Optical Control of Autoionizing States in Argon

Abstract

We use tunable attosecond transient absorption to study the autoionizing polaritonic states in argon. Our approach provides new avenues for optical control of autoionization dynamics in polyelectronic systems. We highlight the stabilization of autoionizing states as a function of the detuning and time-delay of the dressing laser pulse. Furthermore, we use the relative polarization between the pump and probe pulses to control the branching of the polaritons, where the selection rules allow us to include or exclude specific states from the radiative coupling.

1 Introduction

The study and control of autoionization is essential for understanding multi-electron interactions and the formation of ion-electron pairs in atomic and molecular systems. Extreme-ultraviolet (XUV) attosecond pulses are ideal to excite bright localized states above the ionization threshold, which decay to various ionization continua, and which are known as autoionizing states (AISs). In the photoionization spectrum, these states appear as resonances with asymmetric line shapes known as Fano profiles [1]. Polyelectronic atoms feature also dark AISs, which cannot be reached by means of one-photon transitions from the ground state due to dipole selection rules. In the presence of an infrared (IR) dressing-field, the dark states can also be populated thanks to the absorption of one XUV and multiple IR photons, giving rise to features in the XUV spectrum known as autoionizing light-induced states (ALISs). The same dressing field, furthermore, makes available to the bright AISs additional radiative decay channels to continua with different symmetry. The transiently bound electronic component of a bright AIS and of an ALIS are associated with a different number of dressing-field photons. If the laser parameters are chosen so that a bright AIS and an ALIS are nearly degenerate, these two states mix, giving rise to entangled light-matter states referred to as autoionizing polaritons (AIPs).

In this paper, we demonstrate XUV attosecond transient absorption with tunable infrared (IR) pulses as an ideal tool for resolving and modifying light-induced couplings between autoionizing continuum resonances in the argon atom. The frequency tunability of the dressing IR field ($\omega _{\mathrm {IR}}$) provides control over the formation and subsequent dynamics of AIPs. We show how the pump-probe time delay, the intensity, and the frequency of the dressing field play a role in the control and stabilization of the AIPs. The polarization of the laser field is investigated as another control knob that modifies the couplings between AIS, thanks to dipole selection rules, thus affecting the polaritonic branching. The experimental results are in excellent agreement with ab initio theoretical calculations carried out with the NewStock code [2] and open new avenues for applications of optical control of AISs, ALISs, and AIPs in polyelectronic systems.

The manuscript is organized as follows. Section 2 describes the experimental techniques used for our photoabsorption studies in argon. Section 3 provides information on our theoretical methods. In Sect. 4, we present our experimental and theoretical results for optical control of AIP dynamics. Finally, in Sect. 5, we summarize our findings and discuss future research avenues for characterizing and manipulating autoionization dynamics.

2 Experimental Setup

Our attosecond transient absorption setup employs XUV-IR pump-probe schemes and has been described in detail in [3].

Briefly, the experimental setup combines extreme-ultraviolet (XUV) attosecond pulse trains (APT) with strong-field infrared (IR) femtosecond pulses, as shown in Fig. 1. Initially, a Ti:sapphire laser amplifier is used to generate 790 nm, 2 mJ, 1 kHz near-infrared (NIR) pulses. The beam is subsequently divided into two arms of equal pulse energy (50%) with the aid of a beam splitter. The first beam path is used for high harmonic generation in xenon, to produce XUV attosecond pulse trains (APT). The second arm is redirected to an optical parametric amplifier (OPA), which allows us to tune the frequency of the NIR pulse from 1.57 eV to 0.73–1.03 eV. The intensity of these tunable IR pulses is controlled by a half-wave plate and polarizer. In addition, a delay stage controls the relative time delay between the XUV APT and the IR pulses and a shutter allows us to isolate the IR contribution to the XUV spectrum. Finally, an annular mirror combines both the XUV and the IR beams into a gas cell for photoabsorption spectrometry. In the experiments reported here, the XUV APT excites the $3s^{-1}4p$ autoionizing state in argon, which can be subsequently coupled to other states by the tunable IR field.

Fig. 1

Experimental setup for time-resolved photoabsorption studies. A tunable dressing-field provides control over different XUV-induced autoionizing dynamics of polaritons and electronic wave packets

3 Theoretical Simulations

To confirm and interpret the experiment, we conduct time-dependent ab initio simulations for an isolated argon atom, subject to the influence of external light pulses. For full details, see [2, 3]. To reproduce the single-ionization dynamics triggered in the argon atom by the experimental pulses, we build a close-coupling space that comprises the configurations obtained by coupling either the ground ($3p^{-1}$) or the first-excited ($3s^{-1}$) states of the Ar${ }^+$ ion to a set of single-particle states for the photoelectron. The states of the ion are computed at the multi-reference Hartree-Fock level (MRHF), using the ATSP2K package [4], whereas the states of the photoelectron are expanded in a spherical basis, with angular part given by spherical harmonics with orbital angular momentum up to $\ell _{\mathrm {max}}=4$, and radial part given by a set of B-spline functions in a quantization box with radius $R_{\mathrm {box}}=500$ a.u. Furthermore, the configuration space comprises also all those states obtained by augmenting any of the configurations represented in the MRHF parent ion with any of the orbitals active in the parent-ion. The total field-free Hamiltonian $H_0$ is diagonalized in this basis, in the presence of a complex absorbtion potential (CAP), $V_{\textsc {CAP}}$, with support confined in a small radial layer next to the wall of the quantization box. This procedure ensures that any wavepacket built from the eigenstates of such complex Hamiltonian, $\tilde {H}_0=H_0+V_{\textsc {CAP}}$, is vanquished by the CAP before it has the opportunity of reaching the box boundary and give rise to unphysical reflections back to the origin. In particular, autoionizing states appear as eigenstates of the complex Hamiltonian, satisfying outgoing boundary conditions. This circumstance allows us to selectively include in or exclude from the simulation any autoionizing state of the system, to ascertain their individual contribution to spectral features of interest. The use of a spectral basis for a complex Hamiltonian allows us also to eliminate from the basis a large number of states (as many as 99%) that do not appreciably affect the result of the observables of interest in our simulation, thus drastically accelerating the calculations. Starting from the ground state of the atom, the system is evolved under the influence of a sequence of external pulses, by integrating the time-dependent Schrödinger equation, $\varPsi (t+dt)=U(t+dt,t)\varPsi (t)$, where $U(t+dt,t)=\mathrm {exp}(-i\tilde {H}_0 dt/2)\mathrm {exp}\Big [-i\alpha A(t+dt/2)P_z\Big ]\mathrm {exp}(-i\tilde {H}_0dt/2)$ is a second-order split exponential propagator, $\alpha$ is the fine-structure constant, $A(t)$ is the vector potential of the radiation field, and $P_z$ is the z component of the total canonical electronic momentum. From the expectation value of the dipole operator as a function of time, $p_z(t)=\langle \varPsi (t)|P_z|\varPsi (t)\rangle$, we extract the spectral response and the transient absorption spectrum of the atom, $\sigma =-\frac {4\pi }{\omega }\Im \left (\tilde {p}(\omega )/\tilde {A}(\omega )\right )$, where $\tilde {f}(\omega )=\int _{-\infty }^{\infty } dt\, e^{i\omega t}f(t)$ is a Fourier Transform. Figure 2 shows the single-atom XUV absorption spectrum of argon, in the vicinity of the $3s^{-1}4p$ bright resonance, in the presence of an IR dressing pulse with duration $\sim 45$ fs, as a function of the XUV-pump IR-probe delay, for several choices of the laser central frequency and peak intensity.

Fig. 2

ATAS simulated spectrum in the proximity of the $3s^{-1}4p$ resonance, illustrating the profile of the polaritons as a function of the pump-probe delay, for several values of the intensity and frequency of the dressing lasers

As the intensity increases, the resonance features split into two or more components, whose position, width, and relative contrast is altered by the IR frequency. As discussed below, these features illustrate the radiative coupling between multiple autoionizing states of several different symmetries (${ }^1$S${ }^e$, ${ }^1$P${ }^o$, ${ }^1$D${ }^e$, and ${ }^1$F${ }^o$).

4 Optical Control of Autoionizing Polaritons

Figure 3 shows the formation of AIPs in the continuum. These structures arise from the near-resonant interaction between bright (${\left\vert \alpha \right\rangle}$) and dark (${\left\vert \beta \right\rangle}$) AISs in the presence of a strong IR dressing field. The degeneracy between the bright AIS and the ALISs of the nearby dark states leads to a change of the electronic structure, which can be described in terms of entangled light-matter states, termed polaritons [2].

Fig. 3

Schematic representation of AIP formation and subsequent decay pathways. Near resonance, the degeneracy of between a bright (${\left\vert \alpha \right\rangle}$) AIS and an ALIS (${\left\vert \beta -\omega _{\mathrm {IR}}\right\rangle}$) leads to AIP multiplets, which then decay through autoionization and radiative ionization. Destructive interference between these pathways can lead to stabilization of the atom against ionization

In the case of one AIS interacting with one ALIS, as highlighted in Fig. 3, two polaritonic branches result. Each polariton is a superposition of two components, and can decay either through autoionization (AI) or radiative-ionization (RI). In AI, the number of photons does not change, whereas RI is accompanied by the stimulated emission or absorption of one photon. The interference between these different decay pathways to a same continuum can modulate the linewidth and hence the lifetime of the state. In particular, a destructive interference can lead to stabilization against autoionization, as demonstrated in [2].

Our photoabsorption experiment uses the 17th harmonic of the XUV APT to excite the ground state population of argon to the ${3s^{-1}4p}$ bright AIS. The IR dressing field can be tuned to couple the aforementioned state to the $3s^{-1}3d$ (27.51 eV), $3s^{-1}5s$ (27.55 eV), or $3s^{-1}4f$ ($\sim$28.31 eV) dark states through one- and two-photon transitions. Stated otherwise, the ALISs of these dark states can be tuned to be degenerate with the ${3s^{-1}4p}$ bright state using the tunability of IR photons in our setup. Near resonance, different AIP multiplets emerge in the photoabsorption spectra. To clearly observe these AIPs, we compare the photoabsorption spectrum of the IR-dressed medium, $I_{\mathrm {XUV+IR}}(\omega ;\tau )$, with the spectrum of the incident XUV radiation, $I_{\mathrm {ref}}(\omega )$, expressing our results in terms of the absolute optical density (OD), $\mathrm {OD}(\omega ;\tau )=-\log _{10}\left [ I_{\mathrm {XUV+IR}}(\omega ;\tau ) / I_{\mathrm {ref}}(\omega ) \right ]$, where $\tau =t_{\mathrm {XUV}}-t_{\mathrm {IR}}$ is the delay between the XUV and the IR pulses ($\tau <0$ if the IR pulse follows the XUV pulse). Negative values of the OD indicate transparency windows associated to different states in the continuum.

In our earlier work [2], we employed this tunable attosecond transient to explore the impact of different dressing-field parameters (frequency, intensity, and time delay) on the AIP dynamics. Our investigations demonstrated the AIP stabilization through the coherent interference of the AI and RI pathways [2], thus experimentally confirming an effect that was predicted several decades ago [5].

In Fig. 4a, each column corresponds to different $\omega _{\mathrm {IR}}$ values, showing how the AIP structure changes as different ALISs come into resonance with the ${3s^{-1}4p}$ AIS. For each $\omega _{\mathrm {IR}}$ value, the top panels show the experimental results and bottom panels show the ab-initio theoretical results. At large detuning, we only observe an energy shift in the ${3s^{-1}4p}$ absorption line, which is upward (downward) when the ALIS lies below (above) the ${3s^{-1}4p}$ AIS. In the near resonance condition ($\sim$0.94 eV), we observe the splitting of the ${3s^{-1}4p}$ AIS in two AIPs around zero time delay. The lower branch has noticeably smaller width than the upper branch indicating stabilization against autoionization.

Fig. 4

(a) Experimental (top) and theoretical (bottom) XUV photoabsorption in the vicinity of argon $3s^{-1}4p$ AIS, as a function of the IR pulse delay, for several values of IR photon energy. Color map represents the OD. Positive delay implies IR pulse arrives before XUV. Interaction of AISs with ALISs gives rise to the polariton splitting prominently visible between 0.86 and 0.98 eV IR photon energy. Experimental (b) and theoretical (c) polaritonic line shapes for the near resonant case of 0.94 eV IR energy, for several time delays. In the absence of interference between radiative and Auger channels, the two polaritons are expected to have comparable widths. Stabilization is evidenced by the delay-dependent reduction of AIP$-$ width and marked difference between the AIP$\pm$ widths in both experiment (d) and theory (e). Open symbols are for 0.93 eV case [Reused with permission, Fig. 2 in doi.org/10.1103/PhysRevLett.127.023202]

Next, we explored the intensity dependence of the polaritonic widths by using time-delay as a proxy for the instantaneous field strength. The experimental and theoretical results of delay-dependence of Fano profiles of AIP window resonances are shown in the energy line outs plotted in Fig. 4b and c, respectively. We extracted the width of these resonances and plotted them in Fig. 4d and e for experiment and theory. As we move from positive time delays towards zero, we see a clear divergence in polaritonic widths with upper branch getting broader and lower branch getting narrower.

The analysis in terms of two polaritonic branches resulting from the interaction of two AISs is somewhat simplistic, and the presence of other couplings limits the degree of control we can exert. In particular, the region above $\omega _{\mathrm {IR}}$ $>$ 0.90 eV is governed by one-photon couplings (3d and 5s) whereas $\omega _{\mathrm {IR}}$ $<$ 0.90 eV exhibits a significant contribution of two-photon couplings, corresponding to the ${3s^{-1}4f}$ AIS. The radiative coupling between multiple AIS leads to the formation of polariton multiplets near time-delay zero. In a recent work, we discussed the important role of intermediate resonances in such two-photon AIP formation [3].

All these investigations only considered the case in which both the XUV APT and the IR dressing field have relative parallel polarizations. Here we explore the role of the dressing field polarization as an additional knob to control AIP structure and dynamics. Figure 5a and b shows spectrograms in the vicinity of the ${3s^{-1}4p}$ AIS for IR field polarization parallel and perpendicular to the XUV polarization, respectively. The IR frequency is held fixed at 0.85 eV and with a beam intensity of ${\sim }$150 GW/cm${ }^2$. Our results show a remarkable difference in AIP structure, especially in terms of the number of branches. We observe that, when the IR polarization is parallel, three AIP branches are clearly visible in the photoabsorption spectrum. Conversely, when the dressing field polarization is perpendicular, the AIP feature around 26.85 eV disappears, and we see only two observable branches. We emphasize this point by taking lineouts near $\tau \,{\sim }\,0$. in Fig. 5c.

Fig. 5

AIP spectrograms corresponding to (a) parallel and (b) perpendicular dressing-field polarizations. Here the IR frequency is held fixed at 0.85 eV and with a beam intensity of ${\sim }$150 GW/cm${ }^2$. (c) OD line-outs at $\tau \,{=}\,{-}30$ fs corresponding to panels (a) and (b). When the XUV and IR polarizations are perpendicular to each other (blue line), fewer AIP branches are observed in comparison to the parallel case (red line)

We attribute this difference in polaritonic structure to the ${{ }^1P^o}-{{ }^1S^e}$ coupling vanishing in the case of perpendicular polarization. Indeed, if we take the polarization of the XUV pulse to define the quantization axis, $\hat {z}$, then the exchange of an IR photon can only take place between states whose magnetic quantum number $m_\ell$ differ by $\pm 1$. The absorption of an XUV photon from the ground state, populates ${ }^1P^o$ states with $m_\ell =0$, which are coupled, by means of one-photon transitions, only to the ${ }^1D^e$ states with $m=\pm 1$ (there are no metastable ${ }^1P^e$ states in the energy region under consideration). Figure 5a shows a renormalized basis consisting of the 4p, 3d, and 5s states, and Fig. 5b pertains to only 4p and 3d states. This comparison demonstrates yet another form of optical control, one which allows the selection of polaritonic branches.

5 Concluding Remarks

Tunable ATA provides unique insight into the effects the frequency, intensity, and time-delay of a dressing field have on the creation and evolution of AIPs multiplets. Our observations suggest a dynamic control over the AIPs by the laser field, and demonstrate stabilization of the autoionizing states. We used the polarization of IR field as another parameter to control the electron couplings, which in turn determines the number of polaritonic branches observed in our data. In conclusion, the light-induced stabilization and branching of metastable states offers new opportunities for coherent control in the continuum.