Deformation of Atomic $p_{\pm }$ Orbitals in Strong Elliptically Polarized Laser Fields: Ionization Time Drifts and Spatial Photoelectron Separation

We theoretically investigate the deformation of atomic $p_{\pm }$ orbitals driven by strong elliptically polarized (EP) laser fields and the role it plays in tunnel ionization. Our study reveals that different Stark effects induced by orthogonal components of the EP field give rise to subcycle rearrangement of the bound electron density, rendering the initial $p_{+}$ and $p_{-}$ orbitals deformed and polarized along distinctively tilted angles with respect to the polarization ellipse of the EP field. As a consequence, the instantaneous tunneling rates change such that for few-cycle EP laser pulses the bound electron initially counterrotating (corotating) with the electric field is most likely released before (after) the peak of the electric field. We demonstrate that with a sequential-pulse setup one can exploit this effect to spatially separate the photoelectrons detached from $p_{+}$ and $p_{-}$ orbitals, paving the way towards robust control of spin-resolved photoemission in laser-matter interactions.

Figure 1

Upper panels: The instantaneous magnitude of the electric field, the population ratio $\mathcal{R}$, and the phase offset $\mathrm{\Delta }\mathrm{\Phi }$ as functions of time. Lower panels: The orbital shapes (solid, TDSE; thick dashed, three-level model) at ${\tau }_{-}$, ${\tau }_0$, and ${\tau }_{+}$. The alignments of the orbitals (dotted lines), the profile of the electric field (thin dashed curves), and the instantaneous field vectors (arrows) are shown inside the lower panels.

Figure 2

Tunnel ionization rates for the interactions of the initial $p_{\pm }$ orbitals with the EP pulse given in Fig. 1. Their average is presented in the enlarged figure on the right-hand side. The results are obtained from the semiadiabatic formula Eq. (2) (solid curves) and backpropagation (dots), respectively. The vertical dash-dotted lines indicate the maxima of the semiadiabatic ionization rates. The rates have been scaled with respect to the maxima of those for $p_{-}$.

Figure 3

The PADs for the $p_{+}$ [(a),(d)] and $p_{-}$ [(b),(e)] orbitals and the differences [(c),(f)] between the normalized PMDs for the $p_{\pm }$ orbitals, under the EP (upper row) and $\mathrm{CP}$ (lower row) pulses, respectively. The colors are in linear scales. The PADs are normalized to their maxima and the step of the contour is 0.1. The black and white contours in (c) and (f) indicate 97% of the maxima and minima, respectively.

Figure 4

The ellipticity dependence of (a) the offset angles (deviation from $\phi =90°$) of the PADs and (b) the delay of the highest ionization rate with respect to the field maximum. The error bar in (a) indicates the range for the yield higher than 99.95% of the peak value.

Figure 5

The differences between the CEP-averaged, normalized PMDs for the valence current-carrying orbitals of Ne, ${\mathrm{Ar}}^{+}$, and NO. Calculation details are shown in Ref. [39]. Other laser parameters are the same as in Fig. 1.

Figure 6

(a) Control scheme to spatially separate photoelectrons removed from valence current-carrying orbitals. (b) The total PMDs with the surface color indicating the PMD asymmetry of $p_{\pm }$ orbitals. The intensities for the LP and $\mathrm{CP}$ pulses are $9.5\times {10}^{13}$ and $1.0\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, respectively. (c) The PADs for $p_{+}$ (red) and $p_{-}$ (blue) orbitals within the sequential-pulse scheme using the LP pulse with different intensities: $3.6\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (dashed), $6.2\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (dotted), and $9.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (solid). All results have been averaged over the CEP of the $\mathrm{CP}$ pulse.