Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Alberto Biella1,2,3 and Marco Schiró3

1Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
2INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
3JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France

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It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

How an observer influences the fate of a quantum system is a fundamental longstanding question in quantum theory. Recent advances in the experimental manipulation of large ensembles of particles in the quantum regime made this question relevant also for extended systems coupled to a measurement apparatus. In this work we study the emergence of a Zeno phase triggered by the measurement rate in a prototypical spin-1/2 chain with continuous monitoring. We show that the onset of the Zeno regime is sharp and encoded in the rare events of the stochastic dynamics. The latter are governed by a non-Hermitian Hamiltonian which feature a subradiance transition.

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