pulses (29).

We envision several extensions of the above technique. One possibility is the use of a regenerative amplifier to amplify pulses to the mJ level at a repetition rate of 100 kHz. For high-frequency metrology, the resolution is ultimately limited by the comb laser and the interaction time of the atom with the pulses. This interaction time can be increased almost indefinitely if cooled ions in a trap are used in place of an atomic beam, opening the prospect of atomic optical clocks operating at vacuum-ultraviolet or extreme-ultraviolet frequencies. Outside frequency metrology, amplified frequency combs could be used to perform quantum control experiments on a time scale much longer than is currently possible, because phase coherence can be maintained for many consecutive laser pulses.

References and Notes

1. R. Holzwarth etal., Phys. Rev. Lett. 85, 2264 (2000).

3. Th. Udem, R. Holzwarth, T. W. Hunsch, Nature 416, 233 (2002).

4. M. Niering et al., Phys. Rev. Lett. 84, 5496 (2000).

5. Th. Udem et al., Phys. Rev. Lett. 86, 4996 (2001).

6. M. Fischer et al., Phys. Rev. Lett. 92, 230002 (2004).

9. A. Clairon, C. Salomon, S. Guellati, W. D. Phillips, Europhys. Lett. 16, 165 (1991).

10. M. M. Salour, C. Cohen-Tannoudji, Phys. Rev. Lett. 38, 757 (1977).

12. R. Teets, J. N. Eckstein, T. W. Hansch, Phys. Rev. Lett. 38, 760 (1977).

13. M. Bellini, A. Bartoli, T. W. Hunsch, Opt. Lett. 22, 540

14. M. J. Snadden, A. S. Bell, E. Riis, A. I. Ferguson, Opt. Commun. 125, 70 (1996).

16. J. N. Eckstein, A. I. Ferguson, T. W. Haunsch, Phys. Rev. Lett. 40, 847 (1978).

17. A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, J. Ye, Science 306, 2063 (2004); published online 18 November 2004 (10.1126/science.1105660).

18. R. Zerne etal., Phys. Rev. Lett. 79, 1006 (1997).

19. S. Cavalieri, R. Eramo, M. Materazzi, C. Corsi, M. Bellini, Phys. Rev. Lett. 89, 133002 (2002).

20. K. S. E. Eikema, W. Ubachs, W. Vassen, W. Hogervorst, Phys. Rev. A 55, 1866 (1997).

21. S. D. Bergeson et al., Phys. Rev. Lett. 80, 3475

22. A. Apolonski et al., Phys. Rev. Lett. 85, 740 (2000).

23. S. Witte, R. Th. Zinkstok, W. Hogervorst, K. S. E. Eikema, Appl. Phys. B 78, 5 (2004).

24. Standard amplifiers operate in saturated mode to reduce output power fluctuations and can therefore amplify only one pulse. In the present experiment, the number of pulses that can be amplified is limited to three by the EOM, which must be switched off before any backreflections from the amplifier lead to uncontrolled extra pulses. An additional Faraday isolator in the setup would lift this limitation.

25. An EOM and polarizing optics were used to project the interference patterns for two consecutive pulses simultaneously and vertically displaced from one another on a CCD camera. The relative positions on the CCD (up or down) were alternated by switching the EOM; the relative phase shift to the comb laser was then determined by looking at the phase difference in both projection situations, so as to cancel out any alignment effects.

26. The Doppler shift can in principle be reduced on a two-photon transition by measuring with colliding pulses from opposite sides. This arrangement also enhances the signal, as was seen experimentally. However, contrary to CW spectroscopy, Doppler-free signal (photons absorbed from opposite sides) and Doppler-shifted signal (two photons from one side) cannot be distinguished properly in the case of excitation with two ultrashort pulses, because the large bandwidth always contains a resonant frequency. This situation might lead to a calibration error when there is an imbalance in signal strength from opposite sides. Another aspect is that the total Doppler shift has an ambiguity due to the periodicity of the signal. The difference in Doppler shift for the isotopes, which is on the order of a few hundred kHz, therefore provides a valuable initial estimate of about 25 MHz for this shift. From the measurement of the absolute positions, one can then determine the Doppler shift to be 29 MHz for each of the counterpropagating beams.

27. The energy ratio of pulses 1, 2, and 3 is 1.0:0.91:0.6. In all measurements with two pulses, the pulse energies have been kept equal to within about 5%.

28. V. Kaufman, J. Res. Natl. Inst. Stand. Technol. 98, 717 (1993).

29. F. Brandi, W. Hogervorst, W. Ubachs, J. Phys. B 35, 1071 (2002).

30. Two systematic effects dominate the determination of the resonance frequency: the phase shifts induced by the amplifier (100 to 200 mrad in the infrared), and the residual Doppler shift (2 MHz) due to possible misalignment of the counterpropagating beams. Other effects include light-shifts (0.47 ± 0.44 MHz), static field effects (¡100 kHz), the second-order Doppler shift (~1 kHz), and a recoil shift (209 kHz). The phase shift due to the pulse-picker EOM is negligible (<5 mrad) when it is aligned such that it acts as a pure polarization rotator, as verified experimentally. The phase shift due to frequency doubling is negligible as well, on the order of 1 mrad in the ultraviolet, as estimated from the model of (37).

32. Supported by the Foundation for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO), the EU Integrated Initiative FP6 program, and the Vrije Universiteit Amsterdam.

21 October 2004; accepted 30 November 2004

10.1126/science.1106612

Charging Effects on Bonding and Catalyzed Oxidation of CO on Au8 Clusters on MgO

Bokwon Yoon,1 Hannu Häkkinen,1* Uzi Landman,1. Anke S. Worz,2 Jean-Marie Antonietti,2 Stephane Abbet,2 Ken Judai,2 Ueli Heiz2.

Gold octamers (Au8) bound to oxygen-vacancy F-center defects on Mg(001) are the smallest clusters to catalyze the low-temperature oxidation of CO to CO2, whereas clusters deposited on close-to-perfect magnesia surfaces remain chemically inert. Charging of the supported clusters plays a key role in promoting their chemical activity. Infrared measurements of the stretch vibration of CO adsorbed on mass-selected gold octamers soft-landed on Mg0(001) with coadsorbed O2 show a red shift on an F-center-rich surface with respect to the perfect surface. The experiments agree with quantum ab initio calculations that predict that a red shift of the C-O vibration should arise via electron back-donation to the CO antibonding orbital.

The exceptional catalytic properties of small gold aggregates (1, 2) have motivated research (3-17) aimed at providing insights into the molecular origins of this unexpected reactivity of gold. Investigations on size-selected small gold clusters, Aun(2 < n < 20), soft-landed on a well-characterized metal oxide support [specifically, a Mg0(001) surface with and without oxygen vacancies or F centers], revealed (4) that gold octamers bound to F centers of the magnesia surface are the smallest known gold heterogeneous catalysts that can oxidize CO into CO2 at temperatures as low as 140 K. The same cluster bound to a MgO surface without oxygen vacancies is catalytically inactive for CO combustion (4).

Quantum-mechanical ab initio simulations, in juxtaposition with laboratory experiments,

''School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA. Departement Chemie, Lehrstuhl für Physikalische Chemie I, Technische Universität München, Lichtenbergstraße 4, 85747 Garching, Germany.

*Present address: Department of Physics, Nano-science Center, Box 35, FIN-40014, University of Jyväskyla, Finland.

.To whom correspondence should be addressed. E-mail: [email protected] (U.L.); ulrich. [email protected] (U.H.)

led us to conclude (4, 5) that the key for low-temperature gold catalysis in CO oxidation is the binding of O2 and CO to the supported gold nanocluster, which activates the O-O bond to a peroxo-like (or superoxo-like) adsorbate state. This process is enabled by resonances between the cluster's electronic states and the 2p* antibonding states of O2, which are pulled below the Fermi level (EF). Charging of the metal cluster, caused by partial transfer of charge from the substrate F center into the deposited cluster, underlies the catalytic activity of the gold octamers (Au8), as well as that of other small gold clusters (Aun, 8 < n < 20) (4). These investigations predicted that (i) the F centers on the metal oxide support surface play the role of active sites (a concept that has been central to the development of heterogeneous catalysis); (ii) these sites serve to anchor the deposited clusters more strongly than sites on the undefective surface (thus inhibiting their migration and coalescence); and, most important, (iii) these active sites control the charge state of the gold clusters, thus promoting the activation of adsorbed reactant molecules (that is, formation of the aforementioned peroxo or superoxo species) (18).

We have studied the cluster-charging propensity of the F-center active sites, both exper imentally and theoretically, by examining the vibrational properties of adsorbed CO. The internal CO stretch frequency v(CO), measured in the presence of coadsorbed O2 for the octamer bound to the F center of the magnesia substrate [Au8/CO/O2/MgO(FC)], shifted to lower frequency by about 25 to 50 cm"1 compared to the v(CO) frequency recorded for the gold octamer bound to the F-center-free MgO(OOl) surface (Au8/CO/O2/MgO). Systematic ab initio calculations (4, 5) reveal that this shift is caused by enhanced back-donation (from the gold nanocluster) into the antibonding 2p* orbital of the CO adsorbed on the cluster anchored to a surface F center. In addition, calculations addressing free Au8/O2/CO coadsorption complexes provide further evidence that the bonding characteristics and spectral shifts are related to each other and that they are correlated with, and sensitive to, the charge state of the cluster (18).

We reproduced experimentally the results of our earlier investigations pertaining to the enhanced catalytic activity of Au8 clusters deposited on F-center-defective MgO surfaces, and then went beyond those measurements by recording (under the same conditions as for the reactivity studies) the infrared (IR) spectra of the reactants as a function of the annealing temperature (Fig. 1). Size-selected Au8 cations were deposited at 90 K, with low kinetic energy, onto MgO(FC) thin films at low coverages (8 x 1012 clusters/cm2). Several experimental studies [such as the synthesis of monodispersed model catalysts by using soft-landing cluster deposition (19)] have shown that, in general, upon deposition, the clusters are neutralized, maintain their nucle-arity, and stay well isolated at defect sites. These model catalysts were then saturated with isotopicaly labeled 18O2 and 13C16O; the order of the exposure of the reactants (0.2 Langmuir) did not change the activity (unlike the case for other metals). Upon heating, 13C16O18O was produced at 140 and 280 K, as shown in Fig. 1A. No other isotopomer was detected, indicating that only the adsorbed O2 and CO participate in the reaction. We attribute the reaction at 140 K to an ensemble of Au8 clusters, with O2 bound to the top facet of the cluster; and the reaction at 280 K to an Au8 ensemble, with O2 bound to the perimeter of the cluster at the cluster-to-substrate interface (Fig. 2B). These assignments were made by us previously (4) on the basis of calculated activation barriers for the CO oxidation. Specifically for small gold clusters, only a single O2 molecule can be adsorbed, and thus the two ensembles are saturated with O2 via either direct adsorption or reverse spillover.

The corresponding IR study reveals absorption bands of the two reactants. In Fig. 1, C and D, we show only the spectra for adsorbed CO, with the decrease in intensity correlating with the formation of CO2 (Fig. 1C). The IR band corresponding to adsorbed O2 occurs around 1300 cm"1 for both the F-center-rich and perfect MgO surfaces. The IR frequencies (2049 and 2077 cm"1) are typical for on-top adsorbed 13CO on gold. In this context, we recall that the band at 2127 cm"1 originates from 13CO adsorbed directly on defect sites of the Mg0(001) surface (20). On Au single crystals (21-23), as well as on oxide-supported Au particles (9, 24, 25), sharp 13CO absorption bands occur at a single frequency around 2060 cm"1. We infer that the detection of two absorption features reveals the presence of (at least) two types of adsorbed CO molecules, which differ somewhat in how they bind to the Au8 cluster (Fig. 2C and discussion below).

Upon heating, the population of the three bands changes. At an annealing temperature of 220 K (subsequent to the 140 K combustion reaction), a small single absorption band at 2055 cm"1 was observed (Fig. 1C). Earlier studies (26) detected such a band for 13CO adsorbed to Au8/MgO(FC).

In contrast to the above, gold octamers adsorbed on an F-center-free Mg0(001) surface were essentially inactive for the combustion reaction (Fig. 1B). In fact, even under quasi-steady-state conditions with pulsed molecular beams, no CO2 formation was observed. The absorption band of 13CO in this case (2102 cm"1) was shifted to a higher frequency (by 25 to 50 cm"1), as compared to the case of 13CO adsorbed on a gold octamer deposited on MgO(FC).

The above-noted red shift of the CO stretch when the molecule is adsorbed on Au8 supported on Mg0(001)(FC) is a key for elucidating the change in the charge state of the gold octamer bound to F-center defects on the MgO surface. The absorption frequency of CO adsorbed on metal surfaces depends strongly on the population of the 2p* orbital, because occupation of this an-tibonding orbital weakens the C-O bond. Furthermore, results from extensive ab initio calculations, using the method developed in

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