Characterization of the $3d\delta$ Rydberg state of ${\mathrm{MgAr}}^{+}$ using a quantum-control optical scheme

We report a spectroscopic investigation of the $3d{\delta }_{\mathrm{\Omega }}$ ($\mathrm{\Omega }=\frac{3}{2},\frac{5}{2}$) Rydberg states of the ${\mathrm{MgAr}}^{+}$ molecular cation. Vibrational levels of the $3d{\delta }_{3/2}$ spin-orbit component with $v\ge 15$ were observed to directly predissociate into charge-transfer continua correlating to the $\mathrm{Mg}\left(3s^2{}^{1}S\right)$ $+$ ${\mathrm{Ar}}^{+}\left(3p^5{}^{2}P\right)$ dissociation limit, making it possible to record their spectra by isolated-core multiphoton Rydberg dissociation spectroscopy. Vibrational states below $v=15$, which do not predissociate, were characterized with partial rotational resolution using a multiphoton excitation and dissociation quantum-control scheme that radiatively couples the $3d\delta$ vibronic states to predissociative levels of the $3d\pi$ state. An effective Hamiltonian approach was used to theoretically investigate this scheme, including the origin of the control over the spectral lineshapes provided by the laser detuning. This approach provided results in quantitative agreement with the measured spectra. Potential-energy functions were derived for the $3d{\delta }_{\mathrm{\Omega }}$ states from experimental data. They are very similar to the one of the $X^{2+}{}^1{\mathrm{\Sigma }}^{+}$ ground state of the ${\mathrm{MgAr}}^{2+}$ doubly charged ion, highlighting the Rydberg character of the $3d\delta$ state. Whereas homogeneous charge-transfer interactions play a major role in the dynamics of the Rydberg states of molecular ions, the present study shows that heterogeneous interactions leave these states essentially unaffected.

Figure 1

Excitation scheme used to study the $3d{\delta }_{\mathrm{\Omega }}$ Rydberg states of ${\mathrm{MgAr}}^{+}$ and relevant potential-energy functions. The curves of the $X$, $A$, $3d\sigma$, $3d\pi$, and $3d\delta$ states are ab initio data taken from Ref. [15] and the curves of the charge-transfer (CT) states were taken from Ref. [17]. The red horizontal arrow indicates predissociation of $3d\pi$ vibrational levels into the continua associated with the CT states. The horizontal black dashed line indicates the position of the $3d{\delta }_{3/2}(v=15)$ vibrational level.

Figure 2

Schematic view of the photoexcitation region. The molecular beam produced by the laser ablation supersonic expansion source enters the electrode stack (horizontal full lines) from the top and is intersected at right angles by up to four laser beams. Pulsed electric fields are applied to the electrodes to field ionize atoms and molecules in Rydberg states and to accelerate the positively charged particles toward the detector located $\approx 15$ cm below the interaction region. The reference frame used in Sec. 3 is defined in the top right corner of the figure.

Figure 3

Spectra of (a) the $A_{3/2}(v^{\prime }=5)\leftarrow X(v^{″}=3)$ transition of ${\mathrm{MgAr}}^{+}$ recorded by ICMRD (see Refs. [16, 18] for details) and (b) the $3d{\delta }_{5/2}(v=2)\leftarrow X(v^{″}=3)$ two-photon transition for different wave numbers ${\tilde{\nu }}_2$ of the second laser corresponding to the vertical colored bars in panel (a), which match the colors and numbering of the spectra in panel (b) [graphs 1–4 match the bars from left to right in panel (a)].

Figure 4

Simplified photoexcitation and photodissociation scheme used to rationalize the strong effect of ${\tilde{\nu }}_2$ on the lineshapes of the $3d{\delta }_{\mathrm{\Omega }}(v\le 14)$ vibrational levels of ${\mathrm{MgAr}}^{+}$. Isolated rovibrational levels of the $X$, $A_{{\mathrm{\Omega }}^{\prime }}$, and $3d{\delta }_{\mathrm{\Omega }}$ states are considered for simplicity, and the $3d{\pi }_{{\mathrm{\Omega }}_{\text{d}}}$ predissociative state is described as a flat continuum of infinite bandwidth. The arrows show the two major interfering photoexcitation pathways to the $3d{\pi }_{{\mathrm{\Omega }}_{\text{d}}}$ continuum, which lead to the observed asymmetric lineshapes (see text). The direct two-photon pathway is denoted by the dashed arrows and the indirect four-photon pathway via the $3d{\delta }_{\mathrm{\Omega }}$ state is shown by the full arrows. The horizontal dotted line represents the virtual state through which two-photon excitation proceeds.

Figure 5

Experimental (left column) and theoretical (right column) spectra of the $3d{\delta }_{5/2}(v=2)\leftarrow X(v^{″}=3)$ two-photon transition for the same wave numbers ${\tilde{\nu }}_2$ of laser 2 as in Fig. 3. The labeling and color coding is also identical. The theoretical spectra were scaled by a global factor and offset along the vertical axis to account for the presence of a small background signal in the experimental spectra.

Figure 6

Measured (top) and calculated (bottom) spectra of the $3d{\delta }_{5/2}(v=13)\leftarrow X(v^{″}=3)$ two-photon transition of ${\mathrm{MgAr}}^{+}$. The contributions of different initial $N^{″}$ rotational states to the spectrum are also shown in the bottom panel (thin colored lines). They account for about 90% of the total spectrum (thick black line). The assignment bars above the spectra give the positions of the transitions to levels of the $3d{\delta }_{5/2}$ state of increasing values of $J$ for each of the six ${\mathrm{\Delta }}_{J{N}^{″}}=J-N^{″}$ branches. The asterisks in the top panel indicate the narrow lines used to extract the band origin ${\tilde{\nu }}_{3v}$ and rotational constant $B_v$ of the upper state.

Figure 7

Experimental (a) and calculated (b) spectra of the $3d{\delta }_{3/2}(v=15)\leftarrow A_{1/2}(v^{\prime }=10)$ transition recorded by ICMRD. The rotational states of the $A_{1/2}(v^{\prime }=10)$ level with $J^{\prime }=\frac{1}{2},\frac{3}{2},\frac{5}{2}$, and $\frac{7}{2}$ were prepared by photoexcitation from the $X(v^{″}=3)$ ground electronic state and their relative populations were estimated to be $1,0.7,0.7,$ and 0.4, respectively. The assignment bars shown above the spectra and the stick spectrum in the lower panel give the positions of the transitions to levels of the $3d{\delta }_{3/2}$ state of successive values of $J$. See Ref. [17] for details on the calculation of the spectrum.

Figure 8

Potential-energy functions of the $3d{\pi }_{1/2,3/2}$ states [15], the $3d{\delta }_{3/2,5/2}$ states (present work), and the $\text{Mg}{(}^1{S}_0)+{\text{Ar}}^{+}{(}^2{P}_{1/2,3/2})$ charge-transfer states [17] of ${\mathrm{MgAr}}^{+}$. The $3d{\delta }_{3/2}$ and $3d{\delta }_{5/2}$ states are indistinguishable on the scale of the figure. At internuclear distances below their equilibrium distances, charge-transfer states with ${\mathrm{\Omega }}_{\text{d}}=1/2$ and ${\mathrm{\Lambda }}_{\text{d}}=0$ and 1 are strongly mixed by the spin-orbit interaction. The charge-transfer curves are thus labeled by an index (I or II) specifying their dissociation limit and by ${\mathrm{\Omega }}_{\text{d}}$. The vibrational levels of the $3d{\delta }_{3/2}$ and $3d{\delta }_{5/2}$ states measured in the present work are shown by the blue full horizontal lines and red dotted horizontal lines, respectively. Vibrational states of the $3d{\delta }_{3/2}$ state with $v\ge 15$ predissociate into the charge-transfer continua.