Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet

Abstract

Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favorably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the many-body dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.

main text: 7 pages, 4 figures; supplement: 9 pages, 4 figures

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• Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature
• Tunable superdiffusion in integrable spin chains using correlated initial states
• Information scrambling of the dilute Bose gas at low temperature
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Spatiotemporal Quenches in Long-Range Hamiltonians
• Out-of-time-order correlator computation based on discrete truncated Wigner approximation
• Out-of-time-order correlators for Swanson Hamiltonian with interaction terms
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Diffusion in quantum state preparation: From passive cooling to system-bath engineering
• Operator delocalization in disordered spin chains via exact MPO marginals
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• A proposal to extract and enhance four-Majorana interactions in hybrid nanowires
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• Delta-kick Squeezing
• Butterflies dragging the jets: on the chaotic nature of holographic QCD
• Random-matrix approach to time-dependent forcing in many-body quantum systems
• An open-endcap blade trap for radial-2D ion crystals
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics
• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model
• Stabilizing confined quasiparticle dynamics in one-dimensional polar lattice gases
• Relativistic meson spectra on ion-trap quantum simulators
• Quantum transitions, ergodicity, and quantum scars in the coupled top model
• Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system
• Scrambling dynamics across a thermalization-localization quantum phase transition
• Exactly-solved model of light-scattering errors in quantum simulations with metastable trapped-ion qubits