Langen, T., Valtolina, G., Wang, D. & Ye, J. Quantum state manipulation and science of ultracold molecules. Nat. Phys. 20, 702â712 (2024).
Cornish, S. L., Tarbutt, M. R. & Hazzard, K. R. A. Quantum computation and quantum simulation with ultracold molecules. Nat. Phys. 20, 730â740 (2024).
Gorshkov, A. V. et al. Tunable superfluidity and quantum magnetism with ultracold polar molecules. Phys. Rev. Lett. 107, 115301 (2011).
Li, J.-R. et al. Tunable itinerant spin dynamics with polar molecules. Nature 614, 70â74 (2023).
Christakis, L. et al. Probing site-resolved correlations in a spin system of ultracold molecules. Nature 614, 64â69 (2023).
Carroll, A. N. et al. Observation of coherent generalized t-J spin dynamics with tunable dipolar interactions. Preprint at https://doi.org/10.48550/arXiv.2404.18916 (2024).
Choi, J. et al. Robust dynamic Hamiltonian engineering of many-body spin systems. Phys. Rev. X 10, 031002 (2020).
Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138â5143 (1993).
Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).
Sundar, B., Gadway, B. & Hazzard, K. R. A. Synthetic dimensions in ultracold polar molecules. Sci. Rep. 8, 3422 (2018).
Zhou, H. et al. Robust Hamiltonian Engineering for Interacting Qudit Systems. Phys. Rev. X 14, 031017 (2024).
Viola, L. & Lloyd, S. Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733â2744 (1998).
Viola, L., Knill, E. & Lloyd, S. Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417â2421 (1999).
Souza, A. M., Ãlvarez, G. A. & Suter, D. Robust dynamical decoupling for quantum computing and quantum memory. Phys. Rev. Lett. 106, 240501 (2011).
Zhou, H. et al. Robust higher-order Hamiltonian engineering for quantum sensing with strongly interacting systems. Phys. Rev. Lett. 131, 220803 (2023).
Weitenberg, C. & Simonet, J. Tailoring quantum gases by Floquet engineering. Nat. Phys. 17, 1342â1348 (2021).
Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013).
Kwan, J. et al. Realization of 1D anyons with arbitrary statistical phase. Preprint at https://doi.org/10.48550/arxiv.2306.01737 (2023).
Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221â225 (2017).
Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217â220 (2017).
Geier, S. et al. Floquet Hamiltonian engineering of an isolated many-body spin system. Science 374, 1149â1152 (2021).
Martin, L. S. et al. Controlling local thermalization dynamics in a Floquet-engineered dipolar ensemble. Phys. Rev. Lett. 130, 210403 (2023).
Schuster, T. et al. Floquet engineering ultracold polar molecules to simulate topological insulators. Phys. Rev. A 103, 063322 (2021).
Zhang, X., Hu, Z. & Liu, Y.-C. Fast generation of GHZ-like states using collective-spin XYZ model. Phys. Rev. Lett. 132, 113402 (2024).
Liu, Y. C., Xu, Z. F., Jin, G. R. & You, L. Spin squeezing: transforming one-axis twisting into two-axis twisting. Phys. Rev. Lett. 107, 013601 (2011).
Carr, H. Y. & Purcell, E. M. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94, 630â638 (1954).
Waugh, J. S., Huber, L. M. & Haeberlen, U. Approach to high-resolution NMR in solids. Phys. Rev. Lett. 20, 180â182 (1968).
Peng, P., Yin, C., Huang, X., Ramanathan, C. & Cappellaro, P. Floquet prethermalization in dipolar spin chains. Nat. Phys. 17, 444â447 (2021).
Nguyen, L. B. et al. Programmable Heisenberg interactions between Floquet qubits. Nat. Phys. https://doi.org/10.1038/s41567-023-02326-7 (2024).
Scholl, P. et al. Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms. PRX Quantum 3, 020303 (2022).
Zu, C. et al. Emergent hydrodynamics in a strongly interacting dipolar spin ensemble. Nature 597, 45â50 (2021).
Morong, W. et al. Engineering dynamically decoupled quantum simulations with trapped ions. PRX Quantum 4, 010334 (2023).
Chotia, A. et al. Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice. Phys. Rev. Lett. 108, 080405 (2012).
Moses, S. A. et al. Creation of a low-entropy quantum gas of polar molecules in an optical lattice. Science 350, 659â662 (2015).
Picard, L. R. B., Patenotte, G. E., Park, A. J., Gebretsadkan, S. F. & Ni, K.-K. Site-selective preparation and multi-state readout of molecules in optical tweezers. PRX Quantum 5, 020344 (2024).
Ruttley, D. K., Guttridge, A., Hepworth, T. R. & Cornish, S. L. Enhanced quantum control of individual ultracold molecules using optical tweezer arrays. PRX Quantum 5, 020333 (2024).
Bao, Y. et al. Dipolar spin-exchange and entanglement between molecules in an optical tweezer array. Science 382, 1138â1143 (2023).
Holland, C. M., Lu, Y. & Cheuk, L. W. On-demand entanglement of molecules in a reconfigurable optical tweezer array. Science https://doi.org/10.1126/science.adf4272 (2023).
Anderegg, L. et al. An optical tweezer array of ultracold molecules. Science 365, 1156â1158 (2019).
Kaufman, A. M. & Ni, K.-K. Quantum science with optical tweezer arrays of ultracold atoms and molecules. Nat. Phys. 17, 1324â1333 (2021).
Yan, B. et al. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature 501, 521â525 (2013).
Tobias, W. G. et al. Reactions between layer-resolved molecules mediated by dipolar spin exchange. Science 375, 1299â1303 (2022).
Neyenhuis, B. et al. Anisotropic polarizability of ultracold polar 40K87Rb molecules. Phys. Rev. Lett. 109, 230403 (2012).
SeeÃelberg, F. et al. Extending rotational coherence of interacting polar molecules in a spin-decoupled magic trap. Phys. Rev. Lett. 121, 253401 (2018).
Park, A. J. et al. Extended rotational coherence of polar molecules in an elliptically polarized trap. Phys. Rev. Lett. 131, 183401 (2023).
Burchesky, S. et al. Rotational coherence times of polar molecules in optical tweezers. Phys. Rev. Lett. 127, 123202 (2021).
Gregory, P. D. et al. Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules. Nat. Phys. https://doi.org/10.1038/s41567-023-02328-5 (2024).
Brennen, G. K., Micheli, A. & Zoller, P. Designing spin-1 lattice models using polar molecules. New J. Phys. 9, 138 (2007).
Ospelkaus, S. et al. Controlling the hyperfine state of Rovibronic ground-state polar molecules. Phys. Rev. Lett. 104, 030402 (2010).
Hazzard, K. R. A. et al. Many-body dynamics of dipolar molecules in an optical lattice. Phys. Rev. Lett. 113, 195302 (2014).
Altman, E. et al. Quantum simulators: architectures and opportunities. PRX Quantum 2, 017003 (2021).
Luo, C. et al. Hamiltonian engineering of collective XYZ spin models in an optical cavity: from one-axis twisting to two-axis counter twisting models. Preprint at https://doi.org/10.48550/arxiv.2402.19429 (2024).
Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037â1069 (2005).
Haeberlen, U. & Waugh, J. S. Coherent averaging effects in magnetic resonance. Phys. Rev. 175, 453â467 (1968).
Gorshkov, A. V. et al. Quantum magnetism with polar alkali-metal dimers. Phys. Rev. A 84, 033619 (2011).
de Paz, A. et al. Nonequilibrium quantum magnetism in a dipolar lattice gas. Phys. Rev. Lett. 111, 185305 (2013).
Bilitewski, T. et al. Dynamical generation of spin squeezing in ultracold dipolar molecules. Phys. Rev. Lett. 126, 113401 (2021).
Tyler, M., Zhou, H., Martin, L. S., Leitao, N. & Lukin, M. D. Higher-order methods for Hamiltonian engineering pulse sequence design. Phys. Rev. A 108, 062602 (2023).
Signoles, A. et al. Glassy dynamics in a disordered Heisenberg quantum spin system. Phys. Rev. X 11, 011011 (2021).
Borregaard, J., Davis, E. J., Bentsen, G. S., Schleier-Smith, M. H. & Sørensen, A. S. One- and two-axis squeezing of atomic ensembles in optical cavities. New J. Phys. 19, 093021 (2017).
Kajtoch, D. & Witkowska, E. Quantum dynamics generated by the two-axis countertwisting Hamiltonian. Phys. Rev. A 92, 013623 (2015).
Muñoz-Arias, M. H., Deutsch, I. H. & Poggi, P. M. Phase-space geometry and optimal state preparation in quantum metrology with collective spins. PRX Quantum 4, 020314 (2023).
Hald, J., Sørensen, J. L., Schori, C. & Polzik, E. S. Spin squeezed atoms: a macroscopic entangled ensemble created by light. Phys. Rev. Lett. 83, 1319â1322 (1999).
Geier, S. et al. Time-reversal in a dipolar quantum many-body spin system. Preprint at https://doi.org/10.48550/arxiv.2402.13873 (2024).
Davis, E., Bentsen, G. & Schleier-Smith, M. Approaching the Heisenberg limit without single-particle detection. Phys. Rev. Lett. 116, 053601 (2016).
Ni, K.-K. et al. A high phase-space-density gas of polar molecules. Science 322, 231â235 (2008).
De Marco, L. et al. A degenerate Fermi gas of polar molecules. Science 363, 853â856 (2019).
Knill, E. et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008).
Wu, Y., Kolkowitz, S., Puri, S. & Thompson, J. D. Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays. Nat. Commun. 13, 4657 (2022).
Griffiths, D. J. Introduction to Quantum Mechanics (Cambridge Univ. Press, 2017).
