Interaction-enabled topological pumping of Rydberg electrons

This paper reports the experimental observation of interaction-enabled topological pumping in a synthetic lattice of correlated Rydberg electrons, demonstrating how tunable dipolar exchange interactions can shift topological singularities to drive successive transitions between quantized and non-quantized transport regimes.

The Gist

Imagine a tiny, invisible train track made not of steel, but of energy levels that electrons can hop between. In the world of quantum physics, scientists often try to make these electrons move in a specific direction in a perfectly controlled way, a process called "topological pumping." Think of it like a conveyor belt that moves items from one end of a factory to the other without them ever falling off or getting lost.

Usually, this conveyor belt works best when the items (electrons) don't bother each other. But what happens when the items are "social," meaning they strongly interact with one another? That is the big question this paper answers.

Here is the story of their discovery, explained simply:

The Setup: A Dance of Two Electrons

The researchers set up a special experiment using two Rydberg atoms (atoms with a very excited, "puffy" electron). They trapped these atoms with laser tweezers and used microwave beams to create a synthetic "lattice" or track.

Think of the two atoms as a pair of dance partners. They are connected by a force called a "dipolar exchange interaction." In everyday terms, imagine the two dancers are holding a very long, invisible elastic band. If one moves, the other feels it immediately. The strength of this "elastic band" depends on how far apart the dancers stand; the closer they are, the tighter the band pulls.

The Problem: The "Ghost" in the Machine

In a perfect, non-interacting world, the conveyor belt (the pumping mechanism) has a specific path it follows. However, there is a "ghost" or a "singularity" in the mathematical map of this system.

• No Interaction: If the dancers don't hold hands (no interaction), the ghost sits far away from the path. The conveyor belt runs, but nothing moves. It's a "trivial" loop.
• Strong Interaction: If the dancers hold hands very tightly, the ghost moves. It might jump right onto the path, or jump off the other side.

The team discovered that by simply changing how tightly the two atoms are pulled together (adjusting the distance between them), they could move the ghost.

The Discovery: Turning the Pump On and Off

By tuning the "tightness" of the interaction, they observed a fascinating three-stage story:

1. The Off State (Too Weak): When the interaction is weak, the ghost is outside the loop. The electrons stay put. Nothing happens.
2. The On State (Just Right): As they increased the interaction, the ghost moved inside the loop. Suddenly, the conveyor belt kicked into high gear! The pair of electrons moved together, step-by-step, from the start of the track to the next section. This is "quantized transport"—a perfect, reliable jump.
3. The Off State Again (Too Strong): If they made the interaction too strong, the ghost moved out of the loop on the other side. The conveyor belt stopped working again, and the electrons froze.

It's like tuning a radio. You turn the knob (interaction strength) and suddenly, for a specific range, you get a clear, perfect signal (the pumping). Turn it too far in either direction, and the signal disappears.

Why This Matters (According to the Paper)

The paper shows that you don't need to change the track itself to make the pump work; you just need to change how the particles interact with each other. The interaction acts like a remote control that shifts the "magic spot" (the singularity) in and out of the path.

They also checked if this was a fluke:

• Speed: They found that if they moved the track too fast, the electrons couldn't keep up (like trying to run on a treadmill that speeds up too quickly). But if they moved at the right speed, the electrons followed perfectly.
• Wobbly Tracks: They intentionally made the track slightly uneven or "wobbly." Surprisingly, as long as the "ghost" stayed inside the loop and the speed was right, the electrons still moved perfectly. This proves the system is robust and "topologically protected"—it's hard to break.

The Bottom Line

This experiment is like discovering that you can control a complex machine not by rewiring it, but by simply adjusting how much the parts "talk" to each other. The researchers showed that in a world of two interacting electrons, you can turn a "do-nothing" system into a "perfect transporter" and back again, just by changing the strength of their connection.

They did not claim this will build a new computer or cure a disease today. Instead, they established a new way to understand how "social" particles behave in quantum systems, opening a door to studying more complex groups of particles in the future.

Technical Summary

Problem Statement
Topological pumping serves as a paradigmatic realization of quantized transport in band systems. However, the behavior of this phenomenon in strongly correlated regimes, particularly those involving long-range interactions, remains largely unexplored. While theoretical efforts have identified topological invariants for many-body pumping dynamics, and recent experiments have observed interaction effects in nonlinear photonic systems and Hubbard models with short-range contact interactions, it is unclear whether similar mechanisms persist in systems governed by nonlocal, long-range dipolar exchange interactions. Specifically, the few-body regime, where interaction effects are intrinsically prominent, lacks experimental characterization regarding how such interactions modify topological singularities and transport.

Methodology
The authors experimentally investigate interaction-enabled topological pumping using a synthetic lattice of correlated Rydberg electrons. The system consists of pairs of single Rydberg atoms (labeled A and B) trapped in optical tweezers with a tunable interatomic distance $d$.

• Synthetic Lattice Construction: The system utilizes five Rydberg states ($\{42S_{1/2}, 42P_{3/2}, 43S_{1/2}, 43P_{3/2}, 44S_{1/2}\}$) to encode synthetic lattice sites.
• Driving Protocol: A two-color microwave driving scheme is employed to selectively address collective transitions via intermediate triplets. Each nearest-neighbor transition is driven by two microwave tones with independently controlled time-dependent amplitudes $J_{\pm}(t)$ and phases $\theta_{\pm}(t)$.
• Interaction Tuning: Dipolar exchange interactions ($V_n \propto 1/d^3$) are globally tuned by adjusting the separation $d$ between the atom pairs.
• Theoretical Framework: The system is mapped to an effective pair-state Rice-Mele Hamiltonian. In this representation, the dipolar exchange interaction manifests as an effective onsite energy shift for triplet states, thereby shifting the position of the topological singularity in parameter space relative to the fixed pumping trajectory.
• Measurement: State populations are measured via de-excitation to the ground state followed by fluorescence imaging. The pumping efficiency is quantified by the population in the target state after one modulation cycle.

Key Contributions and Results

1. Observation of Interaction-Enabled Pumping: The experiment demonstrates that for a fixed pumping trajectory, quantized directional transport emerges only within an intermediate interaction regime. In the non-interacting limit ($V=0$), the modulation path does not enclose the topological singularity, resulting in negligible transport (a topologically trivial regime).
2. Interaction-Driven Topological Phase Transitions: By tuning the interaction strength $V$, the authors observe two distinct topological phase transitions. As $V$ increases, the interaction-induced shift moves the topological singularity into the pumping trajectory, activating quantized transport. Further increasing $V$ shifts the singularity out of the trajectory, causing the breakdown of quantized transport and a return to a trivial regime.
3. Quantified Efficiency and Robustness: The pumping efficiency ($\eta$) is shown to be topologically protected within the intermediate regime where the singularity is enclosed. The experimental data aligns well with numerical simulations of both the full Hamiltonian and the effective Rice-Mele model. The study further characterizes the adiabaticity of the process, identifying specific frequency scales ($\omega_l$ and $\omega_u$) derived from Landau-Zener criteria that govern the transition from non-adiabatic to adiabatic transport.
4. Perturbation Analysis: The system exhibits robustness against controlled distortions of the driving trajectory (specifically imbalances in intra- and inter-cell couplings) as long as the modulation loop continues to enclose the singularity and the evolution remains adiabatic. However, the quantization is ultimately constrained by adiabaticity requirements rather than solely by topological protection.

Significance
The paper establishes a platform for exploring interaction-controlled topological transport beyond perturbative regimes. It provides a clear, intuitive picture of how long-range dipolar interactions modify the topology of a driven quantum system by shifting topological singularities. The authors claim that this work opens a route toward engineering correlated topological matter in synthetic quantum systems. Furthermore, they note a formal duality between their Rydberg synthetic lattice and Floquet-driven Hubbard wires, suggesting potential future directions for realizing topological pumping of Hubbard doublons and triplons, as well as exploring anyonic Hubbard models in few-body settings. The results support the characterization of adiabaticity and robustness, establishing a foundation for studying interaction-controlled Berry curvature engineering and the topological nature of strongly interacting quantum matter.