Coherent Optical Creation of a Single Molecule

We report coherent association of atoms into a single weakly bound NaCs molecule in an optical tweezer through an optical Raman transition. The Raman technique uses a deeply bound electronic excited intermediate state to achieve a large transition dipole moment while reducing photon scattering. Starting from two atoms in their relative motional ground state, we achieve an optical transfer efficiency of 69%. The molecules have a binding energy of 770.2 MHz at 8.83(2) G. This technique does not rely on Feshbach resonances or narrow excited-state lines and may allow a wide range of molecular species to be assembled atom by atom.

Popular Summary

Systems built from ultracold molecules are promising for many applications such as precision measurements and quantum information thanks to their rich internal states and strong interactions. For most molecular species, however, full control of such inherent complexity remains challenging. Currently, the most successful approach relies heavily on special properties of the system. Here, we experimentally demonstrate a more general approach: using optical transitions to pair a sodium and a cesium atom in the same optical tweezer to form a NaCs molecule.

We achieve full control of the molecule we create by first fully controlling the constituent atoms and then mapping this control to molecules through association. This approach must overcome the large size mismatch between the initial free-atom state and the final molecular bound state through careful selection of all the states involved. We demonstrate the coherence of this mapping by driving the atom pair back and forth to its weakly bound state.

Compared to the most reliable approach to date, which uses magnetic Feshbach resonances, our method uses only optical transitions that are abundant for pairs of atoms and could allow a diverse range of molecules to be associated atom by atom. The molecules we create can be transferred to other states, with stronger interactions to be used for quantum computation and simulation.

Figure 1

Optical creation of single molecules from single atoms in an optical tweezer. (a) Schematic of the optical transition from an atom pair to a weakly bound molecule. The initial state is the relative motional ground state between the two atoms and the final state is the first molecular bound state. The transition is driven by a pair of laser frequencies whose difference ($<1\mathrm{GHz}$) matches the molecular binding energy. The lasers are detuned by $\mathrm{\Delta }$ from an excited vibrational sublevel in the $c^3{\mathrm{\Sigma }}^{+}(\mathrm{\Omega }=1)$ electronic state in order to reduce scattering during the transfer. (b) Calculation of the scattering rate versus laser frequency including all vibrational states of 8 excited-state potentials and the atomic continuum. The assumed excited-state linewidth for molecular lines is 50 MHz. The dotted red line shows the contribution from the near-threshold states, which approximately scales as $1/{\mathrm{\Delta }}_{\text{thresh}}^2$. (c) Comparison between vibrational sublevels of the intermediate excited state for the Raman transition. The lowest sublevel (blue line) has a larger optimum ratio of Raman Rabi frequency to scattering rate than the higher sublevel (orange line). (d) The large scattering length for Na(2, 2), Cs(3, 3) is associated with enhancement of the relative wave function at short internuclear distance ($R$).

Figure 2

Beam path for generating two frequencies in the tweezer for the Raman transition (only essential optics shown). Two filters, one directly after the laser source and one after both optical fibers, clean the light from a fiber amplifier seeded by an external cavity diode laser. The red beam path is the always-present zeroth order of the double pass (DP) AOM. The blue beam path is the switchable first order of the DP AOM. It generates the second frequency for the Raman transition. To reduce interferences that cause relative power fluctuation of the two frequencies, the zeroth order is frequency shifted by $-80\mathrm{MHz}$ before recombination. The experiment typically starts with the single-pass (SP) AOM on and the DP AOM off. When driving the Raman transition, the rf powers for both AOMs are ramped simultaneously to achieve the desired optical power at both frequencies, while keeping the total optical power fixed. Abbreviations: PBS—polarization beam splitter and AOM—acousto-optic modulator.

Figure 3

Coherent transfer of atoms to molecules. The molecular state is dark to the imaging step and corresponds to zero signal. (a) Raman difference frequency scans for various durations showing the resonance as a function of the detuning from the fitted resonance at 770.5715(1) MHz, near the calculated value of 763 MHz. (b) Raman pulse-length scan on resonance. A decaying Rabi oscillation shows the coherence of the Raman transfer process. A model is fitted to (a) and (b) to determine the Raman Rabi frequency and loss rates. Inset: geometry and polarization of trap and Raman beam relative to the magnetic field. The 3.25 mW beam is focused to a waist of $0.9\mu \mathrm{m}$ that confines the atoms and molecule. A perpendicular $B_0=8.83(2)\mathrm{G}$ magnetic field defines the quantization axis and the atoms experience predominantly $\pi$-polarized light.

Figure 4

Raman transition parameters as a function of tweezer power and detuning. (a) The Raman resonance ${\omega }_R$ fitted to $a_P+b_P/\mathrm{\Delta }$, where $a_P$ and $b_P=({\mathrm{\Omega }}_a^2-{\mathrm{\Omega }}_m^2)/2$ are the power ($P$) dependent background and $v^{\prime }=0$ contributions to the light shift and $\mathrm{\Delta }\equiv 2\pi \times (f_{\mathrm{PA}0}-f_{\text{tweezer}})$ is the detuning from the $v^{\prime }=0$ resonance frequency $f_{\mathrm{PA}0}$. $a_P$ is fitted to a model including linear and small quadratic light shift to obtain the Raman resonance frequency at zero tweezer power ${\omega }_{R0}=2\pi \times 770.1969(2)\mathrm{MHz}$, where the statistical uncertainty is shown. (b) Raman Rabi frequency ${\mathrm{\Omega }}_R$ fitted to $c_P+d_P/\mathrm{\Delta }$, where $c_P$ and $d_P={\mathrm{\Omega }}_a{\mathrm{\Omega }}_m/2$ are the background and $v^{\prime }=0$ contributions that scale as $P^{1.29}$. The detuning is calculated from $f_{\mathrm{PA}0}$ fitted in (a). Fit parameters are listed in Table 1. (c) Tweezer power dependency of ${\mathrm{\Omega }}_m$ (top) and ${\mathrm{\Omega }}_a$ (bottom) calculated from $b_P$ and $d_P$ on a log-log scale showing approximate $P^{0.5}$ scaling of ${\mathrm{\Omega }}_m$ and $P^{0.79}$ scaling of ${\mathrm{\Omega }}_a$.

Figure 5

Lifetime measurements with about 3.25 mW optical power. (a) Direct measurement of molecule lifetime. Molecule survival is detected by dissociating back to atoms via a second Raman transition. The lifetime is consistent with the decay of the Rabi oscillation in Fig. 3. Inset: pulse sequence for the lifetime measurement. (b) Two-body atom lifetime of 5(1) ms limited by off-resonance photoassociation. This is used to improve the fitting of the Raman transfer data. Inset: atomic scattering rate scales as $P_{\text{tweezer}}^{2.58}\times 2\pi \times 1.05(6)\mathrm{Hz}/\mathrm{m}{\mathrm{W}}^{2.58}$ on a log-log scale; this is consistent with a two-photon scattering process.

Figure 6

Electronic transition dipole moments calculated via ab initio methods between different electronic states of NaCs. These transition dipole moments are shown in units of $e{a}_0$, where $e$ is the elementary charge and $a_0$ is the Bohr radius. They are plotted as a function of internuclear distance $R$.

Figure 7

Full calculation of the Raman Rabi frequency and scattering rate as a function of the single-photon frequency including all vibrational states of $c^3{\mathrm{\Sigma }}^{+}(\mathrm{\Omega }=1)$ and the atomic continuum. The second frequency in the Raman transition is offset by about 770 MHz and resonant with the two-photon transition. The assumed excited-state linewidth for all molecular lines is 50 MHz. The red line shows the contribution that comes only from the near-threshold states.

Figure 8

The Franck-Condon factor (FCF) between the target molecular state and vibrational state $v^{\prime }$ of $c^3{\mathrm{\Sigma }}_1^{+}$. The potential supports 74 bound states, and the predominant contribution arises from the near-threshold bound states. The total overlap with all the bound states is 0.4822, which is 96.8% of the total triplet fraction of the target molecular state.