Controlling the Orbital Alignment in Atoms Using Cross-Circularly Polarized Extreme Ultraviolet Wave Packets

We report on the use of pairs of 10-cycle extreme ultraviolet wave packets with attosecond-controlled spacing emitted by individual relativistic electrons within an electron bunch passing through a tandem undulator. Based on the temporal coherent control technique with circular polarization, we succeeded in controlling the excited state alignment in the photoexcitation of helium atoms, which we verified through the observation of oscillation in fluorescence yield depending on the attosecond-controlled delay time. Our work demonstrates the potential of undulator radiation for the generation of longitudinally coherent wave packets suitable for attosecond coherent control, an application which has hitherto been hidden in the incoherent nature of the radiation pulse emitted by a bunch of electrons.

Figure 1

(a) Experimental setup for temporal coherent control in the photoexcitation of helium atoms. The tandem undulator consists of two helical undulators and each relativistic electron in the bunch emits a pair of 10-cycle XUV cross-circularly polarized wave packets. The energy spread and beam divergence of the electron beam are $\mathrm{\Delta }E/E\sim 5\times {10}^{-4}$, and ${\sigma }_{\mathrm{ex}}^{\prime }\sim 43\times {\sigma }_{\mathrm{ey}}^{\prime }\sim 26\mu \mathrm{rad}$, respectively. The delay time between the wave packets is controlled by the phase shifter magnet between the two undulators. The stability of the magnetic field in the phase shifter is 0.1%. The pinhole and the focusing mirror are located, respectively, at 9 and 10 m downstream of the middle point of the two undulators. The incidence angle of the focusing mirror is 80° and the focal point locates at 2 m downstream the mirror. The undulator radiation interacts with a helium gas beam at the focal point, and fluorescence photons are detected by the photomultiplier tube. (b) Helium atoms are coherently excited into an atomic superposition state. The fluorescence decay from the $1s6p$ state to the $1s2s$ state is selectively detected.

Figure 2

(a) Interaction between the cross-circularly polarized wave packet pair and single atoms. While the radiation pulse consists of numerous wave packet pairs randomly populated in the radiation pulse, each atom interacts with one of the identical wave packet pairs. (b) The helium atom is excited into the $1s6p$ superposition state which consists of the $M_j=\pm 1$ substates associated with the first (LCP) and second (RCP) parts of the wave packet pair.

Figure 3

Fluorescence yield as a function of wave packet delay in decays from the $1s6p$ to the $1s2s$ states. The gray circles are measured data and the red line shows the theoretical curve in which the 30 as time resolution is taken into account. The derived delay time in the horizontal axis corresponds to the delay produced by the phase shifter magnet. The delay time produced by the phase shifter magnet was calibrated using the sinusoidal curve which oscillates at the resonant frequency of the $1s6p$ state [23], assuming that the delay is proportional to $I^n$ where $I$ is the magnet current. In the fitting, the initial phase of the oscillation was determined to reproduce the measurement and we obtained $n=1.97$ which agree well with the theoretical value of $n=2$ [18]. The current of the phase shifter magnet is shown in the top horizontal axis. Polar plots of the aligned $6p$ orbital (blue) and dipole emission pattern (red) in the $xy$ plane are also shown.