GoKawiilAttosecond pulses produced by high-harmonic generation (HHG) consisting of extreme-ultraviolet (XUV) radiation can ionize any conceivable compound, leading to the formation of a bipartite ion–photoelectron system that is entangled whenever the total wavefunction cannot be written as a single direct product: \(|{\varPsi }_{{\rm{total}}}(t)\rangle \,
e \) \(|{\varPsi }_{{\rm{ion}}}(t)\rangle \otimes |{\phi }_{{\rm{photoelectron}}}(t)\rangle \). This occurs routinely in ionization experiments with narrowband light sources, in which the ion may be left in different eigenstates, each accompanied by photoelectrons with corresponding, well-defined kinetic energies. Ultrashort pulses excite coherent superpositions of states, creating a path towards observation of their time-resolved dynamics. This concept is taken to the extreme in attosecond science, in which bandwidths spanning several tens of eV permit the coherent excitation of several electronic configurations and the creation of electronic wave packets. Attosecond laser-induced ionization can initiate correlated dynamics of the ion and the photoelectron or in the individual subsystems. In the latter case, examining coherent dynamics in the ion (photoelectron) is only possible if a correlated observation of the accompanying photoelectron (ion) does not enable identification of the ion’s (photoelectron’s) quantum state. This situation may be compared with a multi-slit interference experiment, in which a (partial) observation of the slit through which a quantum particle moves reduces or completely removes the interference pattern on a detector: similarly, the existence of an ‘observer’ holding quantum path information compromises the coherence required for observation of a pump–probe signal (Fig. 1a). In other words, coherent dynamics in the ion or photoelectron subsystem is only possible if it is not compromised by quantum entanglement.
Fig. 1: Experimental concept and approach. Full size image a, Time-resolved pump–probe experiments rely on interference, in which each interfering path corresponds to a coherently prepared intermediate state. Observation of the coherent evolution is possible if, and only if, the quantum path cannot be identified. In an entangled ion–photoelectron pair, a photoelectron measurement can provide information on the ionic quantum state, compromising the observation of coherent ionic dynamics. This situation resembles that of the passage of a quantum particle through a pair of slits monitored by two observers (O1 and O2): the modulation depth in the interference pattern is inversely proportional to the overlap between the observations by observers O1 and O2 (see, for example, ref. 39). b, Experimental set-up: a pair of IAPs, created by HHG, and a few-cycle NIR pulse are used to dissociatively ionize H 2 . The left–right asymmetry in the H+ ejection along the XUV/NIR polarization axis is measured using a VMI spectrometer and is used to quantify the electronic coherence in the dissociating H 2 + ion. AF, aluminium filter; BPF, band-pass interference filter; BS, beam splitter; Cam, camera; CW, continuous-wave laser; DM, drilled mirror; EX, extractor; FT, flight tube; NIR, near-infrared laser; PID, proportional-integral-derivative controller; REP, repeller; TM, toroidal mirror; VLG, variable line-space grating. c, Typical VMI measurement: the 3D H+ momentum distribution is obtained by Abel inversion of the measured 2D projection. d, Typical XUV spectra recorded during the experiments, consisting of broad harmonics with a separation of about 3 eV on a continuous background, consistent with the formation of a dominant IAP with a very low intensity of the adjacent XUV pre- or post-pulses. The observed narrow fringe structure depends on the delay between the two IAPs τ XUV–XUV . arb.u., arbitrary units.
Building on several early results5,6,9,10,11, recent research aims to achieve a better understanding of the role of quantum entanglement7,8,12,13,14,15,16 and other sources of decoherence17 in attosecond experiments. This includes previous work on H 2 , investigating the relationship between ion–photoelectron entanglement and the occurrence of vibrational coherence7,8, as well as observations of molecular frame asymmetries in the ejection of photoelectrons15. In the former work, vibrational wave packets were formed in H 2 + by ionizing neutral H 2 with a pair of attosecond pulse trains and the degree of entanglement with the accompanying photoelectrons was measured by dissociating the ions, at a variable delay, using a few-cycle NIR pulse.
A main objective in attosecond molecular science is, however, the observation of ‘electronic’ coherences in ions formed by attosecond photoionization, commonly referred to as ‘attosecond charge migration’. Its interest arises from the fact that, by eliciting an electronic response on timescales preceding nuclear motion1,18, charge-directed reactivity2, that is, controlled chemistry, may be achieved. Several successful experiments have been reported3,4,19,20. However, the precise role of entanglement and its potential use to control coherent charge dynamics is unknown.
Ideally, studies of ion–photoelectron entanglement would use coincident detection of the ions exhibiting electronic coherence together with their corresponding photoelectrons. However, experiments combining the use of isolated attosecond pulses (IAPs) and coincident electron-ion detection have not yet been realized. Therefore, we focus on the dependence of the degree of (1) electronic coherence in an ion and (2) quantum entanglement between the ion and the photoelectron on, first, the delay between a pair of IAPs used to produce the ion and, second, the delay of a co-propagating NIR pulse. We present experiments and theoretical modelling on H 2 , showing how the kinetic energy and—in particular—the orbital angular momentum of the outgoing photoelectron, control the ion–photoelectron entanglement and electronic coherence in the ion.
Dissociative ionization by photons below about 35 eV (Fig. 2) induces fragmentation into H+ + H and provides a direct signature of electronic coherence in the ionic subsystem through the phenomenon of electron localization, that is, a laboratory-frame asymmetry in the ejection of the H+ fragment ion signifying a preferred localization of the single remaining bound electron. Following dissociation, the two lowest electronic states of H 2 + can be written as
$${\psi }_{1{\rm{s}}{\sigma }_{{\rm{g}}}}=\frac{1}{\sqrt{2}}[{\psi }_{1{\rm{s}}}^{{\rm{left}}}+{\psi }_{1{\rm{s}}}^{{\rm{right}}}],\,{\psi }_{2{\rm{p}}{\sigma }_{{\rm{u}}}}=\frac{1}{\sqrt{2}}[{\psi }_{1{\rm{s}}}^{{\rm{left}}}-{\psi }_{1{\rm{s}}}^{{\rm{right}}}]$$ (1)
in which \({\psi }_{1{\rm{s}}}^{{\rm{left}}}\) and \({\psi }_{1{\rm{s}}}^{{\rm{right}}}\) represent 1s atomic orbitals on the left and right atoms, respectively. Rewriting this to
$${\psi }_{1{\rm{s}}}^{{\rm{left}}}=\frac{1}{\sqrt{2}}[{\psi }_{1{\rm{s}}{\sigma }_{{\rm{g}}}}+{\psi }_{2{\rm{p}}{\sigma }_{{\rm{u}}}}],\,{\psi }_{1{\rm{s}}}^{{\rm{right}}}=\frac{1}{\sqrt{2}}[{\psi }_{1{\rm{s}}{\sigma }_{{\rm{g}}}}-{\psi }_{2{\rm{p}}{\sigma }_{{\rm{u}}}}]$$ (2)
... continue reading