Direct observation of a Feshbach resonance by coincidence detection of ions and electrons in Penning ionization collisions

Observation of molecular dynamics with quantum state resolution is one of the major challenges in chemical physics. Complete characterization of collision dynamics leads to the microscopic understanding and unraveling of different quantum phenomena such as scattering resonances. Here we present an experimental approach for observing molecular dynamics involving neutral particles and ions that is capable of providing state-to-state mapping of the dynamics. We use Penning ionization reaction between argon and metastable helium to generate argon ion and ground state helium atom pairs at separation of several angstroms. The energy of an ejected electron carries the information about the initial electronic state of an ion. The coincidence detection of ionic products provides a state resolved description of the post-ionization ion-neutral dynamics. We demonstrate that correlation between the electron and ion energy spectra enables us to directly observe the spin-orbit excited Feshbach resonance state of HeAr+. We measure the lifetime of the quasi-bound HeAr+ A2 state and discuss possible applications of our method.

T he outcome of atomic and molecular collisions is governed by the details of the intermolecular interactions. In some cases, these can be accurately predicted and calculated by state-of-the-art quantum theory. In other instances, experiments serve as a direct probe of interactions. Starting with the pioneering work of Lee and Herschbach 1 , gas phase collisions using adiabatically cooled molecular beams have become a central tool in chemical physics, allowing one to prepare reactants with a well-defined quantum state and collision energy 2 . A complete state resolved detection of all reaction products, however is difficult in current experiments. Only recently Gao et al. 3 reported a fully resolved detection of rotational excitation in bimolecular collisions. The latest advances in molecular beams studies now enable performing precise experiments reaching collision energies as low as 10 mK, and the observation of different quantum phenomena such as scattering resonances 4 , the quantum isotope effect 5 , stereodynamics of chemi-ionization reaction 6 , and the prominent effect of the internal molecular structure on dynamics at low collision energies 7,8 .
Collisions are not the only option for observing molecular dynamics. A molecule can be excited into a nonstationary state in femtosecond transition-state spectroscopy where dynamical information can be recovered from a time-resolved spectroscopy of dissociation fragments 9 . A nonstationary state can also be reached by a sudden quench of a system onto a lower electronic energy manifold. For example, slow photoelectron velocity-map imaging 10 has been used to detect Feshbach resonances in the F + H 2 reaction by measuring the photoelectron energy spectrum of the photodetachment of the FH À 2 molecular anion 11 . Here, we present an experimental approach where ionization induced by collision between excited noble gas and a neutral particle is used to initiate dynamics between ions and noble gas atoms. We show that such a method is capable of quantum state-to-state resolution. Other experimental approaches for probing ion-neutral dynamics include crossed beam studies of a neutral and ionic beams 12,13 , collisions within the orbit of the Rydberg electron 14,15 , and the co-trapping of ions and atoms 16 . During Penning ionization (PI) reaction, sudden ionization of the neutral system takes place with the ejected electron serving as an indicator of the initial ionic quantum state 17 . Following the interaction with the noble gas atom, Penning ions carry information about the final distribution of states. Therefore, the correlation between energy distributions of Penning electrons and Penning ions serves as a state-to-state mapping of the postionization ion-neutral dynamics.
A crucial part in our experiment is the coincidence detection of the momenta of PI charged products. This allows us to detect ion-electron pairs that originate from the same collision event. Coincidence detection of ionization fragments enabled many groundbreaking experiments including observation of the Efimov state of He trimer 18 , determination of chirality of molecules 19 , and other experiments providing the insight the dynamic of photoionization [20][21][22][23] . Many experiments reported separate measurement of electron and ion energy spectrum for several PI systems 17,24 . However, without the correlation, electron energy provides information only about the initial state of the PI ion. As such, it is similar to photoionization spectra and does not necessarily carry additional information. In contrast, the ion energy spectrum does provide information about nuclear dynamics; however, it is always averaged over many initial states that are occupied during the PI process. The correlation is critical in resolving nuclear dynamics for a single initial state. Interestingly, this allows us to achieve quantum state-to-state resolution without any initial state preparation step that requires single quantum level control.
As a first application of our method, we demonstrate a direct detection of Feshbach HeAr + molecule that dissociates on a microsecond timescale due to the spin-orbit coupling. In future, we plan to apply this method to investigate post-PI nuclear dynamics between vibrationally excited H þ 2 molecular ion and helium atom. We will be able to observe state-to-state inelastic processes as well as reactive collisions leading to the formation of HeH + molecule.

Results
Dynamics of PI. As a first demonstration of our approach, we study the PI and associative ionization (AI) channels of the collision between metastable helium and neutral argon A schematic of the relevant potential curves together with calculated wave functions is presented in Fig. 1. The ionization process is described by the projection of the incoming wave function weighted by the square root of the autoionization width Γ(R) on one of the three possible ion-neutral potential surfaces, which are asymptotically separated on energy scale by the spin-orbit interaction energy of Ar + (ΔE SO = 0.178 eV). The energy of the ejected electron corresponds to the difference between the neutral and ionic potential curves 25 ; therefore, information about the formation of a particular state is manifested in the electron energy distribution E(e − ). The projection on the manifold of ionic states may result in a Ar + product (PI), or a HeAr + product (AI). However, a molecular ion generated in the electronically excited A 2 state (Ψ b ) may decay via a Feshbach resonance 26,27 to the continuum of the electronic ground X state (Ψ f ). As a result of the predissociation, the free Ar ion and neutral He acquire kinetic energy on the order of ΔE SO . The kinetic energy distribution of Ar + (E(atoms)) consists of low kinetic energy ions resulting from the direct PI reaction and high kinetic energy ions resulting from the predissociation process. In the following section, we present how the correlation between E(e − ) and E(atoms) provides the observation of the process, by relating the high kinetic energy argon ions to a specific electron energy.
Observation of the scattering resonance. For the purpose of this study we designed and constructed a coincidence double velocitymap imaging (CDVMI) apparatus. A schematic of the setup is presented in Fig. 2. The 2D velocity distribution and the time-offlight (TOF) of ions and electrons are obtained by a two-sided VMI 28 spectrometer. Coincidence ion-electron pairs for a specific ion mass were selected by their TOF (cf. Methods) and their arrival positions were identified by correlation between optical brightness and electronic signal magnitude 29 . Mass-specific VMI images of ions and corresponding electrons are produced with complete mapping between the images.
Mass-selected VMI images of Ar + , HeAr + , and coincidence electrons are presented in Fig. 3. The VMI image of Ar + consists of a central feature that presents low kinetic energy, forwardscattered Ar + produced directly by PI, and a circular feature related to high kinetic energy Ar + , with a velocity magnitude centered at 269 m/s with a width of 16 m/s (all widths reported in this manuscript refer to half width at half maximum of a Gaussian distribution). The velocity magnitude of high kinetic energy Ar + corresponds to a kinetic energy of 0.164 ± 0.019 eV, which is partitioned between Ar + and neutral He. For HeAr + , the ionic VMI image consists of a single central feature at a center-ofmass velocity with an width of 19 and 13 m/s in longitudinal and transverse directions.
The complete mapping between the ionic and the electronic VMI images enables the reconstruction of electronic VMI images   38,39 . Ψ in represents the incoming wave function with wave number matching an energy of k B × 220 K. Ψ b represents the first excited vibrational level of HeAr + at the A 2 electronic state. Ψ f represents the scattering state wave function of the X state that couples to Ψ b . Ψ sc represents the scattering state wave function of the X state with maximal overlap with ffiffiffi Γ p Á Ψ in . E(e − ) represents energy distribution of ejected electrons and E(atoms) represents the energy distributed between He and Ar + ( 2 P 3/2 ). All wave functions were calculated using discrete variable representation 40 , the resonance width Γ(R) is taken from ref. 41   corresponding to a given range of ionic radial velocities. Energy distribution of electrons was obtained by inversion of the rotated electron VMI images using MEVELER 30 (cf. Methods). The electron energy distributions related to low and high kinetic energy Ar ions are presented in Fig. 4 as blue and red curves. The electron energy distribution related to low kinetic energy Ar ions contains two main peaks at 3.89 and 4.06 eV arising from the ionization of Ar by He * ( 3 S). The two smaller peaks at around 4.87 and 4.69 eV correspond to ionization of Ar by He * ( 1 S). The electron energy distribution related to high kinetic energy Ar ions presents a clear preference for electron energies that pinpoints the origin of those ions as the A 2 electronic state. The observed additional kinetic energy of~0.164 eV is gained by resonantly decaying from the quasi-bound A 2 state to the free particle Ar + ( 2 P 3/2 ) + He state as illustrated in Fig. 1.
The complementary dynamical picture is given by inspection of the AI channel. The electron energy distribution for electrons related to HeAr + is presented in Fig. 4 (green curve) and shows clear preference for electron energies representing the formation of molecular ions at the X and A 1 states. Any quasi-bound state formed upon ionization at the electronic A 2 state dissociates with a lifetime much shorter than the particle TOF, and therefore is undetected as a molecular ion.
Free argon ions that originate from the dissociation of the quasi-bound HeAr + A 2 state spend a fraction of their trajectory as a particle with increased mass, which results in a finite addition to their TOF. The lifetime of the quasi-bound A 2 state can be extracted from the TOF of related ions using where t b is the absolute TOF of the quasi-bound HeAr + in the A 2 state before dissociation, ΔTOF is the addition to the ions TOF relative to the center TOF peak of Ar + , and m Ar m HeAr is the mass ratio.     given by the lack of Feshbach ions in previous studies of Ne * + Ar PI reaction due to the long lifetime of the quasi-bound NeAr + A 2 state 31,32 .
In conclusion, we have presented an experimental method that provided a state resolved description of ion-neutral dynamics. For the HeAr + system, this enabled the observation of a Feshbach resonance identified as the predissociation of the HeAr + A 2 molecular state. Although the kinetic energy distributions of He * + Ar PI products were obtained in previous experiments 31,33,34 , the lack of correlation between ionic and electronic data left the details of the postionization dynamics completely hidden. Coincidence detection of ions and electrons provides the mapping between initial and final states and enables the direct observation of the scattering resonance.
Our approach may be generalized to any ion-neutral system accessible via PI reaction. Specifically, study of PI of molecules, where rovibrational degrees of freedom span the manifold of ionneutral potential curves, may pave the way to a multitude of possible experiments studying state-to-state inelastic and reactive collisions between molecular ions and neutral atoms. Specifically, the study of PI ionization of hydrogen molecule by metstable helium will enable the observation of state-to-state collisional quenching of vibrationally excited H þ 2 and state-to-state reactive H þ 2 + He collisions leading to the formation of HeH + .

Methods
Experimental setup. A pulsed supersonic beam of a 50/50% mixture of argon and helium was created by an Even-Lavie (EL) valve 35  Data analysis and coincidence. For every valve shot, the acquired experimental data included ions and electrons arrival times and amplitude of electronic signal as measured on the MCP back plate, arrival position, and the magnitude of the optical signal as obtained from the recorded images of the phosphorus detector. The mass distribution of detected ions was obtained by plotting a histogram of their TOF (cf. Mass spectrum). The obtained mass spectrum provides the limits of ion-electron TOF difference that are used for identification of coincidence in certain mass-tocharge ratio ion-electron pairs. Coincidence by TOF is possible in our experiment due to the narrow spread in the TOF for a given ion mas-to-charge ratio (~0.01 μs) relative to the large overlap in time between the reactant beams (~30 μs). Once an ion-electron pair is identified by TOF, the related ion and electron arrival positions are selected from the measured optical signals based on the correlation between optical phosphorus detector brightness and amplitude of electronic MCP signal 29 . The resulted mass-selected coincidence VMI images of ions and electrons are shown in Fig 3. The ratio between camera pixels and velocity on the ionic VMI images was found by examining the shift in position of center-of-mass velocity for a variety of single beam Ar-He gas mixtures.
Mass spectrum. TOF distribution of detected ions is presented at Fig. 6. We observe two main peaks at TOF of 9.2 and 9.6 μs that correspond to Ar + and HeAr + accordingly. CDVMI performs as a mass spectrometer with a resolving power (FWHM) of m Δm ¼ 1000 for Ar and m Δm ¼ 1500 for HeAr. The use of CDVMI as a mass spectrometer may be applied to any sample containing atoms and molecules with ionization energy smaller then excitation energy of the metastable atom.
Electron energy distributions. Information about energy distribution of electrons requires the inversion of the 2D velocity distribution (Fig. 3b, e) to a 3D velocity distribution 37 . Since any inversion method requires an axis of cylindrical symmetry, the electron images were rotated to the ionic frame of reference (Fig. 3c, f). We attribute the anisotropy of the electron VMI images to a nonuniform collection efficiency, resulting from the mismatch of beams overlap position relative to the VMI orifice. Electron energy distributions presented in Fig. 4 were obtained by inversion of rotated electron VMI images using MEVELER 30 . The resulted velocity magnitude distribution was scaled to energy scale by the known energy difference between metastable states of He.

Data availability
All relevant data are available from the authors upon reasonable request.