Dressed Atoms in Flight through a Periodic Crystal Field: X-VUV Double Resonance

We report the Autler-Townes doublet demonstrating a novel type of coherent interaction of atoms not with photons but with a periodic crystal field when the atom is in flight through a crystal at high velocity. It was observed by the nonoptical X-VUV (vacuum-ultraviolet) double resonance of three-dimensional resonant coherent excitation with good coherence. The states strongly coupled in the VUV region were probed by the excitation in the x-ray region. The characteristic spectra are well interpreted by an analogy of the dressed atom concept often adopted for the atom-photon interaction.

Figure 1

Diagram outlining the experiments. Geometric configuration of a high-velocity ion traversing a periodic array of atomic planes in a crystal is shown. The atomic planes specified by $(k,l,m)=(1,-1,-2)$, i.e., the $(\overline{3}\overline{1}\overline{1})$ planes, and the atomic planes specified by $(k,l,m)=(0,0,-2)$, i.e., the $(\overline{2}\overline{2}0)$ planes are shown in (a) and (b), respectively [16]. Note that the angle between the ion trajectory and the planes is exaggerated for convenience of understanding. Direction of a velocity vector of the ion $\mathbf{v}$ with respect to the basis lattice vectors of the diamond structured crystal is indicated by (c). We define the angle of the ion velocity with respect to the (004) atomic plane as $\theta$, and the angle of the ion velocity projected on the (004) atomic plane with respect to the $[\overline{1}10]$ axis as $\varphi$. (d) Energy diagram of the $\Lambda$-type three-level configuration of heliumlike ${\mathrm{Ar}}^{+16}$ [12]. The dashed arrows represent the spontaneous decays with their lifetimes [13, 17].

Figure 2

Excitation profiles obtained from the survival fraction of heliumlike ${\mathrm{Ar}}^{16+}$ by scanning ${\nu }_p$ with fixed ${\nu }_c$. Profiles are shown at various detunings $h{\delta }_c$ with (solid line) and without (dashed line) the Al foil. The horizontal scale of excitation energy is converted from $\theta$ and $\varphi$ using Eq. (1). The vertical scale is identical for all the profiles (shown only for ${\delta }_c=8.2\mathrm{eV}$). The vertical dashed line indicates the unperturbed transition energy from the ground state to the $1s2p(2{}^{1}P)$ state, $\Delta E_{2P-1S}$.

Figure 3

The excitation energies of the resonance dip as a function of $h{\delta }_c$. The uncertainties of the excitation energies from the fitting procedure are less than the size of the circles. The color (shading) of the circles represents the dip depth. Solid curves show $\Delta E_d^{(\pm )}$ evaluated from Eq. (4) with $|h{\Omega }_0|=3.4\mathrm{eV}$. Their width expresses the fraction of the $|1s2p(2{}^{1}P),{\mathbf{K}}_2⟩$ component in the $|+⟩$ and $|-⟩$ states, i.e., ${cos}^2ϵ$ and ${sin}^2ϵ$, respectively. The dashed lines show $\Delta E_{2P-1S}$ and $\Delta E_{2S-1S}+h{\nu }_c=\Delta E_{2P-1S}+h{\delta }_c$.