Spatially and temporally controlling electron spin polarization in strong-field ionization using orthogonal two-color laser fields

We propose a scheme to produce spatially and temporally controlled spin-polarized photoelectrons by strong-field ionization of atoms. We calculate the momentum-resolved electron spin polarization from two spin-orbit coupled ionic states ($J=1/2$ and $J=3/2$) of krypton atoms in orthogonal two-color laser fields using the strong-field approximation, and obtain the instantaneous spin-polarization degree. With this scheme, the spin-up and -down photoelectrons can be well separated in the space, and the spin polarization is controlled on the sub-laser-cycle timescale. This study illustrates and reveals the mechanism of the generation of spin-polarized photoelectrons with an arbitrary spatially and temporally tailored laser field. We expect this work has implications for controlling the spatiotemporal spin polarization in strong-field physics.

Figure 1

The mechanism of producing spatially separated electron spin polarization in strong-field ionization using an OTC field at the phase delay of zero. (a) The illustration of the rotation senses of the OTC laser field and the $P_{+}$ and $P_{-}$ orbitals of ${}^{2}P_{1/2}$. (b) The synthesized laser electric field. During a half laser cycle, the electric field is clockwise rotating along the path of A–B–C (marked with blue arrow), and in another half cycle it is anticlockwise rotating along the path of C–B–A (marked with red arrow). (c) The distribution of the square of Clebsch-Gordan (CG) coefficients for $m_j$-resolved states of ${}^{2}P_{1/2}$ and ${}^{2}P_{3/2}$ ionic states. From left to right, $m_j=1/2,–1/2$ for ${}^{2}P_{1/2}$, and $m_j=3/2,1/2,–1/2,–3/2$ for ${}^{2}P_{3/2}$. The electron spin states are illustrated with red (up-polarized) and blue (down-polarized) colors.

Figure 2

(a,b) The calculated photoelectron subcycle momentum distributions from the $P_{-}$ and $P_{+}$ orbitals of ${}^{2}P_{1/2}$, respectively. The photoelectron probability is in logarithmic units. (c) The calculated momentum-resolved normalized yield asymmetry using the results in (a,b).

Figure 3

Simulated photoelectron momentum distributions of (a,b) ${}^{2}P_{1/2}$ and (c,d) ${}^{2}P_{3/2}$ ionic states. (a,c) and (b,d) are the results of spin-up and spin-down electrons, respectively.

Figure 4

(a,b) are the total momentum distributions of spin-up and spin-down electrons, respectively. (c) is the total momentum-resolved normalized yield asymmetry calculated with (a,b). (d) shows the $P_y$-integrated normalized yield asymmetries of the two ionic states (calculated with Fig. 3) and the total result [extracted from (c)].

Figure 5

Time-resolved spin-polarization dynamics. (a) shows the synthesized electric field and the probabilities (normalized to 0.06) of the wave packets ionized at the laser crests of A–C. (b) shows the instantaneous angular velocity of the light polarization vector. (c) shows the instantaneous spin-polarization degree of ${}^{2}P_{1/2}$ and ${}^{2}P_{3/2}$ ionic states. (d) shows the instantaneous normalized yield asymmetry of the two ionic states.