GoKawiilMolecule generation
Our experiment is performed on a mixed-species two-ion crystal consisting of 40Ca+ and 40CaOH+ confined in a linear Paul trap28. To form such a crystal, we first load two 40Ca+ ions and then leak in water vapour with a leak valve from a gas chamber that contains mainly water vapour with a pressure of around 10−6 mbar. In the process, we apply 397 nm laser that drives the 42S 1/2 → 42P 1/2 dipole transition in 40Ca+ to cool the ion crystal and monitor the fluorescence from 40Ca+ ions with a camera. As the molecule does not fluoresce, the generation of a molecular ion leads to one of the ions turning dark on the camera. When this is observed, we switch off the leak valve and perform mass spectrometry on the dark ion by measuring the motional frequency of the ion crystal24 to verify the generation of CaOH+. In general, it takes around 5 min to form a molecule. After closing the valve, the pressure in the vacuum chamber returns to around 10−10 mbar within a few minutes.
After generating the mixed-species ion crystal, background gas collisions occur, leading to the atomic and molecular ions swapping positions on the timescale of several seconds. For cat-state spectroscopy measurements, we work with only one of the two-ion crystal configurations because the two configurations exhibit different motional frequencies. This is probably due to imperfect micromotion compensation24. We detect the ion crystal configuration during Doppler cooling before the spectroscopy sequence and attempt to alter the configuration randomly if the wrong configuration is detected. This is done by displacing the ion crystal radially from its trapping position. We repeat this procedure until the ions return to the correct configuration.
Cat-state engineering
The non-classical motional state for probing photon recoil is generated by a bichromatic laser beam applied to the 40Ca+ ion. The two frequency components of equal intensity in the bichromatic beam are detuned by −ω z and +ω z from the atomic quadrupole transition between |↑⟩ and |↓⟩, with ω z being the in-phase motional frequency of the ion crystal4. The Lamb–Dicke parameter of this quadrupole transition in the experiment is given by
$${\eta }_{{\rm{a}}}=\sqrt{\frac{\hbar }{2{M}_{{\rm{a}}}{\omega }_{z}}}{k}_{z,{\rm{a}}}{e}_{z,{\rm{a}}},$$ (7)
where M a is the atomic mass, \({k}_{z,{\rm{a}}}\) is the wavevector component of the quadrupole transition laser along the trap axis, and \({e}_{z,{\rm{a}}}\) is the participation factor of the atomic ion in the in-phase mode. In the Lamb–Dicke regime, the light–ion interaction Hamiltonian can be written as38
$${\hat{H}}_{{\rm{int}}}=\hbar {\eta }_{{\rm{a}}}\frac{{\varOmega }_{0}}{2}({\hat{\sigma }}_{+}\hat{a}{{\rm{e}}}^{{\rm{i}}{\phi }_{{\rm{r}}}}+{\hat{\sigma }}_{+}{\hat{a}}^{\dagger }{{\rm{e}}}^{{\rm{i}}{\phi }_{{\rm{b}}}}+\text{h.c.}),$$ (8)
where Ω 0 is the Rabi frequency, \({\hat{a}}^{\dagger }\) is the creation operator and \(\hat{a}\) is the annihilation operator of the harmonic oscillator describing in-phase motion, ϕ r and ϕ b are the phases of the frequency components with detuning −ω z and +ω z , respectively, in the light field, and h.c. is Hermitian conjugate. This corresponds to a spin-dependent displacement characterized by ϕ ± = (ϕ b ± ϕ r )/2, given by
$$\begin{array}{l}{\hat{H}}_{{\rm{int}}}=\hbar {\eta }_{{\rm{a}}}\frac{{\varOmega }_{0}}{2}({\hat{\sigma }}_{x}\cos {\phi }_{+}-{\hat{\sigma }}_{y}\sin {\phi }_{+})\\ \,\,\,\left[{\rm{i}}(-\hat{a}+{\hat{a}}^{\dagger })\sin {\phi }_{-}+(\hat{a}+{\hat{a}}^{\dagger })\cos {\phi }_{-}\right].\end{array}$$ (9)
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