Long-range coupling of $X{}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ states of the atom pair $\text{K}+\text{Cs}$

The K and Cs atom pair and its $X{}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ electronic molecular states are studied by Fourier-transform spectroscopy with special emphasis on bound states close to the ground state asymptote $\left(4s\right)\text{K}+\left(6s\right)\text{Cs}$. Significant vibrational mixing due to hyperfine coupling was observed leading to improved potential energy curves for both states. The observed intensity pattern of the hyperfine structure for the last vibrational levels of $X{}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ reveals deep insight into the multicomponent wave function of such levels with its influence for modeling the asymptotic behavior of the excited electronic states involved in the reported observations. Examples of derived properties of cold collisions are given and the importance of the present results for efficient production schemes for ultracold KCs is discussed.

Figure 1

Scheme of potential energy curves for selected low-lying singlet (solid lines) and triplet states (dashed lines) of a KCs molecule taken from Ref. [16]. Vertical arrows indicate excitation to $v^{\prime }=44$ by Rhodamine 6G dye laser and possible fluorescence decay.

Figure 2

(a) Part of KCs LIF spectrum excited by the laser frequency 17 815.420 cm${}^{-1}$. The progression marked by long (red) bars below the spectrum originates from the $v^{\prime }=44,J^{\prime }=6$ level of the ${}^{39}$K${}^{133}$Cs $\left(4\right){}^1{\Sigma }^{+}$ state. Spin-forbidden transitions to the $a{}^3{\Sigma }^{+}$ state originating from the same level are marked by short (blue) bars. Asterisks mark the simultaneously excited progression $(45,17)\to (v_X^{\prime \prime },16;18)$ of ${}^{41}$K${}^{133}$Cs. The inset in (a) shows the $PR$ doublet of LIF to $v_a=16$. Each doublet component consists of three hyperfine groups where the central component is marked. (b) A zoom of the high $v^{\prime \prime }$ region of (a). The weak doublets visible around the stronger lines of the progression originate from collisionally populated neighboring rotational levels, which are marked in the figure as $J^{\prime }=4,8$, and 10. The meaning of features A and B is explained in the text.

Figure 3

(a) Part of ${}^{39}$K${}^{133}$Cs LIF spectrum and (b) a zoom of the high $v^{\prime \prime }$ region excited by the laser frequency 17 815.306 cm${}^{-1}$ leading to $v^{\prime }=44,J^{\prime }=10$ instead of $J^{\prime }=6$ in Fig. 2. No overlap with another progression takes place and the structure A/B shows up similarly.

Figure 4

Rovibrational structure of $N=5$ and 7 of ${}^{39}$K${}^{133}$Cs at the asymptote $\left(4s\right)\mathrm{K}+\left(6s\right)\mathrm{Cs}$ compared with coupled-channel calculations. The black and green (gray) bars indicate positions of molecular levels for $N=5$ and 7, respectively, derived from coupled-channel calculations. The length of the bars is determined by the expectation value of the electronic spin $S$: $1.1-\langle S\rangle$. The solid squares show the position of molecular levels from the Born-Oppenheimer potentials of states $X{}^1{\Sigma }^{+}$ (lower squares) and $a{}^3{\Sigma }^{+}$ (upper squares) for $N=5$. The energy axis is given with respect to the atomic asymptote $\left(4s\right)\mathrm{K}+\left(6s\right)\mathrm{Cs}$; the solid triangles at the right give the positions of the atom-pair asymptotes including hyperfine energy; the K splitting is not resolved on this scale. The red open circles give calculated relative transition probabilities using multichannel wave functions in connection with transition moments for state (4) ${}^1{\Sigma }^{+}$ from Ref. [17].

Figure 5

Multicomponent wave function in basis $|bG\rangle$ for $N=5$, $f=4$, and $F=8$ at the energy $-0.60$ cm${}^{-1}$ with respect to the atomic asymptote $\left(4s\right)\text{K}+\left(6s\right)$Cs, mark A in Fig. 4. $a_0$ is the Bohr radius $0.529\times {10}^{-10}$ m.

Figure 6

Upper panel: singlet component; lower panel: triplet component of $G=7/2,f=4$ for $N=5$ at the energy $-0.36$ cm${}^{-1}$ with respect to the atomic asymptote $\left(4s\right)\text{K}+\left(6s\right)$Cs, mark B in Fig. 4. By dashed lines the vibrational wave functions of the Born-Oppenheimer states $X{}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ are given with quantum numbers and with proper amplitudes, which make up the singlet or triplet component. $a_0$ is the Bohr radius $0.529\times {10}^{-10}$ m.

Figure 7

Molecular levels as a function of the magnetic field for ${}^{39}{\mathrm{K}}^{133}\mathrm{Cs}$ for the quantum numbers ${(f=1,m_f=1)}_{\text{K}}$ and ${(f=3,m_f=3)}_{\text{Cs}}$ at the atom-pair asymptote with $l=0$.