Hyperfine structure of the $A^1\mathrm{\Pi }$ state of AlCl and its relevance to laser cooling and trapping

The majority of molecules proposed for laser cooling and trapping experiments have $\mathrm{\Sigma }$-type ground states. Specifically, ${}^2\mathrm{\Sigma }$ states have cycling transitions analogous to $D_1$ lines in alkali-metal atoms while ${}^1\mathrm{\Sigma }$ states offer both strong and weak cycling transitions analogous to those in alkaline-earth atoms. Despite this proposed variety, to date, only molecules with ${}^2\mathrm{\Sigma }$-type ground states have successfully been confined and cooled in magneto-optical traps. While none of the proposed ${}^1\mathrm{\Sigma }$-type molecules have been successfully laser cooled and trapped, they are expected to have various advantages in terms of exhibiting a lower chemical reactivity and an internal structure that benefits the cooling schemes. Here, we present the prospects and strategies for optical cycling in AlCl—a ${}^1\mathrm{\Sigma }$ molecule—and report on the characterization of the $A^1\mathrm{\Pi }$ state hyperfine structure. Based on these results, we carry out detailed simulations on the expected capture velocity of a magneto-optical trap for AlCl. Finally, using ab initio calculations, we identify the photodissociation via a $3^1\mathrm{\Pi }$ state and photoionization process via the $3^1{\mathrm{\Sigma }}^{+}$ state as possible loss mechanisms for a magneto-optical trap of AlCl.

Figure 1

Electronic and rovibrational energy-level structure of AlCl. The $Q$ transitions, which are used for laser cooling, are rotationally closed, unlike the $P$ and $R$ transitions. The rovibronic manifolds of the $X^1{\mathrm{\Sigma }}^{+}(v=0,J=1)$ and $A^1\mathrm{\Pi }(v^{\prime }=0,J^{\prime }=1)$ states include 72 and 144 hyperfine states, respectively, all of which are involved in laser cooling AlCl. Adapted from [170].

Figure 2

Normalized fluorescence data (red circles, UCR; blue diamonds, UConn) and model (black solid line) of the $R\left(J\right)$ transitions, $X^1{\mathrm{\Sigma }}^{+}|v=0,J\rangle \leftarrow A^1\mathrm{\Pi }|v^{\prime }=0,J+1\rangle$, (a) $R\left(0\right)$, (b) $R\left(1\right)$, (c) $R\left(2\right)$, and (d) $R\left(3\right)$. The vertical black lines represent the different transitions predicted by our Hamiltonian model with their heights corresponding to their relative line strengths.

Figure 3

Normalized fluorescence data (red circles, UCR data; blue diamonds, UConn data) and model (black solid line) of the $Q\left(0\right)\text{–}Q\left(5\right)$ transitions of AlCl. The models use the fitting parameters of the $R$ lines from Table 4 and are only optimized to reproduce the measured signal amplitude, the rotational temperature ($T_{\text{rot}}=2.5$ K solid line, $T_{\text{rot}}=1.6$ K dashed line), and the absolute frequency offset. The vertical black lines represent the different transitions predicted by our Hamiltonian model with their heights corresponding to their relative line strengths.

Figure 4

The Zeeman splitting of the $A^1\mathrm{\Pi },(v^{\prime }=0,J^{\prime }=1)$ manifold of AlCl as a function of the external magnetic field.

Figure 5

Simulated capture velocities plotted as a function of laser power per beam for different beam diameters. The beam diameter is defined as the $1/e^2$ diameter of the Gaussian beams. Figure reproduced from [170].

Figure 6

Six selected potential-energy curves (PECs) are plotted for AlCl as a function of the internuclear distance $r$. The three black and one blue PECs correlate to neutral Al $+$ Cl dissociation for large $r$ whereas the red PEC leads to ionization ${\mathrm{Al}}^{+}$ $+$ ${\mathrm{Cl}}^{-}$ and the green PEC leads to ${\mathrm{Al}}^{*}$ $+$ Cl. The two-photon process is indicated by the vertical dashed black and red arrows. The dashed and long-short dashed PECs correspond to increasing and decreasing the slopes of the PECs by 1.5%, respectively.

Figure 7

The normalized photodissociation (blue = $2{}^1\mathrm{\Pi }$ and green = $3{}^1\mathrm{\Pi }$) and photoionization (red) cross sections are plotted as a function of the excitation energy. The energies of the two relevant laser wavelengths (261 nm, main cooling transition; 265 nm, first vibrational repumper) are indicated by the vertical black lines. The dashed and short-long dashed curves quantify the sensitivity of the cross sections to the slopes of the potential-energy curves of the repulsive excited electronic states (see Fig. 6).