Dynamical preparation of U(1) quantum spin liquids in an analogue quantum simulator
Simon Karch, Melissa Will, Irene Prieto Rodriguez, Nikolas Liebster, SeungJung Huh, Michael Knap, Frank Pollmann, Clemens Kuhlenkamp, Immanuel Bloch, Monika Aidelsburger
cond-mat.quant-gascond-mat.str-elhep-latphysics.atom-phquant-phSubmitted Apr 27, 2026• Announced Apr 28, 2026• 0 citations
Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that lack conventional order and are defined by coherent superpositions of an extensive number of many-body configurations. Realising and probing such exotic states experimentally is an outstanding challenge both in solid-state and synthetic quantum systems, not least due to the difficulty of detecting the fragile coherences between many-body states. Here, we report a large-scale (>3,000 sites) realisation of a two-dimensional U(1) lattice gauge theory with ultracold atoms in a square optical superlattice and demonstrate non-equilibrium preparation of extended regions of U(1) quantum spin liquids. We demonstrate Gauss's law validity in a quench experiment, enabled by a new microscopy technique for detecting doubly occupied sites. We observe characteristic real-space correlations and momentum-space pinch points, hallmarks of the emergent U(1) gauge structure. Using round-trip interferometric protocols, we directly observe large-scale coherence between many-body configurations, providing strong evidence for quantum spin liquid regions extending over ~100 lattice sites. Our results establish non-equilibrium quantum simulation protocols as a powerful route for accessing and probing exotic, highly-entangled states beyond those hosted by the engineered Hamiltonian in thermal equilibrium.
Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that lack conventional order and are defined by coherent superpositions of an extensive number of many-body configurations. Realising and probing such exotic states experimentally is an outstanding challenge both in solid-state and synthetic quantum systems, not least due to the difficulty of detecting the fragile coherences between many-body states. Here, we report a large-scale (>3,000 sites) realisation of a two-dimensional U(1) lattice gauge theory with ultracold atoms in a square optical superlattice and demonstrate non-equilibrium preparation of extended regions of U(1) quantum spin liquids. We demonstrate Gauss's law validity in a quench experiment, enabled by a new microscopy technique for detecting doubly occupied sites. We observe characteristic real-space correlations and momentum-space pinch points, hallmarks of the emergent U(1) gauge structure. Using round-trip interferometric protocols, we directly observe large-scale coherence between many-body configurations, providing strong evidence for quantum spin liquid regions extending over ~100 lattice sites. Our results establish non-equilibrium quantum simulation protocols as a powerful route for accessing and probing exotic, highly-entangled states beyond those hosted by the engineered Hamiltonian in thermal equilibrium.
While many-body systems can host long-ranged entangled quantum spin liquids (QSLs), the ingredients for realizing these as ground states can be prohibitively difficult. In many circumstances, one requires (i) a constrained Hilbert space and (ii) an extensive quantum superposition. The paradigmatic example is the toric code, or Z2 spin liquid, which is a superposition of closed loop states. We show how non-equilibrium Hamiltonian dynamics can provide a streamlined route toward creating such QSLs. Rather than cooling into the ground state of a Hamiltonian, we show how a simple parameter sweep can dynamically project a family of initial product states into the constrained space, giving rise to a QSL. For the toric code, this is achieved in systems with a separation in energy scales between the e- and m-anyons, where one can sweep in a way that is adiabatic (sudden) with respect to the former (latter). Although this separation of scales does not extend to the thermodynamic limit, we analytically and numerically show that this method efficiently prepares a spin liquid in finite-sized regions, which we brand ``quantum spin lakes.'' This mechanism elucidates recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. In fact, the slow dynamics of m-anyons suggest that we can capture spin lake preparation by simulating the dynamics on tree lattices, which we confirm with tensor network simulations. Finally, we use this mechanism to propose new experiments, e.g., for preparing a finite-sized U(1) spin liquid as a honeycomb Rokhsar-Kivelson dimer model using Rydberg atoms -- which is remarkable given its equilibrium counterpart is unstable in 2+1D. Our work opens up a new avenue in the study of non-equilibrium physics, as well as the exploration of exotic states of finite extent in NISQ devices.
Abstract The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss’s law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3–6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7, 8, realized mappings onto effective models to integrate out either matter or electric fields9–12, or were limited to very small systems13–16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter–gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss’s law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.
Abstract A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability. Here, we propose an experimentally feasible realization of a large-scale 2 + 1D U(1) gauge theory with dynamical matter and gauge fields in a cold-atom quantum simulator with spinless bosons. We present the full mapping of the corresponding Gauss’s law onto the bosonic computational basis. We then show that the target gauge theory can be faithfully realized and stabilized by an emergent gauge protection term in a two-dimensional single-species Bose–Hubbard optical Lieb superlattice with two spatial periods along either direction, thereby requiring only moderate experimental resources already available in current cold-atom setups. Using infinite matrix product states, we calculate numerical benchmarks for adiabatic sweeps and global quench dynamics that further confirm the fidelity of the mapping. Our work brings quantum simulators of gauge theories a significant step forward in terms of investigating particle physics in higher spatial dimensions, and is readily implementable in existing cold-atom platforms.
A system of ultracold atoms in an optical lattice provides a powerful platform for quantum simulation. In our laboratory, we use a quantum gas microscope to tune lattice parameters not only in a global scale but also at the level of individual sites. This allows us to control and detect the quantum state of interacting many-body systems as well as to engineer a broad class of Hamiltonians with high fidelity. Leveraging this versatility, we can realize several types of strongly correlated bosonic systems, which present intriguing behaviors and implement novel phases of matter. Analyzing snapshots of the atomic distribution with single-site resolution, we measure correlations and entanglement within these systems to reveal their main features, including non-equilibrium dynamics and quantum phase transitions. In this thesis, I present the works performed by our team for four different types of systems. First of all, I briefly introduce the behavior of a 1D disordered system in the critical regime between the thermal and the many-body-localized phases. In particular, we discuss what happens when a disordered and a non-disordered region are coupled via a single site. We find evidence for accelerated transport of thermal inclusion into the localized region, which shows the existence of a quantum avalanche, i.e. thermalization via accelerated transport throughout the localized system. In the second part, we realize a fractional quantum Hall state using an artificial gauge field, by implementing an adiabatic preparation protocol. We identify a topological phase transition in our system and characterize several key physical features expected for a Laughlin state by measuring density correlations and Hall conductivity. The next topic of this thesis relates to quantum magnetism. Mapping nearest hopping in a tilted optical lattice to spin flips, we realize a finite one-dimensional chain of 1/2-spins with closed boundary conditions. We perform an in-depth investigation on behaviors shown across the quantum phase transition between paramagnetic and antiferromagnetic ground states, including the evolution of the magnetization and Néel order parameter. Also, we find evidence for quantum superposition at the many-body level as a result of geometric frustration. In the last chapter, I report the experimental realization of a novel dipolar Bose-Hubbard Hamiltonian, based on a strongly tilted lattice system. When the tilt becomes the dominant energy scale, the Hamiltonian is fragmented, and the system behaves in a way that conserves dipole moment. Starting from a 1D chain of unity filled sites, we generate individual dipolar and anti-dipolar excitations at desired pinpoints. We observe quantum walks of these dipolar quasi-particles as well as their scattering dynamics, which allows us to study this new type of Hamiltonian using a bottom-up approach.
Quantum spin liquids (QSLs) are exotic phases with intrinsic massive entanglements. Instead of microscopic spins, fractionalized particles and gauge fluctuations are emergent, revealing QSLs' exotic natures. Quantum spins with strong spin-orbit coupling on a pyrochlore lattice, for example Pr2Zr2O7, are suggested to host a U(1) QSL with emergent photons, gapless excitations, as well as emergent monopoles. One of the key issues in QSLs is an interplay between emergent degrees of freedom of QSLs and conventional degrees of freedom, and we investigate the interplay by constructing a general theory of spin-lattice coupling in U(1) QSLs. We find that the coupling induces characteristic interplay between phonons and photons. For example, photons become qualitatively more stable than phonons at low temperature. We also propose mechanisms to detect emergent photons in experiments such as sound attenuation and thermal transport relying on spin-lattice coupling in U(1) QSLs.
Large-Scale 2+1D U(1) Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator
A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability. Here, we propose an experimentally feasible realization of a large-scale 2+1D U(1) gauge theory with dynamical matter and gauge fields in a cold-atom quantum simulator with spinless bosons. We present the full mapping of the corresponding Gauss's law onto the bosonic computational basis. We then show that the target gauge theory can be faithfully realized and stabilized by an emergent gauge protection term in a two-dimensional single-species Bose--Hubbard optical Lieb superlattice with two spatial periods along either direction, thereby requiring only moderate experimental resources already available in current cold-atom setups. Using infinite matrix product states, we calculate numerical benchmarks for adiabatic sweeps and global quench dynamics that further confirm the fidelity of the mapping. Our work brings quantum simulators of gauge theories a significant step forward in terms of investigating particle physics in higher spatial dimensions, and is readily implementable in existing cold-atom platforms.