Perturbation-assisted Observation of the Lowest Vibrational Level of the $\mathrm{b}^{3}Π_{0}$ State of Ultracold LiK Molecules

TL;DR

This paper reports the first observation of the lowest vibrational level of the triplet state $|\mathrm{b}^{3}\Pi_{0}, v'=0\rangle$ in ultracold $^{6}\mathrm{Li}^{40}\mathrm{K}$ by probing the weak spin–orbit–induced X^{1}\Sigma^{+}(v=0) → b^{3}\Pi_{0}(v'=0) transition near $\approx 314.2305\ \text{THz}$. By combining ab initio potential curves with perturbation analysis of the A^{1}\Sigma^{+} manifold, the authors refined the predicted resonance to within $\pm 5\ \text{cm}^{-1}$ and subsequently resolved the $J'=0,1,2$ rotational structure using microwave spectroscopy to extract the rotational constant $B_0^{b}=h\times8.576(44)\ \text{GHz}$ and the excited-state energy $E_0^{b}=hc\times10{,}481.03(2)\ \text{cm}^{-1}$. A 954 nm laser system enables spectroscopy with a measured Rabi frequency of $2\pi\times24(1)\ \text{MHz}$, and the determined transition strength implies a small but detectable dipole coupling suitable for driving the transition in a magic-wavelength trap. The results provide precise information on the deeply bound region of LiK’s $b^{3}\Pi_{0}$ potential and pave the way for long-coherence, strongly interacting molecular systems relevant to quantum simulation and computation.

Abstract

The narrow transition from the lowest rovibrational level of the $\mathrm{X}^{1}Σ^{+}$ electronic ground state to the lowest vibrational level of the $\mathrm{b}^{3}Π_{0}$ potential provides opportunities for achieving magic-wavelength trapping of ultracold bialkali molecules for enhancing their rotational coherence times. Guided by existing spectroscopic data of several perturbed and deeply-bound rovibrational states of the $\mathrm{A}^{1}Σ^{+}$ potential [Grochola et al., Chem. Phys. Lett., 2012, 535, 17-20], we conducted a targeted spectroscopic search and report the first observation of the lowest vibrational level of the $\mathrm{b}^{3}Π_{0}$ state in $^{6}\mathrm{Li}^{40}\mathrm{K}$. The transition frequency from $|\mathrm{X}^{1}Σ^{+},\,v=0,\,J=0>$ to $|\mathrm{b}^{3}Π_{0},\,v'=0,\,J'=1>$ is determined to be 314,230.5(5)GHz. Assisted by microwave spectroscopy, we resolved the rotational structure of $|\mathrm{b}^{3}Π_{0},\,v'=0>$ and extracted a rotational constant of $h\times8.576(44)$ GHz for the $\mathrm{b}^{3}Π_{0}$ state. From this, we deducted an energy separation between $|\mathrm{b}^{3}Π_{0},v'=0,J'=0>$ and $|\mathrm{X}^{1}Σ^{+},v=0,J=0>$ of $hc\times$10,481.03(2) $\mathrm{cm}^{-1}$. Our work provides timely and precise information on the deeply-bound region of the $\mathrm{b}^{3}Π_{0}$ triplet excited potential of LiK, and benefits future applications of ultracold LiK isotopologues in quantum simulation and quantum computation that demand long coherence times.

Figures (4)

• Figure 1: Non-relativistic electronic potential energy curves for LiKAllouche as functions of internuclear separation $R$. $\mathrm{X}^{1}\Sigma^{+}$ (blue curve) and $\mathrm{a}^{3}\Sigma^{+}$ (green curve) ground state potentials at large $R$ connect to the Li(2S) plus K(4S) atomic asymptote. Two relevant excited electronic states are the $\mathrm{A}^{1}\Sigma^{+}$ (red curve) and $\mathrm{b}^{3}\Pi_{0}$ (purple curve), which are coupled by the relativistic spin-orbit interaction. The orange arrow indicates the transition from $\ket{\mathrm{X}^{1}\Sigma^{+},v=0}$ to $\ket{\mathrm{b}^{3}\Pi_{0},v'=0}$. $\ket{\mathrm{b}^{3}\Pi_{0},v'=0}$ can also decay via pre-dissociation process due to coupling to the $\mathrm{a}^{3}\Sigma^{+}$ state as indicated by the curved arrow. The $\mathrm{B}^{1}\Pi$ (gray dashed line) and $\mathrm{c}^{3}\Sigma^{+}$ (gray dotted line) excited states are not considered in this work.
• Figure 2: Spin-orbit matrix elements (panel a), state amplitudes $c_1$ and $c_2$ for states A$^1\Sigma^+$ and b$^3\Pi$, respectively (panel b), and electric transition dipole moments (panel c) as functions of internuclear separation $R$. In panel (a) quantity $\Delta^{\rm K}_{\rm{SO}}$ is the spin-orbit splitting between the 4p(P$_{1/2}$) and 4p(P$_{3/2}$) levels of the potassium atom. In panel (c) the dipole moments are in atomic units $ea_0$.
• Figure 3: (a) - (f): Upper panels show the rotational energy progression of six vibrational states of the $\mathrm{A}^{1}\Sigma^{+}$ potential (orange circles) calculated using spectroscopically determined Dunham coefficients for $^{7}\mathrm{Li}^{39}\mathrm{K}$Grochola2012Tiemann2009 together with the rotational energies of a vibrational level in the $\mathrm{b}^{3}\Pi_{0}$ potential (blue circles), calculated using Dunham coefficients based on ab initio potentials Allouche. Both $\mathrm{A}^{1}\Sigma^{+}$ and $\mathrm{b}^{3}\Pi_{0}$ transitions are derived from the same ground state $\ket{\mathrm{X}^{1}\Sigma^{+},v=0, J=J'-1}$ states. The blue curves are energetically shifted simultaneously as indicated by the light blue arrows such that they cross the orange curves at the center of the perturbed region. Lower panels show the error $\Delta E$ (red triangles) between experimentally observed transition energies for the $\mathrm{A}^{1}\Sigma^{+}$ potential and transitions calculated using Dunham coefficients. Observed transitions with $\Delta E$ higher than 0.1$\mathrm{cm}^{-1}$ are considered as perturbation caused by $\mathrm{b}^{3}\Pi_{0}$ rovibrational levels. The vertical dashed lines indicate the center for the perturbation region.
• Figure 4: Spectroscopy measurement for $\mathrm{b}^{3}\Pi_{0}$. (a) The number of Feshbach molecules is recorded (blue circles) while scanning the frequency of spectroscopy laser around $\nu_{0} = 314230.5 \rm{GHz}$. The inset shows a scan of laser frequency around $\nu_{0}$ with finer steps. The solid green curve is a fit to the data, from which we extract an Rabi frequency $\Omega$ of 24 MHz. Details of the fit is explained in the text. (b) Illustration of rotational level scheme for the ground and target excited state. (c) Population of molecules is recorded after a microwave $\pi$ pulse (purple circles), which drives the transition $\ket{J=0,m_{j}=0}\rightarrow\ket{J=1,m_{j}=-1}$. The spectroscopy laser is switched on during the process. The three peaks are caused by the $\ket{J=0}\rightarrow\ket{J'=1}$, $\ket{J=1}\rightarrow\ket{J'=0,2}$ transitions. Green dashed curves are fit to the data.