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# Nuclear spin conservation enables state-to-state control of ultracold molecular reactions

## Abstract

Quantum-state control of reactive systems has enabled microscopic probes of underlying interaction potentials and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. Here, we realize this goal by utilizing the conservation of nuclear spins throughout the reaction. Using resonance-enhanced multiphoton ionization spectroscopy to investigate the products formed in bimolecular reactions between ultracold KRb molecules we find that the system retains a near-perfect memory of the reactants’ nuclear spins, manifested as a strong parity preference for the rotational states of the products. We leverage this effect to alter the occupation of these product states by changing the coherent superposition of initial nuclear spin states with an external magnetic field. In this way, we are able to control both the inputs and outputs of a reaction with quantum-state resolution. The techniques demonstrated here open up the possibilities to study quantum entanglement between reaction products and ultracold reaction dynamics at the state-to-state level.

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## Data availability

The data that support the findings of this study are available in Harvard Dataverse with the identifier https://doi.org/10.7910/DVN/VGHISE. Source data are provided with this paper.

## Code availability

The computer code used to analyse the data is available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank T. Rosenband for providing the code used to calculate the molecular hyperfine structure, J. Bohn for discussions, R. Vexiau for calculations of relevant molecular transitions and N. Hutzler and H. Guo for critical reading of the manuscript. This work is supported by the DOE Young Investigator Program, the David and Lucile Packard Foundation and the NSF through the Harvard-MIT CUA. M.A.N. is supported by a HQI fellowship. G.Q. acknowledges funding from the FEW2MANY-SHIELD Project No. ANR-17-CE30-0015 from Agence Nationale de la Recherche.

## Author information

Authors

### Contributions

M.-G.H., Y.L., M.A.N., L.Z. and K.-K.N. carried out the experimental work and data analysis. M.-G.H., G.Q. and O.D. performed the theoretical work. All authors contributed to interpreting the results and writing the manuscript.

### Corresponding authors

Correspondence to Ming-Guang Hu or Kang-Kuen Ni.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Chemistry thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 The optical setup for generating the REMPI beams.

The 648/674 nm and 532 nm lasers are combined on a dichroic mirror, and are then sent through a dark mask (Thorlabs R1DF100) and an achromatic lens (focal length = 300 mm). The resulting beam profiles in the image plane have a 1 mm outer diameter and a 100 μm inner diameter.

### Extended Data Fig. 2 REMPI spectrum for 40K2 product molecules at 30 G.

By scanning the 648 nm laser frequency to search for rotational lines within the $${X}^{1}\mathop{\sum }\nolimits_{g}^{+}\left(v=0,{N}_{{{\rm{K}}}_{2}}\right)\ \to \ {B}^{1}{\prod }_{u}\left({v}^{\prime}=1,{N}_{{{\rm{K}}}_{2}}^{\prime }\right)$$ vibronic band, we observe strong $${{\mathrm{K}}_{2}}^{+}$$ signals at frequencies corresponding to rotational states with even values of $${N}_{{{\rm{K}}}_{2}}$$ (red filled circles), and highly suppressed signals for odd values (black open circles). The ion count for each data point is normalized by the corresponding number of experimental cycles (~ 16); the error bars denote shot noise. For $${N}_{{{\rm{K}}}_{2}}>0$$, we drive transitions with $${N}_{{{\rm{K}}}_{2}}^{\prime }-{N}_{{{\rm{K}}}_{2}}=0$$ (Q branch), whereas for $${N}_{{{\rm{K}}}_{2}}=0$$, we drive the only allowed transition, with $${N}_{{{\rm{K}}}_{2}}^{\prime }-{N}_{{{\rm{K}}}_{2}}=1$$ (R branch). Blue dashed lines indicate the predicted transition frequencies. We do not observe any signals at frequencies corresponding to states with $${N}_{{{\rm{K}}}_{2}}>12$$. Gaussian fits (black curves) are applied to each signal peak, yielding a typical spectral linewidth (1σ) of ~ 50 MHz.

### Extended Data Fig. 3 REMPI spectrum for 87Rb2 product molecules at 30 G.

The frequency of the 674 nm laser is scanned within the $${X}^{1}\mathop{\sum }\nolimits_{g}^{+}(v=0,{N}_{{{\rm{Rb}}}_{2}})\ \to \ {B}^{1}{\prod }_{u}({v}^{\prime}=4,{N}_{{{\rm{Rb}}}_{2}}^{\prime })$$ vibronic band. We observe strong $${{\mathrm{Rb}}_{2}}^{+}$$ signals for transitions from odd rotational states (blue filled circles), and highly suppressed signals from even ones (black open circles). The ion count for each data point is normalized by the corresponding number of experimental cycles (~ 16); the error bars denote shot noise. We drive Q branch transitions for $${N}_{{{\rm{Rb}}}_{2}}>0$$, and R branch for $${N}_{{{\rm{Rb}}}_{2}}=0$$. Blue dashed lines indicate the predicted transition frequencies. We do not observe any signals at frequencies corresponding to states with $${N}_{{{\rm{Rb}}}_{2}}>19$$. Gaussian fits (black curves) are applied to each signal peak, yielding a typical spectral linewidth (1σ) of ~ 40 MHz.

### Extended Data Fig. 4 REMPI spectrum for 87Rb2 product molecules at 5 G.

The frequency of the 674 nm laser is scanned within the $${X}^{1}\mathop{\sum }\nolimits_{g}^{+}(v=0,{N}_{{{\rm{Rb}}}_{2}})\ \to \ {B}^{1}{\prod }_{u}({v}^{\prime}=6,{N}_{{{\rm{Rb}}}_{2}}^{\prime })$$ vibronic band. We observe strong $${{\mathrm{Rb}}_{2}}^{+}$$ signals for transitions from both even (red filled circles) and odd (blue filled circles) rotational states. The ion count for each data point is normalized by the corresponding number of experimental cycles (~ 20); the error bars denote shot noise. We drive Q branch transitions for $${N}_{{{\rm{Rb}}}_{2}}>0$$, and R branch for $${N}_{{{\rm{Rb}}}_{2}}=0$$. Blue dashed lines indicate the predicted transition frequencies. We do not observe any signals at frequencies corresponding to states with $${N}_{{{\rm{Rb}}}_{2}}>20$$. Gaussian fits (black curves) are applied to each signal peak, yielding a typical spectral linewidth (1σ) of ~ 40 MHz.

## Source data

### Source Data Fig. 2

Product State Distribution Source Data of $${{\mathrm{K}}_{2}}^{+}$$

### Source Data Fig. 3

Product State Distribution Source Data of $${{\mathrm{Rb}}_{2}}^{+}$$

### Source Data Fig. 4

B Field Control Source Data

### Source Data Extended Data Fig. 2

REMPI Spectrum Source Data of $${{\mathrm{K}}_{2}}^{+}$$ at 30 G

### Source Data Extended Data Fig. 3

REMPI Spectrum Source Data of $${{\mathrm{Rb}}_{2}}^{+}$$ at 30 G

### Source Data Extended Data Fig. 4

REMPI Spectrum Source Data of $${{\mathrm{Rb}}_{2}}^{+}$$ at 5 G

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Hu, MG., Liu, Y., Nichols, M.A. et al. Nuclear spin conservation enables state-to-state control of ultracold molecular reactions. Nat. Chem. 13, 435–440 (2021). https://doi.org/10.1038/s41557-020-00610-0

• Accepted:

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• DOI: https://doi.org/10.1038/s41557-020-00610-0

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