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Observation of Quantum Thermalization Restricted to Hilbert Space Fragments and Z2k Scars

Luheng Zhao1,2,3, Prithvi Raj Datla4, Weikun Tian1, Mohammad Mujahid Aliyu1, and Huanqian Loh1,2,3,4,5,*

  • *Contact author: huanqian.loh@duke.edu
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Phys. Rev. X 15, 011035 – Published 18 February, 2025

DOI: https://doi.org/10.1103/PhysRevX.15.011035

Abstract

Quantum thermalization occurs in a broad class of systems from elementary particles to complex materials. Out-of-equilibrium quantum systems have long been understood to either thermalize or retain memory of their initial states, but not both. Here, we achieve the first coexistence of thermalization and memory in a quantum system, where we use both Rydberg blockade and facilitation in an atom array to engineer a fragmentation of the Hilbert space into exponentially many disjointed subspaces. We find that the kinetically constrained system yields quantum many-body scars arising from the Z2k class of initial states, which generalizes beyond the Z2 scars previously reported in other quantum systems. When bringing multiple long-range interactions into resonance, we observe quantum thermalization restricted to Hilbert space fragments, where the thermalized system retains characteristics of the initial configuration. Intriguingly, states belonging to different subspaces do not thermalize with each other even when they have the same energy. Our work sheds light on a subtle aspect of quantum thermalization while experimentally resolving the long-standing tension between thermalization and memory. These results may be applied to control entanglement dynamics in quantum processors and quantum sensors.

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Popular Summary

Out-of-equilibrium processes are present everywhere: Think colliding galaxies, turbulent sea waves, and tempered glass formed from rapid cooling. Typically, a system brought out of equilibrium thermalizes. At the quantum scale, thermalization is well understood, but many-body effects can prevent thermalization from occurring. The absence of thermalization usually implies that the system preserves memory of its initial state. Quantum scientists have long understood an out-of-equilibrium system to either thermalize or preserve memory, but not both. We have shown for the first time that it is possible to have both in a quantum system, experimentally resolving the long-standing tension between thermalization and memory.

To give a sense of how counterintuitive our result is, imagine preparing a cocktail by first pouring a blue drink, followed by a red one. Give the cocktail a stir, and watch it form alternating layers of blue, red, and purple, a pattern that repeats itself from the bottom to the top of the glass. We know that this would never happen classically, but our quantum-mechanical “bartender” makes it possible by engineering precise fractures in the Hilbert space. In our Rydberg atom array, we find that out-of-equilibrium states do thermalize, but only within the subspace that the initial state belongs to. Intriguingly, states from different subspaces do not thermalize with each other, even when they have the same energy. In other words, the thermalized system retains characteristics of the initial state.

Our work opens a path for controlling entanglement dynamics and can be applied to develop more efficient quantum algorithms and tailored quantum sensors.

Article Text

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Phys. Rev. X 15, 011035– Published 18 February, 2025
  • Received 21 April 2024
  • Accepted 2 January 2025
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