Floquet Hamiltonian engineering of an isolated many-body spin system

Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules

Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions1,2. The precise tunability3 of Ising and spin-exchange interactions with both microwave and d.c. electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics4-6. Here we used Floquet engineering7 to realize new quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold 40K87Rb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a d.c. electric field through observations of Ramsey contrast dynamics. This validation sets the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting8 mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in two-dimensional layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement9 or could take advantage of the rich molecular structure for quantum simulation of multi-level systems10,11.

Antiferromagnetic Bosonic t-J Models and Their Quantum Simulation in Tweezer Arrays

The combination of optical tweezer arrays with strong interactions-via dipole exchange of molecules and Van der Waals interactions of Rydberg atoms-has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants. This will enable one to simulate the physics believed to underlie many strongly correlated quantum materials. Here, we propose an experimental scheme to realize bosonic t-J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-T_{c} cuprates can be realized. Since the ground states of the 2D bosonic AFM t-J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants-the simplest instance in which their bosonic statistics plays a role-and compare our results to the fermionic case. We perform large-scale density matrix renormalization group calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t-J models may contain similar physics as the collective phases in strongly correlated electrons.

Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system

It is challenging to probe ergodicity breaking trends of a quantum many-body system when dissipation inevitably damages quantum coherence originated from coherent coupling and dispersive two-body interactions. Rydberg atoms provide a test bed to detect emergent exotic many-body phases and nonergodic dynamics where the strong Rydberg atom interaction competes with and overtakes dissipative effects even at room temperature. Here, we report experimental evidence of a transition from ergodic toward ergodic breaking dynamics in driven-dissipative Rydberg atomic gases. The broken ergodicity is featured by the long-time phase oscillation, which is attributed to the formation of Rydberg excitation clusters in limit cycle phases. The broken symmetry in the limit cycle is a direct manifestation of many-body collective effects, which is verified experimentally by tuning atomic densities. The reported result reveals that Rydberg many-body systems are a promising candidate to probe ergodicity breaking dynamics, such as limit cycles, and enable the benchmark of nonequilibrium phase transition.

Robust Higher-Order Hamiltonian Engineering for Quantum Sensing with Strongly Interacting Systems

Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most ac sensing sequences involve a periodic echolike structure, in which the target signal is synchronized with the echo period. We show that for strongly interacting systems, this construction leads to a fundamental sensitivity limit associated with imperfect interaction decoupling. We present a simple physical picture demonstrating the origin of this limitation, and further formalize these considerations in terms of concise higher-order decoupling rules. We then show how these limitations can be surpassed by identifying a novel sequence building block, in which the signal period matches twice the echo period. Using these decoupling rules and the resulting sequence building block, we experimentally demonstrate significant improvements in dynamical decoupling timescales and magnetic field sensitivity, opening the door for new applications in quantum sensing and quantum many-body physics.

Floquet-tailored Rydberg interactions

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Quasi-Floquet Prethermalization in a Disordered Dipolar Spin Ensemble in Diamond

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing nonequilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing nonequilibrium phenomena in quasiperiodically driven systems.

Picosecond-Scale Ultrafast Many-Body Dynamics in an Ultracold Rydberg-Excited Atomic Mott Insulator

We report the observation and control of ultrafast many-body dynamics of electrons in ultracold Rydberg-excited atoms, spatially ordered in a three-dimensional Mott insulator (MI) with unity filling in an optical lattice. By mapping out the time-domain Ramsey interferometry in the picosecond timescale, we can deduce entanglement growth indicating the emergence of many-body correlations via dipolar forces. We analyze our observations with different theoretical approaches and find that the semiclassical model breaks down, thus indicating that quantum fluctuations play a decisive role in the observed dynamics. Combining picosecond Rydberg excitation with MI lattice thus provides a platform for simulating nonequilibrium dynamics of strongly correlated systems in synthetic ultracold atomic crystals, such as in a metal-like quantum gas regime.

Floquet space exploration for the dual-dressing of a qubit

The application of a periodic nonresonant drive to a system allows the Floquet engineering of effective fields described by a broad class of quantum simulated Hamiltonians. The Floquet evolution is based on two different elements. The first one is a time-independent or stroboscopic evolution with an effective Hamiltonian corresponding to the quantum simulation target. The second element is the time evolution at the frequencies of the nonresonant driving and of its harmonics, denoted as micromotion. We examine experimentally and theoretically the harmonic dual-dressing Floquet engineering of a cold atomic two-level sample. Our focus is the dressing operation with small bare energies and large Rabi frequencies, where frequencies and amplitudes of the stroboscopic/micromotion time evolutions are comparable. At the kHz range of our dressed atom oscillations, we probe directly both the stroboscopic and micromotion components of the qubit global time evolution. We develop ad-hoc monitoring tools of the Floquet space evolution. The direct record of the time evolution following a pulsed excitation demonstrates the interplay between the two components of the spin precession in the Floquet space. From the resonant pumping of the dressed system at its evolution frequencies, Floquet eigenenergy spectra up to the fifth order harmonic of the dressing frequency are precisely measured as function of dressing parameters. Dirac points of the Floquet eigenenergies are identified and, correspondingly, a jump in the dynamical phase shift is measured. The stroboscopic Hamiltonian eigenfrequencies are measured also from the probe of the micromotion sidebands.These monitoring tools are appropriate for quantum simulation/computation investigations. Our results evidence that the stroboscopic phase shift of the qubit wavefunction contains an additional information that opens new simulation directions.

Realizing spin squeezing with Rydberg interactions in an optical clock

Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1-3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6-11. Here we combine these applications to realize spin squeezing-a widely studied operation for producing metrologically useful entanglement-in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10-15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10-17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12-16.

Scalable spin squeezing in a dipolar Rydberg atom array

The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems to enhance the precision of measurements beyond the standard quantum limit1,2. To do so, one can reshape the quantum projection noise-a strategy known as squeezing3,4. In the context of many-body spin systems, one typically uses all-to-all interactions (for example, the one-axis twisting model4) between the constituents to generate the structured entanglement characteristic of spin squeezing5. Here we explore the prediction, motivated by recent theoretical work6-10, that short-range interactions-and in particular, the two-dimensional dipolar XY model-can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to N = 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of -3.5 ± 0.3 dB (before correcting for detection errors, or roughly -5 ± 0.3 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by roughly 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics.

Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays

Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding nonunitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models. We provide a protocol for observing the YLES by detecting kinked dynamical magnetization responses due to broken PT symmetry, thus enabling the physical probing of nonunitary phase transitions in nonequilibrium settings. In particular, scaling analyses based on our nonunitary time evolution circuit with matrix product states accurately recover the exponents uniquely associated with the corresponding nonunitary CFT. We provide an explicit proposal for observing YLES criticality in Floquet quenched Rydberg atomic arrays with laser-induced loss, which paves the way towards a universal platform for simulating non-Hermitian many-body dynamical phenomena.

Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models

We study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.

Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble

Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by exploiting its inherent disorder and use this to uncover the thermalization mechanisms in a three-dimensional, dipolar-interacting spin system with tunable interactions. Utilizing advanced Hamiltonian engineering techniques to explore a range of spin Hamiltonians, we observe a striking change in the characteristic shape and timescale of local correlation decay as we vary the engineered exchange anisotropy. We show that these observations originate from the system's intrinsic many-body dynamics and reveal the signatures of conservation laws within localized clusters of spins, which do not readily manifest using global probes. Our method provides an exquisite lens into the tunable nature of local thermalization dynamics and enables detailed studies of scrambling, thermalization, and hydrodynamics in strongly interacting quantum systems.

Rydberg Macrodimers: Diatomic Molecules on the Micrometer Scale

Controlling molecular binding at the level of single atoms is one of the holy grails of quantum chemistry. Rydberg macrodimers─bound states between highly excited Rydberg atoms─provide a novel perspective in this direction. Resulting from binding potentials formed by the strong, long-range interactions of Rydberg states, Rydberg macrodimers feature bond lengths in the micrometer regime, exceeding those of conventional molecules by orders of magnitude. Using single-atom control in quantum gas microscopes, the unique properties of these exotic states can be studied with unprecedented control, including the response to magnetic fields or the polarization of light in their photoassociation. The high accuracy achieved in spectroscopic studies of macrodimers makes them an ideal testbed to benchmark Rydberg interactions, with direct relevance to quantum computing and information protocols where these are employed. This review provides a historic overview and summarizes the recent findings in the field of Rydberg macrodimers. Furthermore, it presents new data on interactions between macrodimers, leading to a phenomenon analogous to Rydberg blockade at the level of molecules, opening the path toward studying many-body systems of ultralong-range Rydberg molecules.

Tunable itinerant spin dynamics with polar molecules

Strongly interacting spins underlie many intriguing phenomena and applications^1-4 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 attraction^5,6. 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 capabilities^7-13. 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.

Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties^1-11. These include a large set of internal states with long coherence times^12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids¹⁸, quantum spin liquids¹⁹, fractional Chern insulators²⁰ and quantum magnets^21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy²³ to measure the site-resolved dynamics of quantum correlations of polar ²³Na⁸⁷Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model^21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses^26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation^29,30 and metrology³¹.

Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids

Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.

Subdiffusive hydrodynamics of nearly integrable anisotropic spin chains

We address spin transport in the easy-axis Heisenberg spin chain subject to different integrability-breaking perturbations. We find subdiffusive spin transport characterized by dynamical exponent z = 4 up to a timescale parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for finite anisotropy, one eventually recovers diffusion at late times but with a diffusion constant independent of the strength of the perturbation and solely fixed by the value of the anisotropy. We provide numerical evidence for these findings, and we show how they can be understood in terms of the dynamical screening of the relevant quasiparticle excitations and effective dynamical constraints. Our results show that the diffusion constant of near-integrable diffusive spin chains is generically not perturbative in the integrability-breaking strength.

Floquet Hamiltonian engineering of an isolated many-body spin system

[Figure: see text].