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

Piotr Sierant; Giuliano Chiriacò; Federica M. Surace; Shraddha Sharma; Xhek Turkeshi; Marcello Dalmonte; Rosario Fazio; Guido Pagano

doi:10.22331/q-2022-02-02-638

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

Piotr Sierant^1,2, Giuliano Chiriacò^1,3, Federica M. Surace^1,3, Shraddha Sharma¹, Xhek Turkeshi^1,3, Marcello Dalmonte^1,3, Rosario Fazio^1,4, 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

Published:	2022-02-02, volume 6, page 638
Eprint:	arXiv:2107.05669v3
Doi:	https://doi.org/10.22331/q-2022-02-02-638
Citation:	Quantum 6, 638 (2022).

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Abstract

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.

Featured image: Dissipative Floquet Dynamics: (a) Unitary evolutions, namely rotations (blue) and entangling operations (red), are interleaved by measurement processes (yellow). (b) Experimental scheme with trapped atomic ions: local measurement are executed with individual resonant laser beams (blue) while coherent evolution is implemented with off-resonant lasers (purple).

Popular summary

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.

► BibTeX data

@article{Sierant2022dissipativefloquet,
  doi = {10.22331/q-2022-02-02-638},
  url = {https://doi.org/10.22331/q-2022-02-02-638},
  title = {Dissipative {F}loquet {D}ynamics: from {S}teady {S}tate to {M}easurement {I}nduced {C}riticality in {T}rapped-ion {C}hains},
  author = {Sierant, Piotr and Chiriac{\`{o}}, Giuliano and Surace, Federica M. and Sharma, Shraddha and Turkeshi, Xhek and Dalmonte, Marcello and Fazio, Rosario and Pagano, Guido},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {638},
  month = feb,
  year = {2022}
}

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