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Tomonaga-Luttinger Liquid Behavior in a Rydberg-Encoded Spin Chain

Gabriel Emperauger1,*, Mu Qiao1,*, Cheng Chen1,2,*, Filippo Caleca3,*, Saverio Bocini3,*, Marcus Bintz4,*, Guillaume Bornet1, Romain Martin1, Bastien Gély1 et al.

Lukas Klein1, Daniel Barredo1,5, Shubhayu Chatterjee6, Norman Y. Yao4, Fabio Mezzacapo3, Thierry Lahaye1, Tommaso Roscilde3, and Antoine Browaeys1,†

  • *These authors contributed equally to this work.
  • †Contact author: antoine.browaeys@institutoptique.fr
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Phys. Rev. X 15, 031021 – Published 17 July, 2025

DOI: https://doi.org/10.1103/qfnp-6dpz

Abstract

Quantum fluctuations can disrupt long-range order in one-dimensional systems and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasiadiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.

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Popular Summary

In 1D systems, quantum effects play a much bigger role than in higher dimensions, often preventing classical forms of order from forming. A key example of this is the Tomonaga-Luttinger liquid, a universal description of many 1D quantum systems that depends on just two parameters: how stiff the system is and how fast disturbances travel through it. While this theory has been tested in solid-state and cold atom experiments, some important features—like how particle correlations fall off with distance—have been hard to directly observe. In this study, we build a new kind of 1D spin chain using individual atoms to explore these features more directly, allowing us to study how the spins behave at equilibrium and how they evolve over time.

Each spin in our chain is made from a single rubidium atom, trapped and arranged using tightly focused laser beams called optical tweezers. These atoms interact through dipole-dipole forces, creating what is known as a dipolar XY model. This regime of interaction is novel compared to traditionally studied systems, which typically feature short-range interactions. We find that the spins organize into strongly correlated phases of matter, exhibiting either ferromagnetic or antiferromagnetic order. Remarkably, the correlations between spins decay as a power law with distance, a signature of a phenomenon known as “quantum criticality.”

Because we can control and measure each atom individually, we can directly observe how spins influence one another, how a single impurity affects the system, and how the system changes in real time. Our results show how long-range interactions affect collective behavior and pave the way for deeper studies of exotic quantum phases in well-controlled settings.

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Phys. Rev. X 15, 031021– Published 17 July, 2025
  • Received 14 January 2025
  • Accepted 26 June 2025
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