Nonadiabatic tunneling in circularly polarized laser fields: Physical picture and calculations

We consider selectivity of strong-field ionization in circularly polarized laser fields to the sense of electron rotation in the laser polarization plane in the initial state. We show that, in contrast to the textbook examples of one-photon ionization and bound-state excitations with increase in the electron angular momentum, and also in contrast to the well-studied ionization of Rydberg atoms in microwave fields, which all prefer corotating electrons, optical tunneling selectively depletes states where the electron initially rotates against the laser field. We also show that key assumptions regarding adiabaticity of optical tunneling may quickly become inaccurate in typical experimental conditions.

Figure 1

Kinematics of electron tunneling through rotating barrier. (a) Right circularly polarized laser field ${\mathbf{E}}_{+}$ creates the tunneling barrier rotating counterclockwise. The electron observed at the detector placed along the $x$ axis exits the barrier along the $y$ axis, opposite to the direction of the laser field ${\mathbf{E}}_{+}$, i.e. in the negative direction of $y$ axis. (b) Ionization rate estimated with exponential accuracy [Eq. (5)] for $\gamma \sim 1$ (solid red line) is maximal for the initial velocity $v_{xi}<0$ and it corresponds to electron rotating clockwise. In the adiabatic limit ($\gamma \ll 1$) the distribution of initial transversal velocities becomes symmetric and is centered around zero (dashed blue line).

Figure 2

Ionization rate [Eqs. (6, 7, 8, 9)] for $p_{\pm }$ orbitals and right circular polarization. (a) Ionization rate vs laser frequency for Kr ground 4$p$ state ($I_p=0.5$ a.u.) and laser field $\mathcal{E}=0.06$ a.u. (b) Ionization rate vs laser intensity for Kr ground 4$p$ state ($I_p=0.5$ a.u.) and laser frequency $\omega =0.057$ a.u. (c) Photoelectron energy distribution at the detector [Eq. (19)] for $p_{-}$ (solid red line) and $p_{+}$ (dashed blue line) orbitals, for Kr ground 4$p$ state ($I_p=0.5$ a.u.), laser frequency $\omega =0.057$ a.u., $\mathcal{E}=0.06$ a.u. Electrons with energy $E_{\text{kin}}^o=2U_p+I_p$ (vertical line) correlate to nonrotating hole, low-energy electrons $E<E_{\text{kin}}^o$ correlate to counterrotating holes, and higher energy electrons $E>E_{\text{kin}}^o$ correlate to corotating holes. In the adiabatic case ($\gamma =0$) photoelectron distributions are peaked at $2U_p$ and are the same for $p_{+}$ and $p_{-}$ orbitals.