Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Piotr Sierant1,2, Giuliano Chiriacò1,3, Federica M. Surace1,3, Shraddha Sharma1, Xhek Turkeshi1,3, Marcello Dalmonte1,3, Rosario Fazio1,4, and Guido Pagano5

1The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
2Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
3SISSA — International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
4Dipartimento di Fisica, Università di Napoli ``Federico II'', Monte S. Angelo, I-80126 Napoli, Italy
5Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, TX 77005, USA

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Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

Entanglement among many particles is a fundamental feature that allows quantum processors to tackle specific tasks faster than their classical counterparts. The main challenge in creating and protecting entanglement is posed by another puzzling feature of quantum mechanics, namely decoherence: a quantum system “measured” by the environment loses its quantum correlations and is projected into classical states. Errors caused by environmental noise can be modelled as non-unitary operations acting on the qubits. Hence, understanding how correlations propagates in quantum systems in presence of controlled local non-unitary operations, and which tools can be employed to govern its dynamics, are not only fundamental questions, but represent crucial steps towards building reliable and scalable quantum processors where entanglement can be tailored and protected.
In this work we study quantum systems subjected to the interplay between unitary coherent evolution and the interaction with the outside environment. We develop a unified framework to study a prototypical quantum many-body system, one-dimensional long-range interacting spin chains, and investigate two different but related phenomena: A symmetry breaking phase transition that separates an ordered and disordered phase, and a “measurement induced” phase transition that separates two regimes in which entanglement behaves in dramatically different ways. Moreover, we examine the requirements and challenges for an experimental realization of both phenomena with trapped atomic ions.
Our results suggest that the two phenomena are fundamentally related and that induced entanglement phase transitions may be observed in a much broader class of systems than what has been considered so far.

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[1] Andrew C. Potter and Romain Vasseur, Quantum Science and Technology 211 (2022) ISBN:978-3-031-03997-3.

[2] Michele Coppola, Emanuele Tirrito, Dragi Karevski, and Mario Collura, "Growth of entanglement entropy under local projective measurements", Physical Review B 105 9, 094303 (2022).

[3] T. Boorman, M. Szyniszewski, H. Schomerus, and A. Romito, "Diagnostics of entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition", Physical Review B 105 14, 144202 (2022).

[4] Giulia Piccitto, Angelo Russomanno, and Davide Rossini, "Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian", Physical Review B 105 6, 064305 (2022).

[5] Piotr Sierant and Xhek Turkeshi, "Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions", Physical Review Letters 128 13, 130605 (2022).

[6] Kai Klocke and Michael Buchhold, "Topological order and entanglement dynamics in the measurement-only XZZX quantum code", Physical Review B 106 10, 104307 (2022).

[7] Xhek Turkeshi, Marcello Dalmonte, Rosario Fazio, and Marco Schirò, "Entanglement transitions from stochastic resetting of non-Hermitian quasiparticles", Physical Review B 105 24, L241114 (2022).

[8] Xhek Turkeshi, Lorenzo Piroli, and Marco Schiró, "Enhanced entanglement negativity in boundary-driven monitored fermionic chains", Physical Review B 106 2, 024304 (2022).

[9] Matthew Wampler, Brian J. J. Khor, Gil Refael, and Israel Klich, "Stirring by Staring: Measurement-Induced Chirality", Physical Review X 12 3, 031031 (2022).

[10] Shraddha Sharma, Xhek Turkeshi, Rosario Fazio, and Marcello Dalmonte, "Measurement-induced criticality in extended and long-range unitary circuits", SciPost Physics Core 5 2, 023 (2022).

[11] Y. Minoguchi, P. Rabl, and M. Buchhold, "Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics", arXiv:2108.04256.

[12] Davide Rossini and Ettore Vicari, "Coherent and dissipative dynamics at quantum phase transitions", Physics Reports 936, 1 (2021).

[13] Andrew C. Potter and Romain Vasseur, "Entanglement dynamics in hybrid quantum circuits", arXiv:2111.08018.

[14] Oliver Lunt, Jonas Richter, and Arijeet Pal, "Quantum simulation using noisy unitary circuits and measurements", arXiv:2112.06682.

[15] Jeremy T. Young, Alexey V. Gorshkov, and I. B. Spielman, "Feedback-stabilized dynamical steady states in the Bose-Hubbard model", Physical Review Research 3 4, 043075 (2021).

[16] Minjae Jo, Bukyoung Jhun, and B. Kahng, "Resolving mean-field solutions of dissipative phase transitions using permutational symmetry", arXiv:2110.09435.

The above citations are from Crossref's cited-by service (last updated successfully 2022-10-04 19:42:34) and SAO/NASA ADS (last updated successfully 2022-10-04 19:42:35). The list may be incomplete as not all publishers provide suitable and complete citation data.