Theory of high-harmonic generation by low-frequency laser fields

X-ray microprobe of orbital alignment in strong-field ionized atoms

We have developed a synchrotron-based, time-resolved x-ray microprobe to investigate optical strong-field processes at intermediate intensities (10(14) - 10(15) W/cm2). This quantum-state specific probe has enabled the direct observation of orbital alignment in the residual ion produced by strong-field ionization of krypton atoms via resonant, polarized x-ray absorption. We found strong alignment to persist for a period long compared to the spin-orbit coupling time scale (6.2 fs). The observed degree of alignment can be explained by models that incorporate spin-orbit coupling. The methodology is applicable to a wide range of problems.

Attosecond pulse trains generated using two color laser fields

We investigate the spectral and temporal structure of high harmonic emission from argon exposed to an infrared laser field and its second harmonic. For a wide range of generating conditions, trains of attosecond pulses with only one pulse per infrared cycle are generated. The synchronization necessary for producing such trains ensures that they have a stable pulse-to-pulse carrier envelope phase, unlike trains generated from one color fields, which have two pulses per cycle and a pi phase shift between consecutive pulses. Our experiment extends the generation of phase stabilized few cycle pulses to the extreme ultraviolet regime.

Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction

We demonstrate an extremely accurate method for measuring ultrabroadband, sub-10 fs pulses even if they exhibit a highly modulated spectrum, space-time coupling, or both. The method uses a spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction, which allows a zero additional phase measurement to be performed with a relatively low signal-to-noise ratio in real time and single shot.

Role of many-electron dynamics in high harmonic generation

High harmonic generation (HHG) in many-electron atoms is studied theoretically. The breakdown of the frozen-core single active electron approximation is demonstrated, as it predicts roughly the same radiation amplitude in all noble gases. This is in contradiction with experiments, where heavier noble gases are known to emit much stronger HHG radiation than lighter ones. This experimental behavior of the noble gases can be qualitatively reproduced when many-electron dynamics, within a simple approximation, is taken into account.

High-order harmonic generation from ions in a capillary discharge

We demonstrate a significant extension of the high-order harmonic cutoff by using a fully-ionized capillary discharge plasma as the generation medium. The preionized plasma dramatically reduces ionization-induced defocusing and energy loss of the driving laser due to ionization. This allows for significantly higher photon energies, up to 150 eV, to be generated from xenon ions, compared with the 70 eV observed previously. We also demonstrate enhancement of the harmonic flux of nearly 2 orders of magnitude at photon energies around 90 eV when the capillary discharge is used to ionize xenon, compared with harmonic generation in a hollow waveguide. The use of a plasma as a medium for high-order harmonic generation shows great promise for extending efficient harmonic generation to much shorter wavelengths using ions.

Adaptive spatial control of fiber modes and their excitation for high-harmonic generation

We present the control of high-harmonic generation (HHG) in hollow fibers using adaptive pulse shaping techniques. The shaping capabilities of our spatial light modulator (SLM) are demonstrated by the excitation of specific fiber modes inside a hollow fiber with a helium-neon laser. Afterwards spatially shaped ultrashort pulses are used to generate phase-matched high-harmonic radiation in a fiber. We show that by controlling the mode structure, we can manipulate the spatial and spectral properties of the generated harmonics.

Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 microm

We demonstrate an optical parametric chirped-pulse amplifier producing infrared 20 fs (3-optical-cycle) pulses with a stable carrier-envelope phase. The amplifier is seeded with self-phase-stabilized pulses obtained by optical rectification of the output of an ultrabroadband Ti:sapphire oscillator. Energies of -80 microJ with a well-suppressed background of parametric superfluorescence and up to 400 microJ with a superfluorescence background are obtained from a two-stage parametric amplifier based on periodically poled LiNbO3 and LiTaO3 crystals. The parametric amplifier is pumped by an optically synchronized 1 kHz, 30 ps, 1053 nm Nd:YLF amplifier seeded by the same Ti:sapphire oscillator.

Generation of high-energy self-phase-stabilized pulses by difference-frequency generation followed by optical parametric amplification

We produce ultrabroadband self-phase-stabilized near-IR pulses by a novel approach where a seed pulse, obtained by difference-frequency generation of a hollow-fiber broadened supercontinuum, is amplified by a two-stage optical parametric amplifier. Energies up to 20 microJ with a pulse spectrum extending from 1.2 to 1.6 microm are demonstrated, and a route for substantial energy scaling is indicated.

Three-step model for high-harmonic generation in many-electron systems

The three-step model (TSM) of high-harmonic generation (HHG) is generalized to atomic and molecular many-electron systems. Using many-body perturbation theory, corrections to the standard TSM due to exchange and electron-electron correlations are derived. It is shown that canonical Hartree-Fock orbitals represent the most appropriate set of one-electron states for calculating the HHG spectrum. To zeroth order in many-body perturbation theory, a HHG experiment allows direct access, in general, to a combination of occupied Hartree-Fock orbitals rather than to the highest occupied molecular orbital by itself.

Quantitative modeling of single atom high harmonic generation

It is shown by comparison with numerical solutions of the Schrödinger equation that the three step model (TSM) of high harmonic generation (HHG) can be improved to give a quantitatively reliable description of the process. Excellent agreement is demonstrated for the H atom and the H2(+) molecular ion. It is shown that the standard TSM heavily distorts the HHG spectra, especially of H2(+), and an explanation is presented for this behavior. Key to the improvement is the use of the Ehrenfest theorem in the TSM.

Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics

We demonstrate a new scheme for extreme ultraviolet (xuv) Fourier-transform spectroscopy based on the generation of two phase-locked high-harmonic beams. It allows us to measure for the first time interferograms at wavelengths as short as 90 nm, and open the perspective of performing high-resolution Fourier-transform absorption spectroscopy in the xuv. Our measurements also demonstrate that a precise control of the relative phase of harmonic pulses can be obtained with an accuracy on an attosecond time scale, of importance for future xuv pump-xuv probe attosecond spectroscopy.

Nonresonant ionization of oxygen molecules by femtosecond pulses: Plasma dynamics studied by time-resolved terahertz spectroscopy

We show that optical pump-terahertz probe spectroscopy is a direct experimental tool for exploring laser-induced ionization and plasma formation in gases. Plasma was produced in gaseous oxygen by focused amplified femtosecond pulses. The ionization mechanisms at 400- and 800-nm excitation wavelengths differ significantly being primarily of a multiphoton character in the former case and a strong-field process in the latter case. The generation of the plasma in the focal volume of the laser and its expansion on subnanosecond time scale is directly monitored through its density-dependent susceptibility. A Drude model used to evaluate the plasma densities and electron-scattering rates successfully captures the observations for a wide range of pump intensities. In addition, rotational fingerprints of molecular and ionic species were also observed in the spectra.

Optical high harmonic generation in C60

High harmonic generation (HHG) requires a strong laser field, but in C60 a relatively weak laser field is sufficient. Numerical results presented here show that, while its low order harmonics result from the laser field, its high order ones are mainly from the multiple excitations. Since high order harmonics directly correlate with electronic transitions, the HHG spectrum accurately measures transition energies. Therefore, C60 is not only a promising material for HHG, but may also present an opportunity to develop HHG into an electronic structure probing tool.

Frequency-sheared, time-delayed extreme-ultraviolet pulses produced by high-harmonic generation in argon

We report the production of frequency-sheared high harmonics in argon by control of the envelope and chirp of the electric field of the femtosecond driving laser pulse. Using the classic three-step model of high-harmonic generation, we established a direct link between the properties of the harmonics and the fully characterized driving pulses. A simulation of the single-atom response in the strong-field approximation confirms the simple picture and shows good agreement with the experimental results.

Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors

In the race toward attosecond pulses, for which high-order harmonics generated in rare gases are the best candidates, both the harmonic spectral range and the spectral phase have to be controlled. We demonstrate that multilayer extreme-ultraviolet chirped mirrors can be numerically optimized and designed to compensate for the intrinsic harmonic chirp that was recently discovered and that is responsible for temporal broadening of pulses. A simulation shows that an optimized mirror is capable of compressing the duration from approximately 260 to 90 as. This new technique is an interesting solution because of its ability to cover a wider spectral range than other technical devices that have already been proposed to overcome the chirp of high harmonics.

Measurement of harmonic phase differences by interference of attosecond light pulses

By using a self-referencing technique, we have experimentally measured the influence of the carrier-envelope phase of femtosecond light pulses on the phase of the electric field of the radiation produced by high-order harmonic generation. We show that, in particular experimental conditions, the temporal evolution of the electric field of the attosecond pulses, is directly controlled by the carrier-envelope phase of the driving pulses.

Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity

We demonstrate the generation of phase-coherent frequency combs in the vacuum utraviolet spectral region. The output from a mode-locked laser is stabilized to a femtosecond enhancement cavity with a gas jet at the intracavity focus. The resulting high-peak power of the intracavity pulse enables efficient high-harmonic generation by utilizing the full repetition rate of the laser. Optical-heterodyne-based measurements reveal that the coherent frequency comb structure of the original laser is fully preserved in the high-harmonic generation process. These results open the door for precision frequency metrology at extreme ultraviolet wavelengths and permit the efficient generation of phase-coherent high-order harmonics using only a standard laser oscillator without active amplification of single pulses.

Quantum interference during high-order harmonic generation from aligned molecules

High-order harmonic generation (HHG) from atoms and molecules offers potential application as a coherent ultrashort radiation source in the extreme ultraviolet and soft X-ray regions. In the three-step model of HHG, an electron tunnels out from the atom and may recombine with the parent ion (emitting a high-energy photon) after undergoing laser-driven motion in the continuum. Aligned molecules can be used to study quantum phenomena in HHG associated with molecular symmetries; in particular, simultaneous observations of both ion yields and harmonic signals under the same conditions serve to disentangle the contributions from the ionization and recombination processes. Here we report evidence for quantum interference of electron de Broglie waves in the recombination process of HHG from aligned CO2 molecules. The interference takes place within a single molecule and within one optical cycle. Characteristic modulation patterns of the harmonic signals measured as a function of the pump-probe delay are explained with simple formulae determined by the valence orbital of the molecules. We propose that simultaneous observations of both ion yields and harmonic signals can serve as a new route to probe the instantaneous structure of molecular systems.

Second order autocorrelation of an XUV attosecond pulse train

Temporal widths of an attosecond (asec) XUV radiation pulse train, formed by the superposition of higher order harmonics, have been recently determined utilizing a 2nd order autocorrelation measurement. An assessment of the validity of the approach, for the broadband XUV radiation of asec pulses, is implemented through ab initio calculations modeling the spectral and temporal response of the two-XUV-photon He ionization detector employed. The measured width of the asec bursts is discussed in terms of the spectral phases of the individual harmonics, as well as in terms of the spatially modulated temporal width of the radiation, and is found in reasonable agreement with the expected duration.

Nonsequential double ionization as a completely classical photoelectric effect

We introduce a unified and simplified theory of atomic double ionization. Our results show that at high laser intensities (I>/=10(14) W/cm(2)) purely classical correlation is strong enough to account for all of the main features observed in experiments to date.

Mapping attosecond electron wave packet motion

Attosecond pulses are produced when an intense infrared laser pulse induces a dipole interaction between a sublaser cycle recollision electron wave packet and the remaining coherently related bound-state population. By solving the time-dependent Schrödinger equation we show that, if the recollision electron is extracted from one or more electronic states that contribute to the bound-state wave packet, then the spectrum of the attosecond pulse is modulated depending on the relative motion of the continuum and bound wave packets. When the internal electron and recollision electron wave packet counterpropagate, the radiation intensity is lower. We show that we can fully characterize the attosecond bound-state wave packet dynamics. We demonstrate that electron motion from a two-level molecule with an energy difference of 14 eV, corresponding to a period of 290 asec, can be resolved.

Attosecond pulse extreme-ultraviolet photoionization in a two-color laser field

Attosecond-pulse extreme-ultraviolet (XUV) photoionization in a two-color laser field is investigated. Attosecond pulse trains with different numbers of pulses are examined, and their strong dependence on photoelectronic spectra is found. Single-color driving-laser-field-assisted attosecond XUV photoionization cannot determine the number of attosecond pulses from the photoelectronic energy spectrum that are detected orthogonally to the beam direction and the electric field vector of the linearly polarized laser field. A two-color-field-assisted XUV photoionization scheme is proposed for directly determining the number of attosecond pulses from a spectrum detected orthogonally.

Attosecond probing of vibrational dynamics with high-harmonic generation

The numerical solution of the time-dependent Schrodinger equation for vibrating hydrogen molecules in few-cycle laser pulses shows that high-harmonic generation is sensitive to the laser-induced vibrational motion. More intense harmonics are generated in heavier isotopes, the difference increasing with the harmonic frequency. Analytical theory reveals a dependence of the harmonics on the vibrational autocorrelation function. With the help of a genetic algorithm, the nuclear motion can be reconstructed from the harmonic spectra with sub-fs time resolution.

Source of coherent kiloelectronvolt X-rays

Generating X-rays that have the properties of laser light has been a long-standing goal for experimental science. Here we describe the emission of highly collimated, spatially coherent X-rays, at a wavelength of about 1 nanometre and at photon energies extending to 1.3 kiloelectronvolts, from atoms that have been ionized by a 5-femtosecond laser pulse. This means that a laboratory source of laser-like, kiloelectronvolt X-rays, which will operate on timescales relevant to many chemical, biological and materials problems, is now within reach.

Shakeup excitation during optical tunnel ionization

Shakeup of a two-electron system is investigated in the strong infrared laser field limit, both theoretically and experimentally. During tunnel ionization the electron shakes up a second electron to an excited bound state. Theoretically, a complete analytical theory of shakeup in intense laser fields is developed. We predict that shakeup produces one excited sigma(u) D(+)(2) state in approximately 10(5) ionization events. Shakeup is measured experimentally by using the molecular clock provided by the internuclear motion. The number of measured events is found to be in excellent agreement with theory.

Tomographic imaging of molecular orbitals

Single-electron wavefunctions, or orbitals, are the mathematical constructs used to describe the multi-electron wavefunction of molecules. Because the highest-lying orbitals are responsible for chemical properties, they are of particular interest. To observe these orbitals change as bonds are formed and broken is to observe the essence of chemistry. Yet single orbitals are difficult to observe experimentally, and until now, this has been impossible on the timescale of chemical reactions. Here we demonstrate that the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmonics generated from intense femtosecond laser pulses focused on aligned molecules. Applying this approach to a series of molecular alignments, we accomplish a tomographic reconstruction of the highest occupied molecular orbital of N2. The method also allows us to follow the attosecond dynamics of an electron wave packet.

Control of atomic ionization by two-color few-cycle pulses

We have studied the ionization of Rydberg atoms by few-cycle radio-frequency pulses and used two-color fields to control the ionization dynamics. We show that the number of times that electrons are emitted during a pulse can be limited and that the duration of the electron emission can be shortened. These results, once they are transposed to the optical domain, may inspire new strategies for the production of single attosecond pulses.

Highly coherent light at 13 nm generated by use of quasi-phase-matched high-harmonic generation

By measuring the fringe visibility in a Young's double pinhole experiment, we demonstrate that quasi-phase-matched high-harmonic generation produces beams with very high spatial coherence at wavelengths around 13 nm. To our knowledge these are the highest spatial coherence values ever measured at such short wavelengths from any source without spatial filtering. This results in a practical, small-scale, coherent, extreme-ultraviolet source that is useful for applications in metrology, imaging, and microscopy.

Fully differential rates for femtosecond multiphoton double ionization of neon

We have investigated the full three-dimensional momentum correlation between the electrons emitted from strong field double ionization of neon when the recollision energy of the first electron is on the order of the ionization potential. The momentum correlation in the direction perpendicular to the laser field depends on the time difference of the two electrons leaving the ion. Our results are consistent with double ionization proceeding through transient double excited states that field ionize.

Nonsequential double ionization with few-cycle laser pulses

We investigate differential electron momentum distributions in nonsequential double ionization with linearly polarized, few-cycle pulses, using a classical model based on a laser-assisted inelastic (e(-),2e(-)) rescattering mechanism. These yields, as functions of the momentum components parallel to the laser polarization, are highly asymmetric and strongly influenced by the phase difference between the pulse envelope and its carrier oscillation, radically changing their sign around a critical phase. This behavior provides a powerful tool for absolute-phase measurements.

Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime

So far the role of the carrier-envelope phase of a light pulse has been clearly experimentally evidenced only in the sub-6-fs temporal regime. Here we show, both experimentally and theoretically, the influence of the carrier-envelope phase of a multi-optical-cycle light pulse on high-order harmonic generation. For the first time, we demonstrate that the short and long electron quantum paths contributing to harmonic generation are influenced in a different way by the pulse carrier-envelope phase.

Atomic transient recorder

In Bohr's model of the hydrogen atom, the electron takes about 150 attoseconds (1 as = 10(-18) s) to orbit around the proton, defining the characteristic timescale for dynamics in the electronic shell of atoms. Recording atomic transients in real time requires excitation and probing on this scale. The recent observation of single sub-femtosecond (1 fs = 10(-15) s) extreme ultraviolet (XUV) light pulses has stimulated the extension of techniques of femtochemistry into the attosecond regime. Here we demonstrate the generation and measurement of single 250-attosecond XUV pulses. We use these pulses to excite atoms, which in turn emit electrons. An intense, waveform-controlled, few cycle laser pulse obtains 'tomographic images' of the time-momentum distribution of the ejected electrons. Tomographic images of primary (photo)electrons yield accurate information of the duration and frequency sweep of the excitation pulse, whereas the same measurements on secondary (Auger) electrons will provide insight into the relaxation dynamics of the electronic shell following excitation. With the current approximately 750-nm laser probe and approximately 100-eV excitation, our transient recorder is capable of resolving atomic electron dynamics within the Bohr orbit time.

High-order harmonic generation up to 250 eV from highly ionized argon

We demonstrate the generation of very high-order harmonics, up to 250 eV, using argon gas. This extends by 100 eV the highest harmonics previously observed using Ar and exceeds the energies observed using any other medium besides helium. This advance is made possible by using a waveguide geometry to limit plasma-induced laser beam defocusing, making it possible to generate high harmonics from Ar ions. This work shows that high harmonic emission from ions can extend laser-based coherent up-conversion into the soft x-ray region of the spectrum.

Strong field quantum path control using attosecond pulse trains

We show that attosecond pulse trains have a natural application in the control of strong field processes. In combination with an intense infrared laser field, the pulse train can be used to microscopically select a single quantum path contribution to a process that would otherwise consist of several interfering components. We present calculations that demonstrate this by manipulating the time-frequency properties of high order harmonics at the single atom level. This quantum path selection can also be used to define a high resolution attosecond clock.

Attosecond Synchronization of High-Harmonic Soft X-rays

Subfemtosecond light pulses can be obtained by superposing several high harmonics of an intense laser pulse. Provided that the harmonics are emitted simultaneously, increasing their number should result in shorter pulses. However, we found that the high harmonics were not synchronized on an attosecond time scale, thus setting a lower limit to the achievable x-ray pulse duration. We showed that the synchronization could be improved considerably by controlling the underlying ultrafast electron dynamics, to provide pulses of 130 attoseconds in duration. We discuss the possibility of achieving even shorter pulses, which would allow us to track fast electron processes in matter.

Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high-order-harmonic spectra

For the first time single-shot harmonic spectra generated by few-optical-cycle pulses have been measured. Clear carrier-envelope phase effects have been observed in the cutoff harmonic spectral structure. Results have been interpreted in terms of the nonadiabatic single-atom response of the nonlinear medium excited by few-optical-cycle pulses.

Direct observation of attosecond light bunching

Temporal probing of a number of fundamental dynamical processes requires intense pulses at femtosecond or even attosecond (1 as = 10(-18) s) timescales. A frequency 'comb' of extreme-ultraviolet odd harmonics can easily be generated in the interaction of subpicosecond laser pulses with rare gases: if the spectral components within this comb possess an appropriate phase relationship to one another, their Fourier synthesis results in an attosecond pulse train. Laser pulses spanning many optical cycles have been used for the production of such light bunching, but in the limit of few-cycle pulses the same process produces isolated attosecond bursts. If these bursts are intense enough to induce a nonlinear process in a target system, they can be used for subfemtosecond pump-probe studies of ultrafast processes. To date, all methods for the quantitative investigation of attosecond light localization and ultrafast dynamics rely on modelling of the cross-correlation process between the extreme-ultraviolet pulses and the fundamental laser field used in their generation. Here we report the direct determination of the temporal characteristics of pulses in the subfemtosecond regime, by measuring the second-order autocorrelation trace of a train of attosecond pulses. The method exhibits distinct capabilities for the characterization and utilization of attosecond pulses for a host of applications in attoscience.

Temporal structure of attosecond pulses from intense laser-atom interactions

We find that the high harmonics have a power-law spectrum I(omega) approximately omega(-3.3+/-0.25) in a wide frequency domain starting at the ionization potential I(p) and down to the plateau beginning. Our spectrotemporal analysis of the emitted radiation displays clear bowlike structures in the (t,omega) plane. These "bows" correspond to Corkum's reencounters of the freed electron with the atom. We find that the bows are not filled and thus cannot be due to any bremsstrahlung. Rather, it is a resonant process that we call stimulated recombination (SR). It occurs when an electron with momentum p reencounters the incompletely ionized atom, and interferes with itself still remaining in the ground state. The SR leads to a highly efficient resonant emission at Planck's over 2pi omega=p(2)/2m+I(p) in the form of attosecond pulses. The SR relies on a low level of ionization and strongly benefits from the use of few-cycle laser pulses.

High harmonic imaging of few-cycle laser pulses

We show that the strength of the central electric field peaks in a few-cycle laser pulse can be recovered from a frequency-time image of the high harmonic spectrum generated in a gas volume. Pulse intensity, duration, and also the carrier-envelope phase phi(CE) can be determined. A simple and robust observable is defined that provides a gauge of phi(CE) for pulse durations up to three optical cycles, corresponding to 7.8 fs FWHM at the Ti:sapphire wavelength of 800 nm.

Frequency-resolved optical gating of femtosecond pulses in the extreme ultraviolet

Femtosecond extreme ultraviolet (XUV) pulses were fully characterized for the first time by using a newly developed cross-correlation frequency-resolved optical gating (FROG) technique in the XUV region. This method utilizes laser-assisted two-photon ionization as a nonlinear optical process. Near-infrared pulses characterized by FROG were used as a reference. The amplitude and phase of XUV pulses with a pulse duration of 10 fs were found to be in good agreement with a model analysis, taking into account phase modulation by ionization, self-phase modulation, and the atomic dipole phase.

Recent developments in compact ultrafast lasers

Ultrafast lasers, which generate optical pulses in the picosecond and femtosecond range, have progressed over the past decade from complicated and specialized laboratory systems to compact, reliable instruments. Semiconductor lasers for optical pumping and fast optical saturable absorbers, based on either semiconductor devices or the optical nonlinear Kerr effect, have dramatically improved these lasers and opened up new frontiers for applications with extremely short temporal resolution (much smaller than 10 fs), extremely high peak optical intensities (greater than 10 TW/cm2) and extremely fast pulse repetition rates (greater than 100 GHz).

Measurement of the subcycle timing of attosecond XUV bursts in high-harmonic generation

The absolute timing of the high-harmonic attosecond pulse train with respect to the generating IR pump cycle has been measured for the first time. The attosecond pulses occur 190+/-20 as after each pump field maxima (twice per optical cycle), in agreement with the "short" quantum path of the quasiclassical model of harmonic generation.

Attosecond spectral shearing interferometry

We show that the complete characterization of arbitrarily short isolated attosecond x-ray pulses can be achieved by applying spectral shearing interferometry to photoelectron wave packets. These wave packets are coherently produced through the photoionization of atoms by two time-delayed replicas of the x-ray pulse, and are shifted in energy with respect to each other by simultaneously applying a strong laser field. The x-ray pulse is reconstructed with the algorithm developed for optical pulses, which requires no knowledge of ionization physics. Using a 800-nm shearing field, x-ray pulses shorter than approximately 400 asec can be fully characterized.

Probing molecular dynamics with attosecond resolution using correlated wave packet pairs

Spectroscopic measurements with increasingly higher time resolution are generally thought to require increasingly shorter laser pulses, as illustrated by the recent monitoring of the decay of core-excited krypton using attosecond photon pulses. However, an alternative approach to probing ultrafast dynamic processes might be provided by entanglement, which has improved the precision of quantum optical measurements. Here we use this approach to observe the motion of a D2+ vibrational wave packet formed during the multiphoton ionization of D2 over several femtoseconds with a precision of about 200 attoseconds and 0.05 ångströms, by exploiting the correlation between the electronic and nuclear wave packets formed during the ionization event. An intense infrared laser field drives the electron wave packet, and electron recollision probes the nuclear motion. Our results show that laser pulse duration need not limit the time resolution of a spectroscopic measurement, provided the process studied involves the formation of correlated wave packets, one of which can be controlled; spatial resolution is likewise not limited to the focal spot size or laser wavelength.