Twelve-Level Rydberg Lattice Enables Non-Abelian Thouless Pumping

Researchers affiliated with the School of Physics, Central South University, Changsha 410083, China and the Quantum Information Institute, School of Physics, Zhengzhou University, Zhengzhou 450001, China have demonstrated non-Abelian Thouless pumping within a uniquely constructed quantum system. The lattice is encoded in twelve selected microwave-coupled K39 Rydberg levels, moving beyond conventional approaches to quantum control. This system utilizes six degenerate zero-energy states to define a working subspace for manipulating quantum information, enabling a more complex form of processing than systems relying on single states. The team reports that composing two elementary pumping cycles in opposite temporal orders produces distinct projected population maps, a result consistent with noncommuting matrix-valued adiabatic operations. According to the researchers, this quantum implementation of non-Abelian Thouless pumping marks a major milestone in finite-time geometric control and enables transformative applications in holonomic quantum computing with Rydberg synthetic lattices.

This deviates from typical quantum systems reliant on semiconductors or trapped ions, offering a novel platform for manipulating quantum states. The team’s innovation centers on controlling the timing of microwave pulses to induce this pumping effect. Unlike previous methods, they’ve introduced a global adiabatic criterion (GAC) to optimize pulse sequencing, ensuring robustness within the simulated parameter ranges. The researchers explain that “the control problem is not only to specify a cyclic path, but also to choose its timing so that adiabatic following is retained without unnecessary exposure to loss,” highlighting the challenge of maintaining coherence in Rydberg systems. Crucially, the GAC doesn’t require adding extra control parameters; it simply refines the timing of existing Gaussian microwave pulses. The most compelling result lies in the demonstration of non-commutative operations, a hallmark of non-Abelian behavior that suggests the potential for complex quantum information processing. Numerical simulations, incorporating realistic Rydberg loss and perturbations, validate the GAC-selected timing, showing it gives higher target-state population than two literature-adapted Gaussian pulse schedules over the simulated parameter ranges.

Their work focuses on constructing a synthetic Lieb lattice, a specific arrangement of quantum sites, using twelve carefully selected microwave-coupled Rydberg levels rather than solid-state materials or ions. This unusual building block allows for precise control over quantum interactions, moving beyond traditional limitations in quantum system design. The researchers engineered a three-cell structure utilizing these levels, creating a system defined by six degenerate zero-energy states. These states are not passive elements, but form the basis for manipulating quantum information through cyclic modulation of microwave couplings. Importantly, the remaining, higher-energy states act as primary channels for quantum information loss during the experiment, a factor the team directly addresses in their methodology. They explain in their published work that “the six zero-energy states form the working basis for cyclic microwave modulation, whereas the bright states determine the main leakage channels during finite-time evolution.” A key innovation lies in the introduction of a global adiabatic criterion (GAC) to optimize the timing of microwave pulses.

Global Adiabatic Criterion for Finite-Time Pumping Control

Researchers affiliated with the School of Physics, Central South University, and the Quantum Information Institute, School of Physics, Zhengzhou University, are refining quantum control techniques using Rydberg atoms, moving beyond traditional semiconductor or trapped ion systems. Their work centers on a synthetic Lieb lattice constructed from twelve specifically selected microwave-coupled K39 Rydberg levels, a precise foundation for manipulating quantum states. This lattice is available on quant-ph and is not simply a spectroscopic tool; it’s engineered as a finite synthetic structure for quantum information processing. Crucially, the system leverages six degenerate zero-energy states which define the working subspace for cyclic microwave modulation. These states do not act in isolation; their collective behavior is harnessed for complex operations. The remaining, brighter states, however, present a challenge, acting as primary leakage channels that diminish signal fidelity during finite-time evolution.

To counteract this, the researchers introduced a global adiabatic criterion (GAC) which, as they explain, “evaluates the nonadiabatic factor over the full transfer window and uses its mean value and temporal fluctuation to guide the timing choice.” Unlike methods requiring additional control parameters, the GAC optimizes pulse sequencing by intelligently adjusting existing parameters. The results show that the GAC-selected timing, within a family of Gaussian pulses, yields higher target-state population than two literature-adapted Gaussian pulse schedules over the simulated parameter ranges.

Conventional understanding of quantum control often assumes a straightforward relationship between the sequence of operations and the final state of a system. However, recent work utilizing Rydberg synthetic lattices demonstrates a surprising level of nuance; the order in which microwave pulses are applied significantly alters the resulting quantum state. The foundation of this research lies in a meticulously constructed lattice built from twelve selected microwave-coupled K39 Rydberg levels. Within this lattice, six degenerate zero-energy states define the working subspace, enabling precise control over the system’s evolution. These states are not acting in isolation; the remaining states serve as primary leakage channels, a factor carefully considered in the experimental design.

Researchers have demonstrated a method for evaluating the timing of microwave pulses in a complex Rydberg lattice. Central to this advance is a carefully orchestrated sequence of microwave pulses applied to twelve selected, microwave-coupled Rydberg levels, forming the basis of a synthetic lattice. These six states are not merely a single point of control, but a higher-dimensional space enabling more complex operations. The team reports that this approach offers a new way to control quantum systems.