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# Tunable itinerant spin dynamics with polar molecules

## Abstract

Strongly interacting spins underlie many intriguing phenomena and applications1,2,3,4 ranging from magnetism to quantum information processing. Interacting spins combined with motion show exotic spin transport phenomena, such as superfluidity arising from pairing of spins induced by spin attraction5,6. To understand these complex phenomena, an interacting spin system with high controllability is desired. Quantum spin dynamics have been studied on different platforms with varying capabilities7,8,9,10,11,12,13. Here we demonstrate tunable itinerant spin dynamics enabled by dipolar interactions using a gas of potassium-rubidium molecules confined to two-dimensional planes, where a spin-1/2 system is encoded into the molecular rotational levels. The dipolar interaction gives rise to a shift of the rotational transition frequency and a collision-limited Ramsey contrast decay that emerges from the coupled spin and motion. Both the Ising and spin-exchange interactions are precisely tuned by varying the strength and orientation of an electric field, as well as the internal molecular state. This full tunability enables both static and dynamical control of the spin Hamiltonian, allowing reversal of the coherent spin dynamics. Our work establishes an interacting spin platform that allows for exploration of many-body spin dynamics and spin-motion physics using the strong, tunable dipolar interaction.

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## Data availability

The datasets generated and analysed during the current study are available from the corresponding authors on reasonable request.

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## Acknowledgements

This material is based upon work supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. Additional support is acknowledged from the National Science Foundation grant no. QLCI OMA-2016244, the National Science Foundation grant no. Phys-1734006, and the National Institute of Standards and Technology. J.S.H. acknowledges support from the National Research Council postdoctoral fellowship. C.M. acknowledges the NDSEG Graduate Fellowship. We thank T. Bilitewski and A. M. Rey for inspirational discussions and critical reading of the manuscript.

## Author information

Authors

### Contributions

J.-R.L., K.M., C.M., A.N.C., W.G.T., J.S.H. and J.Y. all performed the experiments, analysed the data and contributed to interpreting the results and writing the manuscript.

### Corresponding authors

Correspondence to Jun-Ru Li or Jun Ye.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Nature thanks Guido Pupillo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 A typical molecular number distribution measured via layer-resolved spectroscopy.

Grey circles are the experimental measurements. Black solid line is a fit to a summation of equally spaced Gaussian functions with a global Gaussian envelope. The width of each narrow Gaussian peak is assumed to be the same. The data is taken at |E| = 1.02 kV/cm and α = 36° (magic condition) to reduce broadening of the single-layer transition linewidth due to differential polarizability.

### Extended Data Fig. 2 Noise suppression of the dynamical decoupling sequence.

Data is taken at |E| = 1.02 kV/cm and α = 0°. We use X-echo only, which provides similar performance to XY8 in terms of rejecting noise in Δ. Each data point is extracted from 10 repetitions. The dashed line is the noise floor of our measurement.

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Li, JR., Matsuda, K., Miller, C. et al. Tunable itinerant spin dynamics with polar molecules. Nature 614, 70–74 (2023). https://doi.org/10.1038/s41586-022-05479-2

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• DOI: https://doi.org/10.1038/s41586-022-05479-2