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arXiv:2407.03249 · Nature

Quantum coarsening and collective dynamics on a programmable simulator

Tom Manovitz, Sophie H. Li, Sepehr Ebadi, Rhine Samajdar, Alexandra A. Geim, Simon J. Evered, Dolev Bluvstein, Hengyun Zhou, Nazlı Uğur Köylüoğlu, Johannes Feldmeier, Pavel E. Dolgirev, Nishad Maskara, Marcin Kalinowski, Subir Sachdev A, David A. Huse, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin

Published Feb 5, 2025• 59 citations
arXivHTMLPDF

Abstract

Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter1, fundamental high-energy processes2, quantum metrology3,4 and quantum algorithms5. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains6. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (‘Higgs’) mode7. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes. A programmable quantum simulator based on Rydberg atom arrays is used to study the collective dynamics of a quantum phase transition and observe the phenomenon of quantum coarsening.

DOI
10.1038/s41586-024-08353-5

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Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter1, fundamental high-energy processes2, quantum metrology3,4 and quantum algorithms5. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains6. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (‘Higgs’) mode7. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes. A programmable quantum simulator based on Rydberg atom arrays is used to study the collective dynamics of a quantum phase transition and observe the phenomenon of quantum coarsening.
Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.
Strongly interacting many-body systems exhibit collective properties that emerge from complex correlations among microscopic degrees of freedom. These cooperative phenomena govern the non-equilibrium response of quantum systems, with relevance ranging from condensed matter physics to quantum field theories describing fundamental aspects of our universe. Understanding such emergent dynamics from first principles remains one of the central challenges in quantum many-body physics. Here we report on the observation of collective cluster nucleation dynamics following quenches in 2D ferromagnetic quantum Ising systems implemented in an atomic Rydberg array. Our experiments reveal two distinct regimes: In the confined regime, we observe an energy-dependent cluster size, revealing large collective clusters exceeding ten spins. In contrast, the deconfined regime is characterized by kinetically constrained, avalanche-like nucleation dynamics involving the entire system. Our findings establish a new frontier for quantum simulations with Rydberg arrays, enabling controlled exploration of non-equilibrium phenomena previously out of reach. Beyond advancing experimental capabilities, they provide fundamental insights into highly correlated processes with implications that reach from quantum magnetism and glassy dynamics to cosmological models of the early universe.
Understanding the out-of-equilibrium dynamics of a closed quantum system driven across a quantum phase transition is an important problem with widespread implications for quantum state preparation and adiabatic algorithms. While the quantum Kibble-Zurek mechanism elucidates part of these dynamics, the subsequent and significant coarsening processes lie beyond its scope. Here, we develop a universal description of such coarsening dynamics -- and their interplay with the Kibble-Zurek mechanism -- in terms of scaling theories. Our comprehensive theoretical framework applies to a diverse set of ramp protocols and encompasses various coarsening scenarios involving both quantum and thermal fluctuations. Moreover, we highlight how such coarsening dynamics can be directly studied in today's "synthetic" quantum many-body systems, including Rydberg atom arrays, and present a detailed proposal for their experimental observation.
Relaxation dynamics of complex many-body quantum systems brought out of equilibrium and subsequently trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and new energy-efficient memory devices. Understanding the dynamics of such systems is crucial for exploring fundamental aspects of many-body non-equilibrium quantum physics. In this work we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material where classical dynamics is topologically constrained. The crossover from temperature to quantum fluctuation dominated dynamics in the context of environmental noise is investigated by directly observing charge reconfiguration with time-resolved scanning tunneling microscopy. The process is modelled using a programmable superconducting quantum simulator in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment on the quantum material and the simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics remarkably well. The combined experiment and simulations lead to a better understanding of noise-driven quantum dynamics in open quantum systems. From a practical viewpoint, the results are important for understanding the origin of the retention time in non-volatile memory devices such as those based on 1T-TaS2.
The dynamics of isolated quantum systems following a sudden quench plays a central role in many areas of material science, high-energy physics, and quantum chemistry. Featuring complex phenomena with implications for thermalization, non-equilibrium phase transitions, and Floquet phase engineering, such far-from-equilibrium quantum dynamics is challenging to study numerically, in particular, in high-dimensional systems. Here, we use a programmable neutral atom quantum simulator to systematically explore quench dynamics in spin models with up to 180 qubits. By initializing the system in a product state and performing quenches across a broad parameter space, we discover several stable, qualitatively distinct dynamical regimes. We trace their robustness to Floquet-like prethermal steady states that are stabilized over long emergent timescales by strong dynamical constraints. In addition, we observe sharp peaks in the dynamical response that are quantitatively explained by the structured melting of prethermalization through resonances. In two dimensions, we uncover a sharp dynamical response change that converges with increased system size, that is linked to the proliferation of Néel-order defects and indicative of a dynamical phase transition with no equilibrium analogs. Uncovering an intricate interplay between quantum prethermalization and emergent dynamical phases, our results demonstrate the use of quantum simulators for revealing complex non-equilibrium quantum many-body phenomena.
A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at 1/31/31/3 or 2/32/32/3-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at 1/21/21/2 filling. At finite temperature, U(1)\mathrm{U}(1)U(1) symmetry is emergent at 1/21/21/2 filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.