Time delay in atomic photoionization with circularly polarized light

We study time delay in atomic photoionization by circularly polarized light. By considering the Li atom in an excited $2p$ state, we demonstrate a strong time-delay asymmetry between the photoemission of the target electrons that are co- and counter-rotating with the electromagnetic field in the polarization plane. In addition, we observe the time-delay sensitivity to the polar angle of the photoelectron emission in the polarization plane. This modulation depends on the shape and duration of the electromagnetic pulse.

Figure 1

The photoelectron spectrum of Li ionization from the $2p_{+1}$ state. The field parameters are $\omega =0.5$ au and $\mathcal{E}=0.1$ au and the pulse duration is 10 optical cycles. The calculations with the following pairs of values $L_{\max }/R_{\max }(\mathrm{a}.\mathrm{u}.)$ are plotted. Solid line (red online), 12/500; short dashed line (blue online), 10/500; dots (magenta online), 10/900, all in the velocity gauge; dashed line (green online), 12/500, the length gauge.

Figure 2

The photoelectron momentum distributions in the equatorial $(x,y)$ plane for Li ionization from the $2p_{+1}$ state (left column) and $2p_{-1}$ state (right column). The field parameters are $\omega =13.6$ eV, the pulse durations are 3 optical cycles (upper three rows) and 10 optical cycles (bottom row), and $\mathcal{E}=0.01$ a.u. (first row), $\mathcal{E}=0.05$ a.u. (second row), and $\mathcal{E}=0.1$ a.u. (third and fourth rows).

Figure 3

The photoelectron time delays as functions of the polar angle $\varphi$ in the equatorial plane for the field strengths $\mathcal{E}=0.01$ a.u. (top), $\mathcal{E}=0.05$ a.u. (middle), and $\mathcal{E}=0.1$ a.u. (bottom). Pulse duration: $T_1/T=3$ (left), $T_1/T=10$ (right). Solid line (red online), ionization from the $2p_{+1}$ state; dashed line (green online), ionization from $2p_{-1}$ state. Short dashed line (blue online), ${\tau }_0^d=d{\delta }_2/dE$; dots (magenta online), ${\tau }_0^s=d{\delta }_0/dE$.

Figure 4

Coefficients $-dA/dE$ (solid line, red online) and $B\left(E\right)$ (dashed line, green online) on the energy shell as functions of the pulse duration $T_1/T$. The envelope function $f\left(t\right)$ is defined in Eq. (3).

Figure 5

Top: scattering phase shifts ${\delta }_{l=0}$ (dotted line, red online) and ${\delta }_{l=2}$ (solid line, blue online) ionization channels. Bottom: the energy derivatives $d{\delta }_{l=0}/dE$ (dotted line, red online) and $d{\delta }_{l=2}/dE$ (solid line, blue online) are converted to the units of time delay.

Figure 6

The time delays as functions of the polar angle $\varphi$ in the equatorial plane for the field strength $\mathcal{E}=0.05$ a.u. and the pulse duration $T_1/T=3$. The full TDSE calculations for ionization from the $2p_{+1}$ and $2p_{-1}$ states are plotted with the solid (red online) and dashed (green online) lines, respectively. The reduced TDSE calculations with the $\mu =1,3$ terms suppressed in Eq. (4) for the $2p_{+1}$ state and $\mu =\pm 1$ terms suppressed for the $2p_{-1}$ state are drawn with the short dashed (blue online) and dotted (purple online) lines, respectively.