Observing the quantum Mpemba effect in quantum simulations

Observing the quantum Mpemba effect in quantum simulations

15 Jul 2024 | Lata Kh Joshi, Johannes Franke, Aniket Rath, Filiberto Ares, Sara Murciano, Florian Kranzl, Rainer Blatt, Peter Zoller, Benoît Vermersch, Pasquale Calabrese, Christian F. Roos, and Manoj K. Joshi
This letter reports the first experimental observation of the quantum Mpemba effect (QMPE) in a trapped-ion quantum simulator. The QMPE is a phenomenon where a system with a larger degree of symmetry breaking restores its symmetry more rapidly than a system with a smaller degree of symmetry breaking. The study uses a chain of 12 interacting spin-1/2 particles, initialized in a ferromagnetic product state and then tilted by an angle θ from the z-axis. The symmetry breaking and restoration are monitored through entanglement asymmetry (EA), measured via randomized measurements and post-processed using the classical shadows technique. The EA is defined as the logarithm of the trace of the square of the reduced density matrix of a subsystem minus the trace of the square of the symmetrized counterpart. The results show that the EA decreases more rapidly for a state with a larger initial EA, confirming the QMPE. The study also measures the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, providing direct evidence of subsystem thermalization. The QMPE is observed for various scenarios, including different tilt angles, disorder strengths, and dephasing conditions. The results demonstrate that the QMPE is robust against subsystem choice and disorder, and that it can be observed even in the presence of decoherence. The findings highlight the potential of quantum simulators for studying non-equilibrium dynamics and symmetry restoration in many-body quantum systems.This letter reports the first experimental observation of the quantum Mpemba effect (QMPE) in a trapped-ion quantum simulator. The QMPE is a phenomenon where a system with a larger degree of symmetry breaking restores its symmetry more rapidly than a system with a smaller degree of symmetry breaking. The study uses a chain of 12 interacting spin-1/2 particles, initialized in a ferromagnetic product state and then tilted by an angle θ from the z-axis. The symmetry breaking and restoration are monitored through entanglement asymmetry (EA), measured via randomized measurements and post-processed using the classical shadows technique. The EA is defined as the logarithm of the trace of the square of the reduced density matrix of a subsystem minus the trace of the square of the symmetrized counterpart. The results show that the EA decreases more rapidly for a state with a larger initial EA, confirming the QMPE. The study also measures the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, providing direct evidence of subsystem thermalization. The QMPE is observed for various scenarios, including different tilt angles, disorder strengths, and dephasing conditions. The results demonstrate that the QMPE is robust against subsystem choice and disorder, and that it can be observed even in the presence of decoherence. The findings highlight the potential of quantum simulators for studying non-equilibrium dynamics and symmetry restoration in many-body quantum systems.
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[slides and audio] Observing the Quantum Mpemba Effect in Quantum Simulations.