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Physical Review A

Nonadiabatic tunnel ionization of current-carrying orbitals of prealigned linear molecules in strong circularly polarized laser fields

Kunlong Liu, Ingo Barth

Published Oct 3, 2016• 30 citations
Publisher

Abstract

We derive the analytical formula of the ratio of the ionization rates of degenerate valence ${\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals of prealigned linear molecules in strong circularly polarized (CP) laser fields. Interestingly, our theory shows that the ionization ratio for molecular orbitals with opposite azimuthal quantum numbers $\ifmmode\pm\else\textpm\fi{}|m|$ (e.g., ${\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}$) is identical to that for atomic orbitals with the same $\ifmmode\pm\else\textpm\fi{}|m|$ (e.g., ${p}_{\ifmmode\pm\else\textpm\fi{}}$). In general, the electron counter-rotating to the CP laser field tunnels more easily, not only for atoms but also for linear molecules. Our theoretical predictions are then verified by numerically solving the three-dimensional time-dependent Schr\"odinger equation for the ionization of the prealigned nitric oxide (NO) molecule in strong CP laser fields. Due to the spin-orbital coupling in the electronic ground state of NO and the sensitivity of ionization to the sense of electron rotation, the ionization of NO in CP fields can produce spin-polarized photoelectrons with high controllability of spin polarization up to $100%$.

DOI
10.1103/physreva.94.043402

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We derive the analytical formula of the ratio of the ionization rates of degenerate valence \ensuremathπ\ifmmode±\else\textpm\fi{\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}\ensuremathπ\ifmmode±\else\textpm\fi​ orbitals of prealigned linear molecules in strong circularly polarized (CP) laser fields. Interestingly, our theory shows that the ionization ratio for molecular orbitals with opposite azimuthal quantum numbers \ifmmode±\else\textpm\fi∣m∣\ifmmode\pm\else\textpm\fi{}|m|\ifmmode±\else\textpm\fi∣m∣ (e.g., \ensuremathπ\ifmmode±\else\textpm\fi{\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}\ensuremathπ\ifmmode±\else\textpm\fi​) is identical to that for atomic orbitals with the same \ifmmode±\else\textpm\fi∣m∣\ifmmode\pm\else\textpm\fi{}|m|\ifmmode±\else\textpm\fi∣m∣ (e.g., p\ifmmode±\else\textpm\fi{p}_{\ifmmode\pm\else\textpm\fi{}}p\ifmmode±\else\textpm\fi​). In general, the electron counter-rotating to the CP laser field tunnels more easily, not only for atoms but also for linear molecules. Our theoretical predictions are then verified by numerically solving the three-dimensional time-dependent Schr"odinger equation for the ionization of the prealigned nitric oxide (NO) molecule in strong CP laser fields. Due to the spin-orbital coupling in the electronic ground state of NO and the sensitivity of ionization to the sense of electron rotation, the ionization of NO in CP fields can produce spin-polarized photoelectrons with high controllability of spin polarization up to 100100%100.
The ionization of the prealigned nitric oxide molecule by strong circularly polarized laser fields is studied via theoretical simulations of the spin-resolved photoelectron momentum distributions by solving numerically the three-dimensional time-dependent Schr\"odinger equation. Due to the spin-orbit entanglement in the ground state of nitric oxide and the sensitivity of the tunnel ionization of its doubly degenerate valence $2{\ensuremath{\pi}}_{\ifmmode\pm\else\textpm\fi{}}$ orbitals carrying opposite electron ring currents to the sense of the laser-field rotation, the momentum-resolved spin-polarized photoelectrons are produced. We show that the spin polarization exhibits strong dependence on the kinetic energy as well as the emitting angle of the photoelectron. In addition to the laser control, the momentum gate in strong-field experiments would enable full control of the spin polarization.
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We show that ionization of noble gas atoms by a strong infrared circularly polarized laser field under standard experimental conditions can yield electrons with up to 100% spin polarization in energy-resolved measurements. Spin polarization arises due to the interplay of the electron-core entanglement and the sensitivity of ionization in circularly polarized fields to the sense of electron rotation in the initial state.
The strong-field ionization of dimers is investigated theoretically in counter-rotating circularly polarized laser fields. By numerically solving the two-dimensional (2D) time-dependent Schrödinger equation (TDSE) with the single-electron approximation (SEA) frame, we present the photoelectron momentum distributions (PMDs) and photoelectron angular distribution (PADs) of aligned Ne and Xe dimers. It is found that the PMDs and PADs strongly depend on the time delays by counter-rotating circularly polarized laser pulses. The results can be explained by the ultrafast photoionization model and the evolution of electron wave packets for Ne and Xe dimers. Besides, We make a comparison of PMDs between Ne atom and Ne dimer.
Attosecond chronoscopy represents a major breakthrough in the study of ultrafast phenomena and has the potential to revolutionize our understanding of the fundamental physics of matter. We theoretically investigate the spin-orientation-resolved attosecond chronoscopy for the first time by the circular RABBIT technique for Kr atoms. Due to the spin-orbit interaction and the sensitivity of ionization in circularly polarized fields to the sense of electron rotation in the initial state, the spin-resolved ionization rates of photoelectrons emitted from 2P1/2^2P_{1/2}2P1/2​ and 2P3/2^2P_{3/2}2P3/2​ channels can be expressed via mmm-resolved ionization rates of initial state, where mmm is the orbital magnetic quantum number. We demonstrate that the yields difference between spin-up and spin-down photoelectrons from each channel are closely associated with the different behaviors of corresponding Wigner time delay. We find that the Wigner time delay between spin-up and spin-down photoelectrons in the polarization plane can reach several tens of attoseconds in the co-rotating geometry, but a few attoseconds in the counter-rotating geometry. Our approach opens up a new avenue for probing the spin-dependent behavior of Wigner time delay, and lays the foundation for spin-orientation-resolved attosecond chronoscopy, which can be verified by the current experimental techniques.
Based on the expansion of the time-dependent Dirac equation in the second order on the reciprocal of the speed of light, we derive a simplified second-order time-dependent Pauli equation (second-TDPE) for single-active-electron systems, in which the time-dependent spin-orbit interaction is taken into account. A numerical method is presented for calculating the observables for atoms interacting with the electric fields of laser pulses. It is shown that the energy-level splitting between the ${p}_{+}^{\ensuremath{\uparrow}}$ and ${p}_{+}^{\ensuremath{\downarrow}}$ (as well as the ${p}_{\ensuremath{-}}^{\ensuremath{\uparrow}}$ and ${p}_{\ensuremath{-}}^{\ensuremath{\downarrow}})$ orbitals can be reproduced by the spin-orbit coupling (SOC) term of the second-TDPE. By numerically solving the second-TDPE, we demonstrate the SOC effect in single-photon, multiphoton, and tunneling ionization of atomic Kr with valence ppp orbitals. In particular, a few counterintuitive strong-field ionization phenomena are discussed and analyzed. The present work provides a convenient way to explore the SOC effect in strong-field interactions.