Trapped-Ion Experiment Reveals Chaotic Behaviour in 100-Qubit Quantum System

Scientists investigate the complex behaviour of many-body systems driven far from equilibrium, a challenge addressed in new research demonstrating the quantum simulation of the Dicke model within a two-dimensional ion crystal. Bryce Bullock, Sean R. Muleady, and Jennifer F. Lilieholm, all from the National Institute of Standards and Technology, alongside Yicheng Zhang, Robert J. Lewis-Swan, and John J. Bollinger from The University of Oklahoma and the Center for Quantum Research and Technology, realised this model using approximately 100 trapped ions. This work is significant because it provides direct observation of chaos, entanglement, and non-classical correlations in a large, closed quantum system, establishing scalable analog simulation of light-matter dynamics and offering a controlled platform to study information scrambling and entanglement.

Dicke Model Simulation Reveals Quantum Chaos in Trapped Ion Systems

Scientists have engineered a scalable quantum simulator using approximately 100 trapped ions to demonstrate the Dicke model, a fundamental framework describing light-matter interactions. This configuration enables unitary many-body dynamics extending beyond simplified, mean-field approximations. In the integrable regime of the system, where vibrational motion is minimized, a clear dynamical phase transition was observed between ferromagnetic and paramagnetic spin phases.

However, when the spins and vibrations are strongly coupled, the research reveals definitive signatures of non-integrable chaotic dynamics, evidenced by erratic trajectories in phase space and exponential growth of both excitations and entanglement. Entanglement was quantified using the one-body Rényi entropy, providing a precise measure of the system’s quantum correlations.

By initiating the system from an unstable fixed point, researchers demonstrated that quantum noise can generate correlated spin-phonon excitations. Numerical calculations, aligning closely with experimental results, show the generation of two-mode spin-phonon squeezing, achieving a reduction of 2.6 dB below the standard quantum limit, equivalent to 4.6 dB relative to the initial thermal state.

This squeezing is followed by generalized vacuum Rabi collapses and revivals, showcasing strong spin-boson entanglement. These findings establish large ion crystals as effective analog quantum simulators for exploring non-equilibrium light-matter dynamics and offer a controlled environment for investigating information scrambling and entanglement within closed many-body systems. The study’s success opens new avenues for understanding complex quantum phenomena and developing advanced quantum technologies.

Simulating collective spin dynamics with truncated Wigner approximations and rotating frame transformations

A 100-ion crystal serves as the platform for realizing the Dicke model, a fundamental framework describing light-matter interactions. The ions’ internal states are optically coupled to their collective center of mass vibrational mode using a spin-dependent optical force, facilitating unitary dynamics beyond mean-field approximations.

Initializing the ions in a |(−N/2)x⟩ state with zero first-order coherence in the bosonic mode, the study investigates dynamics driven by quantum noise. To model this behavior, truncated Wigner approximation dynamics were performed on the time-averaged transverse order parameter, revealing non-trivial behavior when the ratio of Ω/δ approaches one.

To further analyze the system, researchers transformed the Hamiltonian into a rotating frame defined by the transverse drive and bosonic field, separating it into spin-pair and oscillator components. When the detuning, δ, equals the drive frequency, Ω, and the magnitude of δ significantly exceeds the coupling strength, g, the oscillator term rapidly oscillates and is neglected, leaving only the correlated spin-boson excitations.

Employing the Holstein-Primakoff approximation, spin operators were mapped to bosonic operators, simplifying the Hamiltonian to a two-mode squeezing form. This approximation reveals that excitations are generated through correlated pair creation, resulting in exponential growth of mode populations and the emergence of entangled pairs.

The work quantifies entanglement using the second-order Rényi entropy, calculated from the reduced density matrix of a single spin, where a value greater than zero indicates entanglement in the global pure state. Probing the dynamical phase diagram involved preparing the spins in a |↓⟩ state and cooling the center of mass mode to a thermal occupation of approximately five phonons, reduced to less than one via electromagnetically induced transparency cooling.

Fluorescence measurements of spin populations, performed after evolution under optical drive and microwave fields, provided data for analyzing the system’s dynamics at a fixed ratio of Ω/δ around 0.1 and a coupling strength of 2π × 0.9kHz, while varying Ω/χ. The ions’ internal state was optically coupled to their center of mass vibrational mode, facilitating unitary dynamics unattainable in mean-field or few-body scenarios.

In the integrable regime, a dynamical phase transition between ferromagnetic and paramagnetic spin phases was observed following adiabatic elimination of the phonons. Conversely, strong coupling between spins and phonons revealed signatures of chaotic dynamics, including erratic trajectories in phase space and exponential growth of excitations.

Quantification of entanglement via the one-body Rényi entropy demonstrated the proliferation of quantum correlations during these chaotic processes. By quenching the system from an unstable fixed point, correlated spin-phonon excitations were generated through quantum noise. Numerical calculations, aligning with experimental data, revealed two-mode spin-phonon squeezing reaching 2.6 dB below the standard quantum limit, which corresponds to 4.6 dB relative to the initial thermal state.

This squeezing was followed by generalized vacuum Rabi collapses and revivals, indicative of strong spin-boson entanglement. The study established that large ion crystals function as scalable analog quantum simulators for non-equilibrium light-matter dynamics. Specifically, the resonant cut parameter sweep exhibited non-trivial dynamics close to resonance, driven by quantum fluctuations from an initial bosonic vacuum state, while mean-field calculations showed no corresponding dynamics.

Furthermore, the observed pair production of correlated spin-phonon excitations, occurring with fully symmetrized spin flips along x accompanied by phonon excitation, contributes to exponential growth of mode populations and the generation of nonclassical correlations. This work provides a controlled platform for investigating information scrambling and entanglement within closed many-body systems.

Dicke Model Realisation Reveals Entanglement, Thermalisation and Quantum Squeezing

Scientists have demonstrated the realization of the Dicke model, a fundamental framework describing light-matter interactions, within a two-dimensional crystal composed of approximately one hundred trapped ions. This achievement enables the exploration of unitary dynamics extending beyond simplified mean-field and few-body approximations.

Observations include a dynamical phase transition between ferromagnetic and paramagnetic spin phases in an integrable regime, alongside signatures of chaotic dynamics when spins and phonons are strongly coupled, evidenced by erratic trajectories and exponential growth of excitations and entanglement. Measurements reveal two-mode spin-phonon squeezing, achieving a reduction of 2.6 decibels below the standard quantum limit, followed by generalized vacuum Rabi collapses and revivals.

The observed decay of collective magnetization correlates directly with the buildup of entanglement and quantum thermalization in the chaotic regime, as quantified by the single-spin Rényi entropy. While acknowledging limitations in directly measuring squeezing, the strong agreement between theoretical calculations and experimental data suggests a pathway towards implementing quantum-enhanced sensing.

This work establishes large ion crystals as scalable analog simulators for investigating non-equilibrium light-matter dynamics. The platform offers a controlled environment for studying information scrambling and entanglement in closed quantum systems. Although the authors note the challenges of extending these observations to longer timescales due to decoherence, future research could explore connections to high-energy physics, quantum information theory, and holographic concepts, potentially harnessing entanglement and chaos for advancements in quantum technologies.