Observation and Control of Laser-Enabled Auger Decay

TL;DR

This paper reports the first experimental observation of single photon laser enabled Auger decay (spLEAD) in neon, demonstrating control over electron emission and highlighting its potential for probing electron correlation and ultrafast dynamics.

Contribution

It provides the first experimental evidence of spLEAD and shows how phase-controlled bichromatic laser pulses can manipulate electron emission patterns.

Findings

Successful detection of spLEAD in neon

Coherent control of electron angular distribution

Potential for probing electron correlation in complex systems

Abstract

Single photon laser enabled Auger decay (spLEAD) has been redicted theoretically [Phys. Rev. Lett. 111, 083004 (2013)] and here we report its first experimental observation in neon. Using coherent, bichromatic free-electron laser pulses, we have detected the process and coherently controlled the angular distribution of the emitted electrons by varying the phase difference between the two laser fields. Since spLEAD is highly sensitive to electron correlation, this is a promising method for probing both correlation and ultrafast hole migration in more complex systems.

Figures

Equations

$$2s^{1}2p^6+\omega \to 2s^{2}2p^4{(}^{1}S{,}^{1}D)+{\mathrm{e}}^{-}.$$

$$2s^{2}2p^5+\omega \to 2s^{1}2p^6,$$

$$2s^{2}2p^5+2\omega \to 2s^{2}2p^4{(}^{1}S{,}^{1}D{,}^{3}P)+{\mathrm{e}}^{-}.$$

$$2s^{2}2p^5+\omega +\omega$$

$$\to 2s^{2}2p^4{(}^{1}S{,}^{1}D)+{\mathrm{e}}^{-}.$$

$$I(\theta ,\varphi )\propto {\left|Y_{20}(\theta ,\varphi )e^{i\eta }+\sqrt{c}{Y}_{10}(\theta ,\varphi )e^{i{\delta }_{pd}}\right|}^2,$$

$$A(\eta )=\frac{\sqrt{15}}{4}\frac{\sqrt{c}}{1+c}\cos (\eta -{\delta }_{pd}).$$

$$2s^{2}2p^6+\omega \to 2s^{2}2p^5+{\mathrm{e}}^{-},$$

$$2s^{2}2p^6+2\omega \to 2s^{2}2p^5+{\mathrm{e}}^{-},$$

$$2s^{2}2p^6+2\omega \to 2s^{1}2p^6+{\mathrm{e}}^{-}.$$

$$2s^{1}2p^6+2\omega \to 2s^{1}2p^5{(}^{1,3}P)+{\mathrm{e}}^{-}$$

$$M({\nu }_f,{\nu }_0;l_n)=\left\{\sum _{{\epsilon }_{{\nu }_n}<0}+{\int }_0^{\infty }d{\epsilon }_{{\nu }_n}\right\}\frac{d_{{\nu }_f{\nu }_n}(\omega )D_{{\nu }_n{\nu }_0}}{{\omega }_{n0}-\omega -i\delta }.$$

Full text

When isolated atoms or molecules are excited, they relax to their ground state in two ways: via nuclear motion or electronically, and two possible ways of releasing electronic energy are by radiation and by Auger decay. The Auger process 1 ; 2 first reported by Lise Meitner, has played an important part in modern physics, particularly surface science, because it is by far the strongest decay channel for core holes of light elements such as carbon, nitrogen and oxygen. However, for ionization of some inner valence levels of atoms and molecules, the Auger process is energetically forbidden, because the energy of the doubly ionized final state is higher than the energy of the initial ion.

It was predicted some time ago that such states could decay by the novel process of Interatomic/Intermolecular Coulombic Decay (ICD) 3 , if the excited or ionized species was weakly bound to its environment. In this process, the final state of the system contains two positive charges, but the charge is distributed between the original atom or molecule and its neighbor, thus lowering the energy because the Coulomb repulsion between the charges is reduced. This prediction led subsequently to intense research activity, with many new discoveries reported, as it was found that ICD and its variants could occur in many different ways Jahnke2010 ; Mucke2010 ; Gokhberg2014 ; Trinter2014 ; Stumpf2016 ; You2016 .

Another recently reported exotic electronic decay process is Laser Enabled Auger Decay (LEAD) Ranitovic2011 . Like ICD, LEAD is a new decay mode of excited states, and both mechanisms depend on the environment of the atom or molecule: in one case neighboring neutral atoms or molecules, and in the second case, the surrounding photon field. LEAD was observed for $3s$ ionized argon which normally decays by fluorescence Ranitovic2011 . In the presence of a strong infrared field, the ion can absorb multiple photons and decay to a doubly $3p$ ionized state. Another class of LEAD, single photon LEAD (spLEAD), has been theoretically predicted Cooper2013 but so far has never been observed. Because spLEAD relies on electron correlations, it can potentially provide novel information such as correlation-induced ultrafast hole migration in molecules Cooper2013 ; Calegari2014 ; Kraus2015 .

In this work, we report the first observation of spLEAD, and moreover we show that the emission can be coherently controlled. The process itself can be viewed as a control of the decay of the ion by the laser field. With coherent control, we also manipulate the angular distribution of the emitted Auger electrons using the relative phase of the ionizing and enabling laser beams.

The processes studied are illustrated graphically in Fig. 1. The spLEAD takes place for the $2s$-hole state in Ne*+*:

[TABLE]

Within LS coupling, only the ${}^{1}S$ and ${}^{1}D$ final states are allowed in spLEAD even though the $2s^{2}2p^{4}$ configuration can, in principle, couple into the ${}^{3}P$ term. This is because the $2s^{1}2p^{6}$ is in the $S$ state and the Auger electron emitted from the $2p$ orbital is in the $s$ or $d$ state before the photoabsorption step leading to spLEAD.

The $2s$-hole state is prepared by absorption of a single photon by the ionic ground state $2s^{2}2p^{5}\,{{}^{2}}P_{3/2}$ of Ne*+*:

[TABLE]

where $\omega=26.91$ eV is tuned to the energy difference between $2s^{2}2p^{5}$ and $2s^{1}2p^{6}$. In addition, we simultaneously ionize the ground state $2s^{2}2p^{5}$ of Ne*+* by the phase-locked second harmonic $2\omega$ (53.82 eV) to access all of the ${}^{1}S$, ${}^{1}D$ and ${}^{3}P$ final states, Ne2+  (Fig. 1, right):

[TABLE]

The $2s^{2}2p^{5}$ ionic states can be directly ionized by process (3), or indirectly by processes (2) and (1)  (Fig. 1, left):

[TABLE]

The key point is that the two light pulses $\omega$ and $2\omega$ are phase coherent. As a result, the two paths (3) and (4) to the same final states ${}^{1}S$ and ${}^{1}D$ interfere, but only path (3) leads to ${}^{3}P$, so no interference occurs.

To investigate the spLEAD process exhibited in Fig. 1, we chose to use the recently demonstrated capability of the FERMI light source to produce intense bichromatic radiation with controllable phase Prince2016 . We provided conditions in which there are two quantum paths to a photoelectron state with a defined linear momentum, and we coherently controlled these quantum paths. With this approach, we observed a signal proportional to the amplitude, rather than intensity, of the quantum processes. This approach brings considerable advantages when detecting a weak signal with a strong background Gunawardena_Elliott .

We illustrate here how the spLEAD emission can be coherently controlled and detected in the photoelectron angular distribution (PAD), using that of the ${}^{1}S$ final state as an example. Process (4) emits a $p$ wave electron while process (3) is assumed to emit mainly a $d$ wave electron, by the Fano propensity rule PhysRevA.32.617 . The angular distribution can then be written as:

[TABLE]

where $Y_{nl}(\theta,\phi)$ denote spherical harmonics, and $c(\ll 1)$ is proportional to the intensity of the spLEAD path (4) relative to the direct photoionization (3), $\delta_{pd}$ is their phase difference, and $\eta$ is the $\omega-2\omega$ relative phase. Note that the relative intensity enters the equation as the term $\sqrt{c}$, that is, as the relative amplitudes of the two coherent beams. Then the asymmetry of the electron emission, defined as the difference between the emission in one hemisphere ($0<\theta<\pi/2$) and the other ($\pi/2<\theta<\pi$), divided by the sum, is expressed as

[TABLE]

This oscillates as a function of the relative phase $\eta$ between the two harmonics, and its amplitude is approximately $\sqrt{c}(\gg c)$ instead of $c$.

The experiment was performed at the Low Density Matter beamline Lyamaev of FERMI. The sample consisted of a mixture of neon and helium (for calibration purposes) and was exposed to a bichromatic beam of temporally overlapping first and second harmonic radiation with controlled phase relationship Prince2016 . In the present experiment, the FEL fundamental wavelength was generated by tuning the sixth undulator of the radiator to the 5th harmonic of the seed wavelength (230.4 nm). The second harmonic of the FEL was generated by tuning the first five undulators to the 10th harmonic of the seed, giving rise to bichromatic phase-locked pulses. The photon energies were $\omega=26.91$ eV and $2\omega=53.82$ eV; where $\omega$, as stated, was equal to the difference in energy between the $2s^{2}2p^{5}$ and $2s^{1}2p^{6}$ Ne*+* ionic states (see Fig. 1). The light was focused to a spot size of approximately 5 $\mu$m FWHM. The calculated pulse durations were 75 fs for the first and 60 fs for the second harmonic.

Under the above conditions, the kinetic energies of the photoelectrons emitted by the fundamental $\omega=26.91$ eV (from the $2p$ sub-shell) and by the second harmonic $2\omega=53.82$ eV (from the $2s$ sub-shell) are identical. Furthermore, similar ionization rates of $2p$ by the fundamental ($\omega$) and 2s by the second harmonic ($2\omega$) were set. Single ionization generates our sample, which is a mixture of $2s^{2}2p^{5}$ and $2s^{1}2p^{6}$ Ne*+* ions formed by three different processes: $2p$ ionization by $\omega$:

[TABLE]

$2p$ ionization by $2\omega$:

[TABLE]

and $2s$ ionization by $2\omega$:

[TABLE]

These ionic states, which are our target initial states of processes (1)-(4), are independent and have no quantum phase relationship.

The Ne-He mixture was introduced into the experimental chamber using a pulsed valve (Parker model 9, convergent-to-cylindrical nozzle with flat aperture of 250 micron diameter) at room temperature. Helium was added as a calibrant and as a cross-check for spurious artefacts. The electron spectra were measured using a velocity map imaging (VMI) spectrometer, and the spectra reconstructed from the raw data using the pBASEX algorithm Garcia2004 .

The spectrum (at fixed relative phase) is shown in Fig. 2, together with the line assignments. Several features are present in the spectrum, of which the most prominent are the single-photon emission of $2p$ and $2s$ electrons at 5.3 eV (by $\omega$ and $2\omega$ respectively; the photoelectrons have the same kinetic energy), single photon ionization of $2p$ by $2\omega$ (32.2 eV), and emission corresponding to doubly ionized Ne2+ final states ${}^{1}S$, ${}^{1}D$ and ${}^{3}P$.

In principle, spLEAD may be observed directly as an increase in the photoelectron yield of the ${}^{1}S$ and ${}^{1}D$ final states when the $\omega$ field is applied, Eq. 4. However, the increase ($\sim 0.05\%$ in the present case from the estimation described below) is too small. Indeed, within experimental error, the intensities of the 1S and 1D peaks in Fig. 2 did not change when the first harmonic was added. In the PAD, however, we observed an oscillation of the asymmetry $A(\eta)$ as a function of phase difference between the harmonics, see Fig. 3. Note that the zero of the relative phase is not absolute, but has an arbitrary offset. We observe strong modulation of the $2p$4 ${}^{1}S$ and ${}^{1}D$ states as a function of phase, while the ${}^{3}P$ state shows much weaker or negligible modulation. The helium and neon single ionization peaks show no effect, as expected. The oscillation in the PADs indicates that indeed the final states can be reached from an initial state by more than one pathway, and that these pathways are coherent.

We note that our measurement belongs to the Brumer-Shapiro class of bichromatic experiments. In such experiments, the phase-locked first and second harmonics create two quantum paths for the emission of a photoelectron of given momentum, causing interference Brumer_Shapiro , for example, by single-photon and two-photon ionization of the same electron state. The conditions we have chosen also set up interference, but in a quite different way from the usual Brumer-Shapiro approach. Here the interference appears as a phase dependent asymmetry of the PADs as given by Eq. (6).

In order to confirm that the observed oscillations stem from coherently controlled spLEAD, we estimate the amplitudes for the oscillation of $A(\eta)$ in Fig. 3. We use the experimental conditions captured in the photoelectron spectra in Fig. 2, and the calculated spLEAD cross section. From the spectrum in which only the second harmonic was present (dashed blue curve in Fig. 2), we extract the intensities of the photoelectron peaks corresponding to processes (3), (8) and (9), as well as the following process:

[TABLE]

with electron kinetic energies of 3.85 eV (${{}^{1}}P$) and 14.4 eV (${{}^{3}}P$). In ion spectra (data not shown), the ratio of ${\rm Ne}^{+}/{\rm Ne}^{2+}$ was found to be 3.85. This was combined with the known photoionization cross sections [6.7, 6.8, and 0.3 Mb for (3), (8), and (9), respectively, and estimated cross section of 6.8 Mb for (10)], to give an estimate of the intensity of $2\omega$ of $2.0\times 10^{13}$ W/cm2. This was done by solving the rate equations and taking account of the pulse duration and the spot size given above; Gaussian temporal and spatial profiles were used. From the spectrum (continuous red curve in Fig. 2), where fundamental radiation $\omega$ was added without altering the intensity of $2\omega$, we again extract photoelectron intensities including that for process (7). From the intensity ratios of photoelectrons of processes (7)-(9) and known cross sections for these processes [8.4 Mb for (7)], we estimate the intensity ratio between $\omega$ and $2\omega$ to be 1:52, and hence, the intensity of $\omega$ to be $3.8\times 10^{11}$ W/cm2.

Furthermore, as can be seen in Fig. 2, the addition of $\omega$ leads to a significant enhancement of the overlapping peak of $2p$ and $2s$ photoelectrons for the processes (7) and (9) respectively, and of the intensity for the process (10). These observations clearly illustrate that the fundamental radiation $\omega$ indeed enhances the population of $2s^{1}2p^{6}$ via the $2s$-$2p$ hole coupling Eq. (2). From the magnitude of the enhancement of the photoelectron peak arising from the process (10), relative to the photoelectron peak intensities of the processes (7) and (8), we estimate the effective probability of process (2) to be 0.065.

The amplitude for the oscillation of $A(\eta)$ in Fq. (6) is equal to the amplitude of the spLEAD process (4) relative to the direct ionization process (2), i.e. $\HF\sqrt{c}$ in Eq. (5); both follow practically the same first step ionization dominated by process (8). The only missing parameter needed to estimate $\sqrt{c}$ is therefore the amplitude of the spLEAD process (1). The estimate of $\sqrt{c}$ employing the spLEAD cross section reported in the literature Cooper2013 , however, resulted in $\sqrt{c}\HF 0.001$, roughly one order smaller than the present observation $\sqrt{c}\HF 0.02$. Our own calculations including only the static correlations (i.e. configuration mixing in $2s$1$2sp$6 2$S$1/2) are in good agreement with the literature value. We thus extended the calculations to include the dynamic correlations (continuum-continuum coupling) using the the following expression:

[TABLE]

Here $\nu_{0}$ is the initial $2s$ state, $\nu_{n}$ is an intermediate state $2p^{4}n\ell$ or $2p^{4}\varepsilon\ell$, $\ell=0,2$ and $\nu_{f}$ is the $\epsilon p$ or $f$ final state, $\omega_{n0}$ is the energy difference between the intermediate and initial state. The Auger decay matrix element $D_{\nu_{n}\nu_{0}}(\omega_{j})$ is calculated using the computer code described in Amusia1997 . The discrete sum in this equation is equivalent to inclusion of the static correlation in Cooper2013 . The dipole matrix elements $d_{\nu_{f}\nu_{n}}$ for the continuum-continuum transitions are singular. Their integration is handled using the numerical recipe Korol1993

The oscillation amplitudes calculated using these estimates are 0.82% for the ${}^{1}S$ peak and 1.4% for ${}^{1}D$, in rough agreement with our observation, 2.40 $\pm$ 0.34% for ${}^{1}S$ and 2.33 $\pm$ 0.18% for ${}^{1}D$. The discrepancy may stem from the experimental uncertainties and theoretical approximations involved. Note that here, unlike in Eqs. (5) and (6), more exact treatments, with inclusion of the weaker $s$ wave for process (3) and taking account of the ${}^{1}D$ final state, are used. The observed oscillations of the ${}^{1}S$ and ${}^{1}D$ asymmetry show a phase difference of 0.36$\pm$ 0.14 rad, in qualitative agreement with the predictions of theory, but significantly smmaller than the calculated value of 1.27 rad. The discrepancy is most likely due to the limits of the accuracy with which relative phases and matrix elements can be calculated.

In summary, we have shown how the technique of coherent control can be applied to observe a new phenomenon, spLEAD, which for the present case of neon is too weak to be observed directly as an intensity enhancement. We detected the process by using a method which depends on amplitude rather than intensity. Furthermore, we manipulated the outcome of the ionization process, in terms of the emission direction of the photoelectrons. Cooper and Averbukh Cooper2013 calculated that oxygen $2s$ holes of glycine have a far higher cross-section for spLEAD, implying detection is much easier. Our results suggest that spLEAD may be observable as an increase in cross-section for molecules containing oxygen, which includes many biomolecules. Noting that sudden creation of the O $2s$ hole causes ultrafast charge dynamics, our work shows the way to investigating charge dynamics not only by the pump-probe methods proposed by Cooper and Averbukh Cooper2013 , but also by the sophisticated methods of coherent control. The complex and ultrafast dynamics of inner-valence hole wavepackets, or electron correlations, may now be investigated and coherently controlled by using the coherence of bichromatic light with resolution of a few attoseconds.

Acknowledgments

This work was supported in part by the X-ray Free Electron Laser Utilization Research Project and the X-ray Free Electron Laser Priority Strategy Program of the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT) and IMRAM program of Tohoku University, and Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials program. K.L.I. gratefully acknowledges support by the Cooperative Research Program of “Network Joint Research Center for Materials and Devices (Japan)”, Grant-in-Aid for Scientific Research (No. 25286064, 26600111, and 16H03881) from MEXT, the Photon Frontier Network Program of MEXT, the Center of Innovation Program from the Japan Science and Technology Agency, JST, and CREST (Grant No. JPMJCR15N1), JST. We acknowledge the support of the Alexander von Humboldt Foundation (Project Tirinto), the Italian Ministry of Research (Project FIRB No. RBID08CRXK and PRIN 2010ERFKXL_006), the bilateral project CNR-JSPS “Ultrafast science with extreme ultraviolet Free Electron Lasers”, and funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 641789 MEDEA (Molecular Electron Dynamics investigated by IntensE Fields and Attosecond Pulses). We thank the machine physicists of FERMI for making this experiment possible by their excellent work in providing high quality FEL light.