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arXiv:2404.18916 · Science

Observation of generalized t-J spin dynamics with tunable dipolar interactions

Annette N. Carroll, Henrik Hirzler, Calder Miller, David Wellnitz, Sean R. Muleady, Junyu Lin, Krzysztof P. Zamarski, Reuben R. W. Wang, John L. Bohn, Ana María Rey, Jun Ye

Published Apr 24, 2025• 38 citations
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Abstract

Long-range and anisotropic dipolar interactions profoundly modify the dynamics of particles hopping in a periodic lattice potential. We report the realization of a generalized t-J model with dipolar interactions using a system of ultracold fermionic molecules with spin encoded in the two lowest rotational states. We independently tuned the dipolar Ising and spin-exchange couplings and the molecular motion and studied their interplay on coherent spin dynamics. Using Ramsey spectroscopy, we observed and modeled interaction-driven contrast decay that depends strongly both on the strength of the anisotropy between Ising and spin-exchange couplings and on motion. This study paves the way for future exploration of kinetic spin dynamics and quantum magnetism with highly tunable molecular platforms in regimes that are challenging for existing numerical and analytical methods.

DOI
10.1126/science.adq0911

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Long-range and anisotropic dipolar interactions profoundly modify the dynamics of particles hopping in a periodic lattice potential. We report the realization of a generalized t-J model with dipolar interactions using a system of ultracold fermionic molecules with spin encoded in the two lowest rotational states. We independently tuned the dipolar Ising and spin-exchange couplings and the molecular motion and studied their interplay on coherent spin dynamics. Using Ramsey spectroscopy, we observed and modeled interaction-driven contrast decay that depends strongly both on the strength of the anisotropy between Ising and spin-exchange couplings and on motion. This study paves the way for future exploration of kinetic spin dynamics and quantum magnetism with highly tunable molecular platforms in regimes that are challenging for existing numerical and analytical methods.
Abstract : With the production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate understanding of strongly interacting many-body quantum systems and to realize lattice spin models for exploring quantum magnetism. In ordinary atomic systems, where contact interactions require wavefunction overlap, effective spin interactions on a lattice can be mediated by tunnelling, through a process referred to as superexchange; however, the coupling is relatively weak and is limited to nearest-neighbour interactions. In contrast, dipolar interactions exist even in the absence of tunnelling and extend beyond nearest neighbours. This allows coherent spin dynamics to persist even for gases with relatively high entropy and low lattice filling. Measured effects of dipolar interactions in ultracold molecular gases have been limited to the modification of inelastic collisions and chemical reactions. Here we use dipolar interactions of polar molecules pinned in a three-dimensional optical lattice to realize a lattice spin model. Spin is encoded in rotational states of molecules that are prepared and probed by microwaves. Resonant exchange of rotational angular momentum between two molecules realizes a spin-exchange interaction. The dipolar interactions are apparent in the evolution of the spin coherence, which shows oscillations in addition to an overall decay of the coherence. The frequency of these oscillations, the strong dependence of the spin coherence time on the lattice filling factor and the effect of a multipulse sequence designed to reverse dynamics due to two-body exchange interactions all provide evidence of dipolar interactions. Furthermore, we demonstrate the suppression of loss in weak lattices due to a continuous quantum Zeno mechanism. Measurements of these tunnelling-induced losses allow us to determine the lattice filling factor independently.
We show that dipolar interactions between ultracold polar alkali-metal dimers in optical lattices can be used to realize a highly tunable generalization of the ttt-JJJ model, which we refer to as the ttt-JJJ-VVV-WWW model. The model features long-range spin-spin interactions Jz{J}_{z}Jz​ and ${J}_{\ensuremath{\perp}}$ of XXZXXZXXZ type, long-range density-density interaction VVV, and long-range density-spin interaction WWW, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling ttt. The ``spin'' is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed-matter systems. Realistic experimental imperfections are discussed.
By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the $t\mathrm{\text{\ensuremath{-}}}J$ model, which we refer to as the $t\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}W$ model. In addition to XXZXXZXXZ spin exchange, the model features density-density interactions and density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the $t\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}W$ model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.
We study a bulk fermionic dipolar molecular gas in the quantum degenerate regime confined in a two-dimensional geometry. Using two rotational states of the molecules, we encode a spin 1/2 degree of freedom. To describe the many-body spin dynamics of the molecules, we derive a long-range interacting XXZ model valid in the regime where motional degrees of freedom are frozen. Because of the spatially extended nature of the harmonic oscillator modes, the interactions in the spin model are very long ranged, and the system behaves close to the collective limit, resulting in robust dynamics and generation of entanglement in the form of spin squeezing even at finite temperature and in the presence of dephasing and chemical reactions. We discuss how the internal state structure can be exploited to realize time reversal and enhanced metrological sensing protocols.
Abstract Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87 Rb 133 Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.