Ionization of argon by two-color laser pulses with coherent phase control

We present a joint experimental and theoretical study of ionization of argon atoms by a linearly polarized two-color laser field (${\lambda }_1=800$ nm, ${\lambda }_2=400$ nm). Changing the relative phase $\phi$ between the two colors, the forward-backward asymmetry of the doubly differential momentum distribution of emitted electrons can be controlled. We find excellent agreement between the measurements and the solution of the time-dependent Schrödinger equation in the single-active electron approximation. Surprisingly we also find good agreement between the quantum and classical calculations of electron momentum distributions generated by lasers at optical wavelengths.

Figure 1

Schematic representation of the two-color Mach-Zehnder interferometer used to generate two-color laser pulses. See text for description.

Figure 2

Laser electric fields and vector potentials of two-color laser pulses for the two-color phases $\phi =0$ (black solid line) and $\phi =\pi /2$ (red dashed line). The intensities are $I_1={10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ and $I_2={10}^{13}{\mathrm{W}/\mathrm{cm}}^2\mathrm{.}$

Figure 3

Experimental (black solid line) and simulated energy spectra for two-color phase $\phi =0$. TDSE (red thin solid line), CVA (green dot-dash line), SFA (blue dotted line), and CTMC (black dashed line). In the calculations, we have used the same laser intensities as in Fig. 2. To facilitate the comparison the curves have been normalized to agree with the TDSE data at around 4 eV.

Figure 4

Electron momentum distributions for ionization of Ar by two-color laser pulses averaged over the phase $\phi$ on a linear color scale in arbitrary units. (a) Experiment, (b) TDSE, (c) CTMC, (d) CVA, and (e) SFA. All calculations take into account the intensity average over the focal volume. The arrows in (a) point to the double ring due to Freeman resonances (see text).

Figure 5

Momentum distributions of photoelectrons emitted from Ar calculated using (a) single intensity (no focal averaging) TDSE, (b) intensity-averaged TDSE, and (c) intensity-averaged CTMC simulations for the two-color phase $\phi =0$ on a linear color scale in arbitrary units. See Supplemental Material [54] for $\phi$ dependence. The right panels show a cut of the doubly differential distributions for $k_z=0.37$, marked as a dotted line in the 2D plots.

Figure 6

Electron energy versus angular momentum as calculated by TDSE and CTMC for $\phi =0$ on a logarithmic color scale covering four orders of magnitude. The TDSE results have been calculated without (left panel) and with intensity averaging (center panel). Depending on the two-color phase $\phi$, the structures 1 and 2 marked in the CTMC distribution (right panel) appear differently pronounced (see animation in Supplemental Material) [54].

Figure 7

(a) Measured (upper panel) and calculated (lower panel) ionization yield as a function of the two-color phase. (b) Measured (upper panel) and calculated (lower panel) mean value of the electron energy $\langle E\rangle$ as a function of $\phi$. (c) Calculated mean value of the electron angular momentum $\langle L\rangle$. TDSE calculations for a single intensity (black solid line) and averaged over the focal volume (red full data points). CTMC calculations with average over the focal volume (open diamonds). The experimental data have been phase-shifted to match the theoretical phase.

Figure 8

(a) Measured and (b) calculated longitudinal momentum distributions as a function of the two-color phase $\phi$ on a linear color scale in arbitrary units. Experimental (red thick solid line), TDSE (black thin solid line), and CTMC (open circles) mean values of the longitudinal momentum $\langle k_z\rangle$ in (c) and asymmetry parameter $a$ in (d) as a function of $\phi$. The TDSE calculations are for a single intensity only.

Figure 9

Measured (left column) and calculated (right column) electron momentum distributions for fixed two-color phases: $\phi =0$ on a linear color scale in arbitrary units (a) and (f), $0.25\pi$ (b) and (g), $0.5\pi$ (c) and (h), $0.75\pi$ (d) and (i), and $\pi$ (e) and (j). The TDSE calculations have been performed including intensity averaging over the focal volume.