Influence of an atomic resonance on the coherent control of the photoionization process

In coherent control schemes, pathways connecting an initial and a final state can be independently controlled by manipulating the complex amplitudes of their transition matrix elements. For paths characterized by the absorption of multiple photons, these quantities depend on the magnitude and phase between the intermediate steps, and are expected to be strongly affected by the presence of resonances. We investigate the coherent control of the photoemission process in neon using a phase-controlled two-color extreme ultraviolet pulse with frequency in proximity of an excited energy state. Using helium as a reference, we show that the presence of such a resonance in neon modifies the amplitude and phase of the asymmetric emission of photoelectrons. Theoretical simulations based on perturbation theory are in fair agreement with the experimental observations.

Figure 1

Coherent control of photoionization in neon (a), (b) and helium (c), (d). A photoelectron can be emitted via two different pathways, characterized by the absorption of two photons of the fundamental $\omega$ (resonant, blue lines; nonresonant, light-blue lines) or one photon of the second harmonic $2\omega$ (purple lines). The position of the $4s$ resonance in neon (a) and that of the $2p$ in helium (c) are indicated. The dashed lines indicate the ionization threshold. The magnitude (black) and phase (red) of the dipole matrix element using the classical Lorentz model are shown for neon in (b) and helium in (d). The shaded yellow area indicates the photon energy range investigated in the present work.

Figure 2

(a) Experimental setup. Schematic view of the six undulators available at FERMI. The phase shifter PS placed between the fifth and sixth undulator was used to change the relative phase $2\omega \tau$ between the two colors. The gas jet was composed of a mixture of neon and helium (shown with red and blue circles). (b) VMI spectrum (noninverted and background corrected) showing the angular-resolved photoelectron spectra emitted by the two-color fields in a mixture of neon and helium. The inner and outer rings correspond to the photoelectrons generated in helium (white) and neon (red), respectively. The gray line indicates the polarization direction of the FEL pulse. The angle $\theta$ defines the emission direction of the photoelectrons.

Figure 3

Ratio of ionization probability by the second harmonic and the fundamental for different detunings $\mathrm{\Delta }$ (0 eV: solid, black line; 0.05 eV: red, dotted line; 0.1 eV: blue, dashed line), as calculated using the TDSE model.

Figure 4

Photoionization cross section obtained in the length (solid line) and velocity gauge (dashed lines) of polarized $4s$ and $4s^{\prime }$ (a) and $3d$ (b) states by linearly polarized fields. The shaded (yellow) region indicates the range of photon energies used in the experiment.

Figure 5

(a)–(p) Experimental asymmetry (solid circles) as a function of the relative phase $2\omega \tau$ between the two harmonics measured in neon (a), (c), (e), (g), (i), (k), (m), (o) and helium (b), (d), (f), (h), (j), (l), (n), (p) for the photon energies $E=19.6$ eV (a), (b), $E=19.7$ eV (c), (d), $E=19.75$ eV (e), (f), $E=19.8$ eV (g), (h), $E=19.9$ eV (i), (j), $E=20.0$ eV (k), (l), $E20.1$ eV (m),(n), and $E=20.2$ eV (o), (p). The solid lines represent the sinusoidal fit of the asymmetry curves. The definitions of $A_{\omega }^{\left(k\right)}$ and ${\varphi }_{\omega }^{\left(k\right)}$ [see Eq. (2)] for neon ($k=n$) and helium ($k=h$) are shown in panels (g) and (l), respectively.

Figure 6

The relative amplitude ratio $A_{\omega }=A_{\omega }^{\left(n\right)}/A_{\omega }^{\left(h\right)}$ (a) and relative phase difference ${\varphi }_{\omega }={\varphi }_{\omega }^{\left(n\right)}-{\varphi }_{\omega }^{\left(h\right)}$ (b) of the hemisphere-integrated asymmetry from Eq. (2) as functions of the photon energy. The positions of the resonance states in neon are indicated on the energy axis. The solid dark-blue and dashed red lines correspond to PT calculations in the length (L) and velocity (V) gauges, respectively, while the blue circles represent the experimental points.