Session X11: V: Ultrafast Photoionization and Imaging

Relativistic and Quadrupole Effects in Photoionization Time Delay in Atoms

Eisenberg-Wigner-Smith (EWS) time delay [1] in atomic photoionization is sensitive to the dynamics of atomic electrons on the attosecond time scale, the natural time scale of atomic electron motion [2].  Time delay generally has an angular dependence and calculations have been performed including only dipole transitions [3,4].  In the nonrelativistic dipole approximation, the time delay for atomic ns-states does not depend upon angle; inclusion of  relativistic effects of spin-flip transitions and nondipole (quadrupole) effects renders the time-delay angle-dependent. Since the amplitude for the dominant dipole photoionization channel (without spin-flip) vanishes at certain angles as a result of angular momentum geometry, quadrupole and spin-flip transitions dominate; specifically, where the dipole amplitude vanishes, the time delay is a combination of spin-flip dipole and quadrupole photoionization time delay, and the attosecond dynamics of these channels can be investigated.  Relativistic expressions have been derived showing where quadrupole and/or spin-flip channels determine the time delay.  Relativistic random phase approximation (RRPA) [5] calculations for the angular dependance of time delay of ns-subshells of noble gas atoms for the angular distribution of time delay including both dipole and quadrupole channels have been studied and the phenomenology is demonstrated. [1]  E. P. Wigner, Phys. Rev. 98, 145 (1955); [2] R. Pazourek, S. Nagele and J. Burgdörfer, Rev. Mod. Phys. 87, 765 (2015); [3] J. Wätzel, et al,  J. Phys. B 48, 025602 (2015); [4] A. Mandal, et al, Phys. Rev. A 96, 053407 (2017); [5] W. R. Johnson and C. D. Lin, Phys. Rev. A 20, 964 (1979).   

ASTRA: a scalable wave-function approach to the photoionization of polyatomic molecules

Ultrafast laser technologies keep extending the intensity and frequency of attosecond pulses [1,2]. In molecules, these pulses excite coherent ionization wavepackets that require a correlated wave-function approach to accurately describe their evolution. We present several ionization observables for diatomic (nitrogen and carbon monoxide) and polyatomic (formaldehyde and ethylene) molecules, computed with the ASTRA suite of codes [3]. ASTRA implements a new approach to the close-coupling representation of the molecular electronic continuum based on high-order transition density matrices (TDM) between correlated ionic states with arbitrary multiplicity, obtained with an extension of LUCIA, a general large-scale configuration-interaction code [4], and on hybrid Gaussian-B-spline integrals [5], where the latter can be extended to reach quantization boxes of hundreds atomic units. Total and partial photoionization cross sections together with photoelectron angular distributions compare well with established benchmarks [6,7]. The efficient spin-string formalism of TDM's algorithms in LUCIA [8] makes ASTRA scale favorably with molecular size, thus opening the way to study correlated dynamics in complex molecules. This work is supported by the DOE CAREER grant No. DE-SC0020311. Part of the calculations used NERSC resources under the contract No. DE-AC02-05CH11231 and the award BES-ERCAP0024720.

[1] Duris J et al, Nat. Phot. 14, 30 (2020)

[2] Saito N et al, Optica 6, 1542 (2019)

[3] Randazzo J M et al, arXiv:2211.10316 [physics.atom-ph] (2022).

[4] Olsen J et al, JCP 104, 8007 (1996)

[5] Masin Z et al, CPC 249, 107092 (2020)

[6] Klinker M et al, JPCL 9, 756 (2018)

[7] Cacelli I et al, CPC 347, 261 (2001)

[8] Olsen J et al, JCP 89, 2185 (1988)   

ITVOLT: An Iterative Solver for the Time-Dependent Schrödinger Equation

Solutions to the time-dependent Schrödinger equation (TDSE) are important for understanding a variety of phenomena in atomic and molecular physics, yet many common numerical approaches struggle to achieve both accuracy and efficiency on the problem. Motivated by this gap, we have developed a new approach that solves the TDSE via an equivalent Volterra integral equation. By applying a Lagrange interpolation of the integrand, our approach converts the Volterra integral equation to a linear system, which is then solved iteratively. The resulting method, which we call ITerative VOLTerra propagator (ITVOLT), is relatively simple to implement, but capable of solving the TDSE over large step sizes and with high accuracy. In this talk, we derive the method, explore its numerical details, and demonstrate with a few examples that it is capable of outperforming more standard approaches such as the short-iterative Lanczos and fourth-order Runge-Kutta (RK4).  While more complex problems require further exploration, we suggest that ITVOLT be considered as a new, front line computational tool for researchers in atomic, molecular, and optical physics.   

Withdrawn

Ionization and the resulting sample bleaching is regarded as detrimental for X-ray imaging. The X-ray scattering signal generally decreases as electrons are removed from the parent ion, a process which ultimately limits the quality of X-ray images. However, in this study we find that ionization can create short-lived electronic states which are beneficial for imaging and increase the scattering cross section compared to the neutral atom. We compared snapshots from individual 100 nm Xe nanoparticles as a function of the X-ray pulse duration and incoming X-ray intensity in the vicinity of the Xe M-shell resonance. Surprisingly, images recorded with few femtosecond and sub-femtosecond pulses are up to 10 times brighter than the static linear model predicts. Our Monte-Carlo simulation and statistical analysis of the entire data set confirms these findings and attributes the effect to transient resonances. Our simulations suggest that the scattering cross section may increase by several orders of magnitude when targeting specific resonances. Our study guides the way towards CDI with unprecedented combination of spatial and temporal resolution at the nanoscale.   

Ultrafast 3D X-Ray Fluorescence Imaging

Coherent diffraction imaging with X-ray free-electron lasers (FELs) combines high spatial and temporal resolutions, but is limited to forward scattering and thus, 2D projections of the sample. Here, we study the potential of incoherent diffractive imaging (IDI) proposed by Classen et al. (2017) which is based on fluorescence emission from the specimen into the full solid angle.

 

Classen et al. (2017) suggested that intensity correlations calculated from X-ray fluorescence speckle patterns can be used for structure determination of the sample if the exciting FEL pulse duration is of the order of the corresponding transition lifetime. Inoue et al. (2019) and Nakamura et al. (2020) experimentally demonstrated how IDI can be utilized for FEL pulse duration measurements and FEL nanofocus characterization respectively.

 

In this contribution, we will present recent experimental IDI data recorded using sub-femtosecond FEL pulses available at SLAC/LCLS from thin metal samples. We reproduce the findings of Inoue et al. and Nakamura et al. for X-ray pulse duration measurements and nanofocus characterization. Furthermore, we present evidence confirming the 3D structure determination capabilities of IDI.   

Relativistic and correlation effects in np photoionization Cooper minimum of high-Z atoms

When the initial bound state radial function involved in the photoionizing transition has a node, the photoionization often passes through a zero, or near-zero, that leaves imprints on photoionization parameters like cross section, angular distribution asymmetry parameter, phase shift and time delay. This minimum is well-known as the Cooper minimum (CM) [1,2] which is quite sensitive to relativistic and correlation effects. Earlier, the CM for the 6p subshell were studied for high-Z atoms up to Z=100 using uncorrelated nonrelativistic Dirac-Slater central-field wave functions [3,4].  The present work extends these studies up to Z=120, using the correlated relativistic random phase approximation (RRPA) [5] and the Dirac-Fock independent particle approximation [6] for comparison; photoionization also from the 5p and 4p shells has also been examined. In particular, the atoms Rn (Z=86), Ra (Z=88), No (Z=102), Cn(Z=112), Og (Z=118), Ubn (Z=120) are investigated. Spin-orbit and interchannel coupling effects are of crucial importance to location of the CM at high Z. [1] J. W. Cooper, Phys. Rev. A, 128, 681 (1962). [2] W. R. Johnson and K. T. Cheng, Phys. Rev. A 20, 978 (1979). [3] S. T. Manson, et al, Phys. Rev. A 28 (1983). [4] P. C. Deshmukh, B. R. Tambe and S. T. Manson, Austral. J. Phys. 39, 679 (1986). [6] M. Reiher and A. Wolf, Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, 2nd Edition (Wiley-VCH, Wertheim, Germany, 2015). [5] W.R. Johnson and C.D. Lin, Phys. Rev. A 20, 964 (1979).   

The impact of nonessential states in near-resonant two-photon ionization of hydrogen

By numerically solving the three-dimensional time-dependent Schrodinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the 1s-2p transition. Due to the Rabi oscillations between the 1s and 2p states, the photoelectron energy spectrum exhibits the Autler-Townes (AT) doublet and we focus on its spectral characteristics. Developing a minimal three-level model that is fully supported by the accurate 3D TDSE simulations, we demonstrate the role of the ac Stark shifts and the nonresonant ionization pathway in the energy splitting, asymmetry and angular distribution of the lower and higher energy peaks of the AT doublet. Furthermore, we show how these spectral features can be controlled with the actual choice of the laser parameters (Phys. Rev. A 106, 063114, 2022).   

Trojan Wave Packets in the Circularly Polarized and the Magnetic Fields on the multi-layer Langmuir type $(1)$ Helium trajectories with the inter-layer polygon type change

Some time ago we have discovered the theorem stating that the number of a distinct classically rotating frozen electron configurations in the external magnetic field, the nuclear ion field and the co-rotating electric field may be at least the product of all foldings of total force surfaces (the maximal number any straight line may cut the surface which notrivially is 2) obtained by putting each of the multi-dimensional gradient component of the Zero Velocity Surface to zero. Consistently with it we have discovered a several highly symmetric configurations originated from the Langmuir type $(1)$ ``Hoop Earrings" rotating Helium-like model trajectories [1] with further small discrete rotational symmetry distortion by the Circularly Polarized electromagnetic field without the loss of its nature. Those were the multi-electron atom trajectories consisting of two or many layers of electrons moving in phase on circles with electron configurations placed at the vertexes of angles of identical by type but only scaled regular polygons parallel in space which additionally could be also symmetrically twisted between each other. Here we extend the case to the situation when the neighboring layer polygons are plane-symmetrically of a different kind. For example the hexagon in the central plane may accompany two triangles placed symmetrically one in the upper paraller plane and the other in the lower or the octagon may similarly neighbor two squares etc. The classical stabilization of the trajectories by the combination of fields further leads to the existence of non-dispersing localized Trojan-like wave packets moving around the trajectories. The time dependent Hartree simulations of such Wave Packets as well as those with the Time Dependent Quantum Diffusion Monte Carlo Method are conducted. [1] M. Kalinski, et al., Phys. Rev. Lett. {bf 95}, 103001, (2005).   

Time-resolved photo-induced dynamics of cis,cis-1,3-cyclooctadiene (COD) studied by Ultrafast Electron Diffraction

We investigated real-time photo-induced structural dynamics of a large-flexible cyclic conjugated diene molecule cis,cis-1,3-cyclooctadiene (COD), with an aim to extend the current knowledge beyond small rigid systems, such as 1,3-cyclohexadiene (CHD). We excited COD in the gas-phase with a 200 nm laser and performed measurements with the ultrafast electron diffraction set-up in the SLAC MeV-UED facility. We followed the photo-induced structural dynamics and determined photo products by a fitting-based analysis with the aid of trajectory surface hopping calculations. We found hot ground-state of COD and the electrocyclic ring closure product bicyclo[4.2.0]oct-7-ene (BCO) to be the main products. Our results indicate that most of the population reaches the ground state within a time of 200 fs and that the BCO is formed soon after the wavepacket reaches the ground state. Through comparison of the measured and calculated observables, we identified a periodic breathing motion from the hot ground-state of COD. The combination of a structurally sensitive experiment and high-level theory highlights the photochemistry and unique structural dynamics in the larger cyclic conjugated molecular system.   

Revealing multi-time quantum statistics without measurement back-action

Due to the principle of quantum mechanics that measurement disturbs a quantum state, it is a major challenge in obtaining quantum statistics, such as quantum correlation function and quasi-probability distribution. We propose an ancilla-assisted measurement scheme to detour the measurement-induced back-action, which can be applied for any multi-time measurements. With performing sequential positive operator-valued measurements at each time-point, the quantum statistics are reconstructed by weighting their outcomes differently. We employ ¹⁷¹Yb-¹³⁸Ba ions as the system-ancilla system to demonstrate the multi-time measurements without disturbing the system state, and the two- and three-time quantum correlation functions and quasi-probability distributions are reconstructed from the ancilla measurement outcomes. The marginal distribution is verified to be unaffected by the measurement at each time-point, and the nonclassical feature of the reconstructed distribution is identified by the negativity in the joint quasi-probability distribution and the violation of the Leggett-Garg inequality.