Entanglement and electronic coherence in attosecond molecular photoionization | Nature

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Subjects

- Attosecond science

- Quantum mechanics

Abstract

Electronic coherences resulting from molecular photoionization underlie the process of attosecond charge migration, widely investigated as a possible path towards controlled charge-directed reactivity1,2,3,4. However, photoionization often creates entangled ions and photoelectrons. This entanglement compromises the ability to explore coherent ultrafast electron dynamics within ions or of their accompanying photoelectrons5,6,7,8. Here we present experiments and calculations in which hydrogen molecules are ionized by the combination of a phase-locked pair of isolated attosecond laser pulses and a few-cycle near-infrared (NIR) laser pulse. The electronic coherence in the dissociating H2+ ion is influenced by ion–photoelectron entanglement. We demonstrate experimental control over the degree of entanglement by varying the delay between the two attosecond pulses and the delay between these pulses and the few-cycle NIR pulse. Our work demonstrates the importance of proper consideration of the role of quantum entanglement for the optimal observation of electronic coherences in attosecond experiments.

Main

Attosecond 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: \(|{\varPsi }_{{\rm{total}}}(t)\rangle \,\ne \) \(|{\varPsi }_{{\rm{ion}}}(t)\rangle \otimes |{\phi }_{{\rm{photoelectron}}}(t)\rangle \). 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 H2. 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 H2+ 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 τXUV–X