Probing Topological Spin Liquids on a Programmable Quantum Simulator (2104.04119v1)

Abstract: Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several decades. Such phases feature long-range quantum entanglement that can potentially be exploited to realize robust quantum computation. We use a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms are placed on the links of a kagome lattice and evolution under Rydberg blockade creates frustrated quantum states with no local order. The onset of a quantum spin liquid phase of the paradigmatic toric code type is detected by evaluating topological string operators that provide direct signatures of topological order and quantum correlations. Its properties are further revealed by using an atom array with nontrivial topology, representing a first step towards topological encoding. Our observations enable the controlled experimental exploration of topological quantum matter and protected quantum information processing.

• The paper demonstrates experimental realization of quantum spin liquids using a 219-atom Rydberg array, revealing robust topological order.
• It employs precise two-photon optical transitions and Rydberg blockade techniques to simulate dimer coverings and measure nonlocal string operators.
• The work offers actionable insights for fault-tolerant quantum computation by dynamically preparing states beyond equilibrium models.

Probing Topological Spin Liquids on a Programmable Quantum Simulator

This paper explores the experimental realization and paper of quantum spin liquids (QSLs) on a programmable quantum simulator, specifically using a 219-atom Rydberg atom array. The work is predicated on the theoretical concept of QSLs, which are phases of matter with topological order and characterized by long-range quantum entanglement. Such entanglement offers potential applications in robust quantum computation, particularly via topological quantum error correction.

Quantum Simulator and Experimental Techniques

The researchers employ Rydberg atom arrays arranged in the geometric configuration of a kagome lattice, which naturally facilitates the frustration necessary for QSL states. The underlying mechanism for the emergent QSL is the Rydberg blockade, which restricts simultaneous excitation of neighboring atoms, thus promoting states reminiscent of the toric code model. The Rydberg blockade creates entangled quantum states by preventing local order and allowing the system to explore a superposition of configurations.

The methodological innovation consists of using a two-photon optical transition to manipulate the Rydberg states, along with controlling lattice spacings and blockade radii to emulate a dimer model at desired filling fractions. This careful tuning allows researchers to generate states that are analogous to dimer coverings, a haLLMark of QSLs. The evolution of the system is monitored by projective measurements after a quasi-adiabatic sweep, transitioning the system from a trivial phase to a state with QSL characteristics.

Topological Order and String Operators

To distinguish a QSL from other phases, the paper focuses on nonlocal observables known as topological string operators. Two primary operators are measured: a diagonal string operator $Z$, indicating the presence of dimers, and an off-diagonal string operator $X$, probing quantum coherence between dimer states. The execution of a strategic "basis rotation," achieved through post-evolution Rydberg Hamiltonian manipulations, allows the researchers to measure the $X$ operator, thus confirming the presence of coherent superpositions necessary for a QSL.

Phases and Quasiparticles

The article also delineates how different parameter sets lead to states with properties of a QSL versus those of valence bond solid (VBS) or trivial phases. A meticulous examination is conducted using string order parameters from Bricmont, Frölich, Fredenhagen, and Marcu (BFFM) to define phase boundaries. Notably, the paper highlights how different effective filling and detuning values impact the emergence of monomers or "e-anyons" and how these defects manifest in experimental systems.

Computational and Experimental Alignment

Through both experimental observations and numerical simulations using density-matrix-renormalization-group (DMRG) techniques, the paper concludes that while equilibrium properties of the underlying model may favor a VBS in ground state scenarios, dynamical state preparation tends to favor QSL characteristics, presumably owing to the freezing-out of magnetic ($m$-anyon) excitations. This reveals a potential metastability and a unique class of states not captured by equilibrium models but accessible through non-equilibrium state preparation.

Implications and Future Directions

These findings corroborate the theoretical predictions about the robustness of topological states even under non-ideal conditions, enabling them to be potential candidates for fault-tolerant quantum computing. Extending this research, experimental frameworks could pivot towards realizing more complex lattice geometries, incorporating more diverse interaction terms, or exploring systems with deliberate defects or nontrivial topologies to manipulate topological qubits. Moreover, the research paves the way for higher-fidelity operations through improved laser control and coherence times.

This work marks a significant advancement in both the experimental techniques available for probing QSLs and our understanding of their physics in practical systems, suggesting a promising future for topologically protected quantum information processing. Future exploration into mitigating environmental decoherence and enhancing quasi-adiabatic preparation protocols may deepen insight into QSLs and other topologically ordered phases, bolstering the exploration of new states of matter within quantum simulators.