Experimental Separation of Sub-Cycle Ionization Bursts in Strong-Field Double Ionization of H$_2$

TL;DR

This paper reports the first clear observation of sub-cycle ionization bursts in strong-field double ionization of H$_2$, achieved through advanced laser pulse techniques and coincidence imaging, enabling detailed study of molecular electron dynamics.

Contribution

It introduces a method to disentangle sub-cycle ionization bursts in molecular double ionization using few-cycle laser pulses and coincidence momentum imaging.

Findings

Observation of sub-cycle ionization bursts in H$_2$

Disentanglement of ionization events in molecular frame

Potential to study intramolecular electron dynamics

Abstract

We report on the unambiguous observation of the sub-cycle ionization bursts in sequential strong-field double ionization of H$_2$ and their disentanglement in molecular frame photoelectron angular distributions. This observation was made possible by the use of few-cycle laser pulses with a known carrier-envelope phase in combination with multi-particle coincidence momentum imaging. The approach demonstrated here will allow sampling of the intramolecular electron dynamics and the investigation of charge-state specific Coulomb-distortions on emitted electrons in polyatomic molecules.

Full text

The creation of free or bound electron wave packets with a sub-laser-cycle temporal structure using intense ultrashort laser pulses is at the heart of most processes in attosecond physics Kienberger et al. (2002); Xu et al. (2010); Haertelt et al. (2016); Xie et al. (2012a). The strong oscillating electric field of the laser light can cause ionization of a system via half-cycle periodic emissions of electron wavepackets and imprints a dominant sub-cycle temporal structure onto them. In addition, these periodically emitted wavepackets, known as the sub-cycle ionization bursts, may be modulated by the non-adiabatic response of the strongly driven system Takemoto and Becker (2010); Odenweller et al. (2011); Xie et al. (2012a); Spanner et al. (2012). In strong-field double ionization the sub-cycle ionization bursts from the first ionization step can be correlated with the ionization bursts from the second ionization step. Since each ionization burst corresponds to a specific time within the laser pulse envelope, various delays between the two ionization steps are sampled within a single pulse. In molecules, the delay between the two ionization steps can determine the outcome of molecular fragmentation reactions Xie et al. (2015); Sándor et al. (2016), constitutes the probe delay for intramolecular electron dynamics Takemoto and Becker (2010); Spanner et al. (2012); Hennig et al. (2005), and determines the molecular site from where the photoelectron originates Ohmura et al. (2006); Wu et al. (2012); Liu and Barth (2017). To extract the ultrafast dynamics underlying these processes from experiments it is necessary to disentangle the separate contributions of the sub-cycle ionization bursts in measured photoelectron or photoion distributions. However, so far such disentanglement has been achieved only for atomic systems in both the sequential Schöffler et al. (2016) and nonsequential Bergues et al. (2012) regimes of double ionization.

In this Letter, we demonstrate a method that allows for the unambiguous identification and extraction of the contributions from specific sub-cycle ionization bursts in electron momentum distributions measured for molecular double ionization. Using the example of the H2 molecule we show that we can measure the molecular frame photoelectron angular distributions (MF-PADs) for a specific pair of two time-ordered sub-cycle ionization bursts in the sequential double ionization (SDI) process $\textrm{H}_{2}\rightarrow\textrm{H}_{2}^{+}+e^{-}\rightarrow\textrm{H}^{+}+\textrm{H}^{+}+2e^{-}$. The observation of the sub-cycle bursts and the unambiguous assignment of the two detected electrons to the first and second ionization burst was accomplished by combining our technique developed for atoms Schöffler et al. (2016) with our recently published method for the reconstruction of molecular dynamics during laser interaction Hanus et al. (2019).

In our experiments, we used a reaction microscope (Dörner et al., 2000) to measure in coincidence the momenta of two protons and two electrons created upon interaction of a cold jet of H2 with intense, elliptically polarized few-cycle laser pulses. The ellipticity, defined as the ratio of the electric field strength perpendicular and parallel to the main axis of the polarization ellipse, was $E_{\perp}/E_{\parallel}=0.85$, cf. Fig. 1(a). The laser center wavelength was $\lambda=750$ nm. Thus, the laser oscillation period $T=2\pi/\omega=2.5$ fs with $\omega=2\pi c/\lambda$ the frequency and $c$ the speed of light. The duration of the pulses (\approx$$4.5\text{\,}\mathrm{fs}) and their carrier-envelope phases (CEPs) were measured with a stereo electron spectrometer in phase-tagging mode (Rathje et al., 2012). The laser beam was focused in an ultra-high vacuum chamber (base pressure 10*-10* mbar) onto a supersonic gas jet of H2. Ions and electrons emerging from the interaction volume were guided by weak electric (21 V/cm) and magnetic fields (12 G) to two position-sensitive detectors. The momentum of the second electron was calculated from the momenta of the measured electron and both ions by exploiting momentum conservation. The laser peak intensity in situ was $9\text{\times}{10}^{14}\text{\,}\mathrm{W}\text{\,}{\mathrm{cm}}^{-2}$ (Smeenk et al., 2011). Further details on the reaction microscope can be found in Refs. Xie et al. (2012b); Zhang et al. (2014); Xie et al. (2017) and on the optical setup in Ref. Schöffler et al. (2016).

When $\textrm{H}_{2}$ undergoes SDI in a strong elliptically polarized laser field, the first ionization step at time $t_{1}$ triggers vibronic dynamics in the molecular cation $\textrm{H}_{2}^{+}$, and the second ionization step at time $t_{2}=t_{1}+\Delta t$ initiates Coulomb explosion into $\textrm{H}^{+}+\textrm{H}^{+}$, cf. the sketches in Figs. 1(b) and 1(c). While the kinetic energy released, $\textrm{KER}=1/R$, with $R$ the internuclear distance at which the Coulomb explosion is initiated, provides a precise measure for the nuclear motion in between the two ionization steps Niikura et al. (2003); Ergler et al. (2006); Hanus et al. (2019), the momenta of the two emitted electrons, $\textbf{p}_{e1,e2}$, provide information on the emission times of the two electrons within a laser cycle. This is because in elliptically polarized light the ionization phase within a laser cycle, $\omega t_{i}$, is mapped onto the emission angle of the photoelectron via the relation $\textbf{p}_{ei}=-\textbf{A}(t_{i}),\>i=\{1,2\}$ Faisal (1973); Reiss (1980), cf. Fig. 1(a). The laser vector potential $\textbf{A}(t)$ is connected to the laser electric field by $\textbf{A}(t)=-\int_{-\infty}^{t}\textbf{E}(t^{\prime})dt^{\prime}$. Thus, measurement of the electron emission angle in the laboratory frame determines the ionization time $t_{i}$ within one cycle (Maharjan et al., 2005; Eckle et al., 2008a; Schöffler et al., 2016; Hanus et al., 2019).

In the case of SDI, the momenta of the two emitted electrons are reflected in the recoil momentum vector of the two protons, $\textbf{p}_{\textrm{rec}}=\textbf{p}_{\textrm{H}^{+}}+\textbf{p}_{\textrm{H}^{+}}=-(\textbf{p}_{e1}+\textbf{p}_{e2})$ Schöffler et al. (2016); Pfeiffer et al. (2011); Maharjan et al. (2005). Fig. 1(e) shows the measured distribution of $\textbf{p}_{\textrm{rec}}$ in the polarization plane, integrated over all values of the CEP and KER. In elliptical light, ionization takes place preferentially around the times when the field vector $\textbf{E}(t)$ passes the major axis of the polarization ellipse during its rotation, i.e., twice during the optical cycle. Depending on the ionization delay $\Delta t$, the two electrons can be streaked by the laser field into the same or into opposite hemispheres. If the two electrons are ejected with a delay of an even number of half cycles [$\Delta t=2n\frac{T}{2};n=0,1,2,\ldots$], the electrons are emitted into the same hemisphere and their momenta add up to a large value of $\textbf{p}_{\textrm{rec}}$. Examples of electron momentum vectors consistent with such SDI dynamics are indicated as the upper and lower sketches in Fig. 1(d). In contrast, if the two electrons are emitted with an odd number of half cycles [$\Delta t=(2n+1)\frac{T}{2},\;n=0,1,2,\ldots$], they are streaked into the opposite hemisphere and their momenta cancel to a small value of $\textbf{p}_{\textrm{rec}}$, see the center sketch in Fig. 1(d).

The three lobes in the momentum distribution in Fig. 1(e) are, thus, the signatures of the sub-cycle ionization bursts emitted during various combinations of half-cycle peaks of $|\textbf{E}(t)|$, numbered 1–6 in Fig. 1(b), integrated over the whole pulse duration and over all values of the CEP and KER. Because the ionization delay $\Delta t$ is mapped onto KER, cf. Fig. 1(c), depending on their ionization delay $\Delta t=n\frac{T}{2},\;n=0,1,2,\ldots$, a certain pair of sub-cycle bursts leads to a certain value of KER. The three lobes in the momentum distribution Fig. 1(e), thus, appear as separated peaks A/A’, B, C/C’ in the KER vs. $\textbf{p}_{\textrm{rec},\perp}$ distribution shown in Fig. 1(f). Hence, selection of a certain range in KER allows selecting a well-defined range of $\Delta t$ values Hanus et al. (2019).

To understand how the peaks A/A’, B, C/C’ can be disentangled into the different contributions of specific SDI bursts, we first resolve them as a function of CEP for three different ranges of KER, each 2 eV wide, corresponding to about $0.5T$-wide ranges of $\Delta t$ around $1T,1.5T$ and $2T$, see Figs. 2(a)-(c). A pronounced dependence on the CEP of both the momentum and yield is clearly visible for all peaks. Particularly strong yield modulations are observed for peaks A/A’ and C/C’, where for certain values of the CEP the two electrons are predominantly emitted into one hemisphere only. Additional analysis of this asymmetric two-electron emission and its application to the calibration of the CEP in the experimental distributions is provided in the Supplemental Material SMH .

A qualitative understanding of the CEP-dependence of the SDI dynamics can be obtained with the help of semi-classical simulations. The numerical model underlying these simulations is described in the Supplemental Material SMH , results are shown in Fig. 3. First, we apply our model to the measured momentum distributions for the highest KER-range, shown in Fig. 2(a), for which $\Delta t\approx 1T$. For this ionization delay the two electrons are both streaked into the same hemisphere, either both upwards or both downwards, depending on the specific combination of sub-cycle bursts. The strong yield-asymmetry and the dominance of the lower peak A’ in Fig. 2(a) for $\textrm{CEP}=205^{\circ}$ shows, because of $\textbf{p}_{\textrm{rec},\perp}=-(\textbf{p}_{e1,\perp}+\textbf{p}_{e2,\perp})$, that for this CEP-value the two electrons are predominantly emitted only into the upwards hemisphere. For $\textrm{CEP}=25^{\circ}$ ($=205^{\circ}-180^{\circ}$) the opposite emission scenario and the dominance of peak A is observed. This implies that for these CEP-values the two ionization steps each take place during predominantly only one sub-cycle burst: up-bursts for $\textrm{CEP}=205^{\circ}$ and down-bursts for $=25^{\circ}$.

The simulated data for $\textrm{CEP}=205^{\circ}$ shown in the leftmost column of Fig. 3 confirm this single-burst ionization dynamics and the experimentally observed yield-asymmetry. For intermediate values of the CEP, e.g. for $\textrm{CEP}\approx 110^{\circ}$, the numerical model reveals that more than one pair of sub-cycle bursts contribute and both up- and down-pairs are emitted. Accordingly, the measured electron yield in Fig. 2(a) does not show any asymmetry for $\textrm{CEP}\approx 110^{\circ}$ and peaks A and A’ are equally strong. The two-electron emission dynamics for $\Delta t=2T$ that results in the peaks C/C’ takes place analogously to the case $\Delta t=1T$. The measured CEP-dependence of the corresponding yield-distributions in Fig. 2(c) can therefore be explained qualitatively using the same argumentation.

Of particular interest is the case $\Delta t=1.5T$. For this value, the two electrons are streaked into opposite hemispheres and dominantly only peak B is observed. The corresponding CEP-resolved momentum distribution in Fig. 2(b) for $\Delta t=1.5T(\pm 0.25T)$ shows that the mean value of peak B oscillates with CEP. To explain this CEP-oscillation, we turn to the simulated distributions in Fig. 3. The center column shows that for $\textrm{CEP}\approx 90^{\circ}$ dominantly only one pair of sub-cycle bursts is emitted symmetrically around the pulse peak. One electron is streaked upwards, the other one downwards, and their momenta almost cancel, resulting in very small sum momentum close to zero. For $\textrm{CEP}\approx 180^{\circ}$ (Fig. 3, rightmost column), in contrast, each electron is emitted during two sub-cycle peaks and streaked both up- and downwards. Hence, the photoelectrons are no longer emitted symmetrically around the pulse maximum, explaining the CEP-oscillation of $\textbf{p}_{\textrm{rec},\perp}$. We conclude from this analysis that it is possible to control the SDI process with the CEP such that the two emitted electrons can be disentangled in the experimental distributions, i.e., that a situation as in the center column of Fig. 3 can be achieved.

The value of the CEP for which this is possible can be determined directly from experimental data without the need to consult simulations. To demonstrate this, we consult the electron energy distribution over CEP shown in Fig. 4(a). The mean energy of the electrons emitted towards the detector, marked by a red line, shows a clear oscillation with the CEP. If those electrons that are streaked into the opposite hemisphere (away from the detector) are selected, an oscillation phase-shifted by 180∘ is obtained (blue line). From the discussions above we know that if each electron is emitted during one sub-cycle burst only, the two electrons will be emitted symmetrically around the pulse peak—one upwards the other downwards. As a consequence, both electrons must have very similar energy. Thus, for symmetry reasons, the CEP at which this situation occurs is that where the energy of the upward and downward electrons is the same. This is, in accordance with the simulations, the case for $\textrm{CEP}=90^{\circ}$ (and $\textrm{CEP}=270^{\circ}$), indicated by a black circle in Fig. 4(a). The corresponding emission scenario and the simulated sub-cycle bursts in the time-domain (reproduced from Fig. 3) are sketched in Fig. 4(b). On the contrary, when the electrons are emitted during more than one pair of sub-cycle bursts, the upwards and downwards electrons will have markedly different energy. This is the case for $\textrm{CEP}=180^{\circ}$, indicated by a grey circle in Fig. 4(a); the corresponding emission scenario is sketched in Fig. 4(c).

Fig. 4 thus holds experimental proof that for $\textrm{CEP}\approx 90^{\circ}$ and $\textrm{CEP}\approx 270^{\circ}$ it becomes possible to disentangle the contributions of the sub-cycle bursts in electron momentum distributions simply by selecting one electron from the upwards and the other from the downwards hemisphere. Moreover, based on the known rotation direction of $\textbf{E}(t)$ determined by the helicity of the laser field it is even feasible to determine during which of the two sub-cycle bursts a specific electron has been emitted. For the helicity used in the experiment and for $\textrm{CEP}=90^{\circ}$ the first emitted electron is streaked downwards [cf. Fig. 4(b)], for $\textrm{CEP}=270^{\circ}$ the first emitted electron is streaked upwards. With that, by fixing the CEP to one of the two values, the SDI dynamics is completely determined.

This opens up the possibility to obtain an experimental trace of the attosecond evolution of the sub-cycle ionization bursts. By exploiting the fact that the electron emission dynamics is streaked into the angular direction by the rotating laser field we can represent the attosecond evolution of the sub-cycle two-electron bursts as photoelectron angular distributions (PADs). Moreover, because in our experiment we also measure the orientation of the molecules in the lab frame via the momentum vectors of the two protons, we are able to plot the PADs in the molecular frame (MF) of reference. The MF-PADs for $\textrm{CEP}=90^{\circ}$ and $\textrm{CEP}=180^{\circ}$ are shown in Fig. 4(d) and (e). Because for $\textrm{CEP}=180^{\circ}$ two pairs of sub-cycle bursts are emitted, the MF-PAD cannot be separated without ambiguity, cf. Fig. 4(e). In contrast, the dominant single pair emitted for $\textrm{CEP}=90^{\circ}$ can be unambiguously disentangled in the MF-PAD, see Fig. 4(d).

The capability of obtaining absolutely defined traces of the attosecond two-electron emission for specific molecular orientations in the laser polarization plane opens up intriguing possibilities. For example, it allows to trace the intramolecular electron dynamics in between the two ionization steps Hennig et al. (2005); Takemoto and Becker (2010); Odenweller et al. (2011). These dynamics can lead to very complicated pattern of the intramolecular charge density Spanner et al. (2012); Hennig et al. (2005) that may modulate the sub-cycle ionization behavior. We could, however, show that such localization dynamics is not significant in H${}_{2}^{+}$ for the small ionization delays $\Delta t\lesssim 2T$ considered here Hanus et al. (2019). Our method can also be applied to separately determine the Coulomb-distortion Eckle et al. (2008b); Torlina et al. (2015) imparted by the singly respectively doubly charged parent ion onto the first respectively second emitted electron.

In conclusion, we observed the sub-cycle ionization bursts in SDI of H2 with elliptically polarized intense few-cycle laser pulses with a known CEP using multi-particle coincidence momentum imaging. This permitted us to measure the MF-PAD for a single pair of sub-cycle bursts leading to double ionization, and the unambiguous assignment of each burst to one of the two detected electrons. Although demonstrated for H2, we expect that the approach demonstrated here will allow the observation of the sub-cycle ionization bursts also in more complicated molecules, as the only requirement for the molecule is a suitably fast fragmentation dynamics. This will grant experimental access to the Coulomb distortion for specific charge states and to the intramolecular electron localization dynamics on attosecond time-scales in polyatomic molecules.