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arXiv:2606.28664

Temporal Dynamical Quantum Phase Transition in Dicke Model with Trapped Ions

Ji Bian, Wei Wu, Zihan Xie, Mengxiang Zhang, Yi Li, Yue Li, Rixin Yao, Yuqi Zhou, Xu Cheng, Han Pu, Yiheng Lin

quant-phSubmitted Jun 27, 2026• Announced Jun 30, 2026• 0 citations
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Abstract

Temporal non-analyticities in the rate function of the Loschmidt echo manifests a class of dynamical quantum phase transitions (DQPTs) that has emerged as a powerful framework for understanding far-from-equilibrium many-body dynamics. While such DQPT has been extensively studied theoretically in spin-boson systems such as the Dicke model, their experimental observation remains elusive. In particular, the dynamics of DQPT in asymmetric spin subspaces and under the influence of spin dissipation are largely unexplored. Here, we report an experimental study of temporal DQPT in a generalized Dicke model using a trapped-ion quantum simulator. By coupling a linear chain of $\rm{^{40}Ca^{+}}$ ions to a collective center-of-mass motional mode, we probe the quench dynamics starting from both symmetric and asymmetric initial states. We extract the rate function and identify temporal turn-around points that are in quantitative agreement with theoretical predictions. Additionally, we investigate the impact of spin dissipation on these dynamics. Our results establish an experimental platform for probing complex many-body out-of-equilibrium phenomena and advance the development of hybrid oscillator-spin quantum simulators.

Comments
9 pages, 11 figures

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Temporal non-analyticities in the rate function of the Loschmidt echo manifests a class of dynamical quantum phase transitions (DQPTs) that has emerged as a powerful framework for understanding far-from-equilibrium many-body dynamics. While such DQPT has been extensively studied theoretically in spin-boson systems such as the Dicke model, their experimental observation remains elusive. In particular, the dynamics of DQPT in asymmetric spin subspaces and under the influence of spin dissipation are largely unexplored. Here, we report an experimental study of temporal DQPT in a generalized Dicke model using a trapped-ion quantum simulator. By coupling a linear chain of 40Ca+\rm{^{40}Ca^{+}}40Ca+ ions to a collective center-of-mass motional mode, we probe the quench dynamics starting from both symmetric and asymmetric initial states. We extract the rate function and identify temporal turn-around points that are in quantitative agreement with theoretical predictions. Additionally, we investigate the impact of spin dissipation on these dynamics. Our results establish an experimental platform for probing complex many-body out-of-equilibrium phenomena and advance the development of hybrid oscillator-spin quantum simulators.
We study dynamical phase transitions in the generalized dissipative Dicke model in an array of trapped Rydberg ions, where their density-density interactions compete with the collective spin-phonon coupling, laser driving and dissipation. This setting offers a versatile approach to study equilibrium as well as non-equilibrium many-body phenomena, as parameters, such as the Ising interaction, laser-ion and spin-phonon coupling can be tuned. Through analyzing the mean-field phase diagram, we find a variety of distinct phases and the emergence of a tricritical point that are sensitively dependent of the interaction between Rydberg ions. We then study the quantum dynamics for a finite system size and characterize parameter dependent dynamics using the spin average, entropy, and Loschmidt echo. Distinctive signatures of the dynamical phases, such as slow relaxation and metastability, arise near the phase transition. This analysis predicts rich quantum dynamics of the finite system that link to the non-equilibrium mean-field phases. Our study widens the exploration of collective and non-equilibrium phases in Dicke models, and reveals that the Rydberg ion interaction drastically affects the phase diagram and dynamics.
Quantum many-body systems driven far from equilibrium can exhibit phase transitions, chaos and entanglement, but probing these phenomena in large, nearly closed systems remains challenging. The Dicke model, which couples an ensemble of two-level systems collectively to a single bosonic mode, provides a fundamental framework for exploring these phenomena in light-matter interactions. Here we show that a two-dimensional crystal of approximately 100 trapped ions realizes this model and accesses integrable dynamical phase transitions, signatures of chaotic dynamics and fluctuation-driven spin-phonon excitation growth. Adiabatic elimination of the vibrational mode reveals ferromagnetic and paramagnetic dynamical spin phases, whereas strong spin-phonon coupling produces irregular trajectories and local relaxation consistent with quantum thermalization. Following a quench from an unstable fixed point, correlated excitation growth precedes generalized vacuum Rabi collapses and revivals; calibrated calculations identify two-mode squeezing 2.6 dB below the standard quantum limit, supported by reconstruction from spin measurements. By connecting collective dynamical instabilities to experimentally accessible signatures of quantum correlations, these results establish large ion crystals as a scalable platform for investigating non-equilibrium light-matter dynamics and generating resources for quantum-enhanced sensing.
We demonstrate the existence of a dynamical quantum phase transition (DQPT) in a dissipative collective-spin model that exhibits the boundary time crystal (BTC) phase. We initialize the system in the ground state of the Hamiltonian in either the BTC or the non-BTC phase, and drive it across the BTC transition. The driving is done by an abrupt quench or by a finite-time linear ramp of a Hamiltonian control parameter under Markovian Lindblad dynamics. We diagnose DQPTs through zeros of the fidelity-based Loschmidt echo between the initial state and the evolving mixed state, which induce nonanalytic cusp-like features in the associated rate function. For quenches into the BTC phase, the Loschmidt echo exhibits repeated zeros due to the emergent time-periodic steady state, whereas for quenches into the non-BTC phase, the overlap vanishes and remains zero once the dynamics relaxes to a stationary state. We further show that the DQPT persists under the ramp protocol followed by unitary evolution with the final Hamiltonian. Finally, we analyze the finite-size scaling of the first critical time and find convergence to a constant in the thermodynamic limit, with distinct power-law approaches for the quench and the ramp protocols.
In the context of closed quantum systems, when a system prepared in its ground state undergoes a sudden quench, the resulting Loschmidt echo can exhibit zeros, resembling the Fisher zeros in the theory of classical equilibrium phase transitions. These zeros lead to nonanalytical behavior of the corresponding rate function, which is referred to as the dynamical quantum phase transition (DQPT). In this paper, we investigate DQPTs in the context of open quantum systems that are coupled to both Markovian and non-Markovian dephasing baths via a conserved quantity. The general framework is corroborated by studying the nonequilibrium dynamics of a transverse-field Ising ring. Our paper might shed light on theoretical developments of DQPTs in the strong system-bath coupling regime.
Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. With the strong ongoing experimental drive to quantum simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin-SU(1)S U(1)SU(1) quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of S=1/2S=1/2S=1/2 for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length S>1/2S>1/2S>1/2 this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the Wilson-Kogut-Susskind limit and its representation through the quantum link formalism.
We explore trapped ions as a setting to investigate nonequilibrium phases in a generalized Dicke model of dissipative spins coupled to phonon modes. We find a rich dynamical phase diagram including superradiantlike regimes, dynamical phase coexistence, and phonon-lasing behavior. A particular advantage of trapped ions is that these phases and transitions among them can be probed in situ through fluorescence. We demonstrate that the main physical insights are captured by a minimal model and consider an experimental realization with Ca+ ions trapped in a linear Paul trap with a dressing scheme to create effective two-level systems with a tunable dissipation rate.