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arXiv:2507.01087 · npj Quantum Information

Quantum quenches from the critical point: theory and experimental validation in a trapped-ion quantum simulator

Chenxu Wang, András Grabarits, Jin‐Ming Cui, Hua-Bi Zeng, Yun‐Feng Huang, Chuan-Feng Li, Adolfo del Campo

Published Aug 22, 2026• 0 citations
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Abstract

Abstract We investigate quantum quenches starting from a critical point and experimentally probe the associated defect statistics using a trapped-ion quantum simulator of the transverse-field Ising model. The cumulants of the defect number distribution exhibit universal scaling with quench depth, featuring Gaussian behavior at leading order and systematic subleading corrections. Our results provide direct experimental validation of existing theoretical predictions and extend them to the full statistical characterization of defects. Beyond this, they establish, to the best of our knowledge, the first controlled experimental benchmark for fast-quench defect statistics near quantum criticality, providing a solid foundation for future studies of more complex, non-integrable quantum systems, thereby guiding both theoretical and experimental investigations of nonequilibrium quantum critical phenomena.

DOI
10.1038/s41534-026-01281-4

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Abstract We investigate quantum quenches starting from a critical point and experimentally probe the associated defect statistics using a trapped-ion quantum simulator of the transverse-field Ising model. The cumulants of the defect number distribution exhibit universal scaling with quench depth, featuring Gaussian behavior at leading order and systematic subleading corrections. Our results provide direct experimental validation of existing theoretical predictions and extend them to the full statistical characterization of defects. Beyond this, they establish, to the best of our knowledge, the first controlled experimental benchmark for fast-quench defect statistics near quantum criticality, providing a solid foundation for future studies of more complex, non-integrable quantum systems, thereby guiding both theoretical and experimental investigations of nonequilibrium quantum critical phenomena.
Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
We analyze the quantum phase transitions taking place in a one-dimensional transverse-field Ising model with long-range couplings that decay algebraically with distance. We are interested in the Kibble-Zurek universal scaling laws emerging in nonequilibrium dynamics and in the potential for the unambiguous observation of such behavior in a realistic experimental setup based on trapped ions. To this end, we determine the phase diagram of the model and the critical exponents characterizing its quantum phase transitions by means of density-matrix renormalization group calculations and finite-size scaling theory, which allows us to obtain good estimates for different range of ferromagnetic and antiferromagnetic interactions. Beyond critical equilibrium properties, we tackle a nonequilibrium scenario in which quantum Kibble-Zurek scaling laws may be retrieved. Here, it is found that the predicted nonequilibrium universal behavior, i.e., the scaling laws as a function of the quench rate and critical exponents, can be observed in systems comprising an experimentally feasible number of spins. Finally, a scheme is introduced to simulate the algebraically decaying couplings accurately by means of a digital quantum simulation with trapped ions. Our results suggest that quantum Kibble-Zurek physics can be explored and observed in state-of-the-art experiments with trapped ions realizing long-range Ising models.
We derive an extension of the generalized Kibble-Zurek mechanism (KZM), which provides a stochastic approach to defect formation, to reverse quench protocols. While the universal scaling behavior of defects in reverse quenches has been observed previously in certain 1D chains, we argument from a probability-theoretical perspective that this scaling persists in general, and is given by the double of the defect density variance in forward quenches. We validate these results analytically for the one-dimensional transverse field Ising model and numerically for its bond-disordered variant governed by an infinite randomness fixed point. Starting from the paramagnetic phase, this protocol relies solely on global control of the system's magnetic field and global magnetization measurements, enabling the extraction of critical exponents without microscopic access to individual defects. This approach offers a robust and experimentally feasible method for probing quantum critical behavior through entirely global operations.
Abstract The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one-dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.
The trapped-ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions.In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena, such as quantum phase transition, localization, thermalization, and information propagation.For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters.Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism.By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite-size effect.For ferromagnetic interaction, our experimental result agrees with the previous numerical prediction.As for the antiferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory.