Laser-induced Coulomb explosion of heteronuclear alkali-metal dimers on helium nanodroplets

A sample mixture of alkali-metal homonuclear dimers, ${\mathrm{Ak}}_2$ and ${\mathrm{Ak}}_2^{\prime }$, and heteronuclear dimers, ${\mathrm{AkAk}}^{\prime }$, residing on the surface of helium nanodroplets are Coulomb exploded into pairs of atomic alkali-metal cations, $({\text{Ak}}^{\text{+}},{\text{Ak}}^{\text{+}})$, $({\text{Ak}}^{\prime +},{\text{Ak}}^{\prime +})$, and $({\text{Ak}}^{\text{+}},{\text{Ak}}^{\prime +})$, following double ionization induced by an intense 50-fs laser pulse. The measured kinetic-energy distribution $P\left(E_{\text{kin}}\right)$ of both the ${\text{Ak}}^{\text{+}}$ and ${\text{Ak}}^{\prime +}$ fragment ions contains overlapping peaks due to contributions from Coulomb explosion of the homonuclear and heteronuclear dimers. From $P\left(E_{\text{kin}}\right)$, we determine the distribution of internuclear distances $P\left(R\right)$ via the Coulomb-explosion imaging principle. Using coincident filtering based on momentum division between the two fragment ions, we demonstrate that the individual $P\left(E_{\text{kin}}\right)$ distributions pertaining to ions from either hetero- or homonuclear dimers can be retrieved. This filtering method works through the concurrent detection of two-dimensional velocity images of the ${\text{Ak}}^{\text{+}}$ and the ${\text{Ak}}^{\prime +}$ ions implemented through the combination of a velocity-map-imaging spectrometer and a TPX3CAM detector. The key finding is that $P\left(R\right)$ can be measured for any specific dimer in the unavoidably mixed sample of hetero- and homonuclear alkali-metal dimers. We report results for $\mathrm{LiK}$ and $\mathrm{NaK}$, which were previously unmeasurable by the Coulomb-explosion technique. Our method should also work for other heteronuclear dimers and for differentiating between different isotopologues of any of the dimers.

Figure 1

Illustration of laser-induced Coulomb explosion of an alkali-metal dimer using ${\mathrm{K}}_2$ as an example. The energy diagram depicts the potential curves for the $1{}^1{\mathrm{\Sigma }}_g^{+}$ state [22] and the $1{}^3{\mathrm{\Sigma }}_u^{+}$ state [23], with the square of the corresponding vibrational ground-state wave functions given in red. The potential curve for ${\mathrm{K}}_2^{2+}$ is shown as a Coulomb potential [see Eq. (2)]. The black arrows represent the photons (not to scale) of the laser pulse, illustrating the multiphoton absorption process that causes double ionization of ${\mathrm{K}}_2$ and thereby Coulomb explosion into a pair of ${\mathrm{K}}^{+}$ ions.

Figure 2

(a) Schematic of the doping process and following probing process in the experiment (see the text). Not to scale. (b) Mass-to-charge spectrum obtained when the laser pulse irradiates droplets that passed through the two pickup cells containing gases of Li and K atoms.

Figure 3

(a1)–(a5) ${}^7\mathrm{Li}^{+}$ results and (b1)–(b5) ${}^{39}\mathrm{K}^{+}$ results. (a1) and (b1) Two-dimensional velocity images. (a2) and (b2) Radial-velocity distributions $P\left(v_r\right)$. (a3) and (b3) Kinetic-energy distributions $P\left(E_{\text{kin}}\right)$. (a4) and (b4) Covariance maps of $P\left(v_r\right)$. (a5) Covariance map of the angular distribution for ${}^7\mathrm{Li}^{+}$ ions with 5.3 $\le v_r\le$ $7.6\mathrm{km}/\mathrm{s}$. (b5) The same as (a5), but for ${}^{39}\mathrm{K}^{+}$ ions with 2.2 $\le v_r\le$ $2.8\mathrm{km}/\mathrm{s}$.

Figure 4

(a) Covariance map of the radial-velocity distribution between the ${}^7\mathrm{Li}^{+}$ ions and the ${}^{39}\mathrm{K}^{+}$ ions. (b) Covariance map of the angular distribution between the ${}^7\mathrm{Li}^{+}$ ions with 7.5 $\le v_r\le$ $9.6\mathrm{km}/\mathrm{s}$ and the ${}^{39}\mathrm{K}^{+}$ ions with 1.0 $\le v_r\le$ $1.8\mathrm{km}/\mathrm{s}$.

Figure 5

(a) Illustration of the detection of the 2D velocity ($v_y$, $v_z$) of the ${}^7\mathrm{Li}^{+}$ and ${}^{39}\mathrm{K}^{+}$ fragment ions from Coulomb explosion of ${}^7\mathrm{Li}{}^{39}\mathrm{K}$. (b) Illustration of the principle of the coincidence filter for the ${}^7\mathrm{Li}{}^{39}\mathrm{K}$ dimer. Here ${\sigma }_{v_r}$ and ${\sigma }_{\theta }$ define the velocity and angular tolerance of the filter. The values used are given in Eqs. (5) and (6).

Figure 6

Kinetic-energy distributions (black solid lines) of (a1)– (c1) ${}^7\mathrm{Li}^{+}$ ions and (a2)–(c2) ${}^{39}\mathrm{K}^{+}$ ions determined from those ions that passed the coincidence filter indicated at the top of each panel. Blue dashed lines show the kinetic-energy distributions of ${}^7\mathrm{Li}^{+}$ ions in (b1) and of ${}^{39}\mathrm{K}^{+}$ ions in (b2) obtained from droplets doped only with Li or K.

Figure 7

The distribution of internuclear distances for ${}^7\mathrm{Li}{}^{39}\mathrm{K}$ determined from the ${}^{39}\mathrm{K}^{+}$ fragment ions (black dashed curve) and from the ${}^7\mathrm{Li}^{+}$ fragment ions (red dotted curve). The blue solid curve shows the calculated square of the internuclear wave function for the vibrational ground state of ${}^7\mathrm{Li}{}^{39}\mathrm{K}$ in the $1{}^3{\mathrm{\Sigma }}^{+}$ state.

Figure 8

Kinetic-energy distributions (black solid lines) of (a1)–(c1) ${}^{23}\mathrm{Na}^{+}$ ions and (a2)–(c2) ${}^{39}\mathrm{K}^{+}$ ions determined from those ions that passed the coincidence filter indicated at the top of each panel. Blue dashed lines show the kinetic-energy distribution of ${}^{23}\mathrm{Na}^{+}$ ions in (b1) and of ${}^{39}\mathrm{K}^{+}$ ions in (b2) obtained from droplets doped only with Na or K, respectively.

Figure 9

The distribution of internuclear distances for ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ determined from the ${}^{39}\mathrm{K}^{+}$ fragment ions (black dashed curve) and from the ${}^{23}\mathrm{Na}^{+}$ fragment ions (red dotted curve). The blue solid curve shows the calculated square of the internuclear wave function for the vibrational ground state of ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ in the $1{}^3{\mathrm{\Sigma }}^{+}$ state.

Figure 10

(a1)–(a5) ${}^{23}\mathrm{Na}^{+}$ results and (b1)–(b5) ${}^{39}\mathrm{K}^{+}$ results. (a1) and (b1) Two-dimensional velocity images. (a2) and (b2) Radial-velocity distributions $P\left(v_r\right)$. (a3) and (b3) Kinetic-energy distributions $P\left(E_{\text{kin}}\right)$. (a4) and (b4) Covariance maps of $P\left(v_r\right)$. (a5) Covariance map of the angular distribution for ${}^{23}\mathrm{Na}^{+}$ ions with 2.9 $\le v_r\le$ $4.0\mathrm{km}/\mathrm{s}$. (b5) The same as (a5), but for ${}^{39}\mathrm{K}^{+}$ ions with 1.1 $\le v_r\le$ $3.3\mathrm{km}/\mathrm{s}$.

Figure 11

(a) Covariance map of the radial-velocity distribution between the ${}^{23}\mathrm{Na}^{+}$ ions and the ${}^{39}\mathrm{K}^{+}$ ions. (b) Covariance map of the angular distribution between the ${}^{23}\mathrm{Na}^{+}$ ions with 2.9 $\le v_r\le$ $4.3\mathrm{km}/\mathrm{s}$ and the ${}^{39}\mathrm{K}^{+}$ ions with 1.6 $\le v_r\le$ $2.5\mathrm{km}/\mathrm{s}$.