Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics

Stefano Marcantoni; Marco Merkli

doi:10.22331/q-2025-03-06-1656

Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics

Stefano Marcantoni¹ and Marco Merkli²

¹Laboratoire J. A. Dieudonné (LJAD), Université Côte d'Azur, Parc Valrose, 06108 Nice, France
²Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7 Canada

Published:	2025-03-06, volume 9, page 1656
Editor:	Francesco Ciccarello
Eprint:	arXiv:2411.06817v2
Doi:	https://doi.org/10.22331/q-2025-03-06-1656
Citation:	Quantum 9, 1656 (2025).

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Abstract

We study the dynamics of an open quantum system linearly coupled to a bosonic reservoir. We show that, in the ultrastrong coupling limit, the system undergoes a nonselective measurement and then evolves unitarily according to an effective Zeno Hamiltonian. This dynamical process is largely independent of the reservoir state. We examine the entanglement breaking effect of the ultrastrong coupling on the system. We also derive the evolution equation for systems in contact with several reservoirs when one coupling is ultrastrong. The effective system dynamics displays a rich structure and, contrarily to the single reservoir case, it is generally non-Markovian. Our approach is based on a Dyson series expansion, in which we can take the ultrastrong limit termwise, and a subsequent resummation of the series. Our derivation is mathematically rigorous and uncomplicated.

Featured image: Different coupling regimes: From noninteracting to ultrastrong. Here, $\Delta$ represents a typical system Bohr frequency. Energy shifts in the system due to the interaction with the reservoir are typically proportional to $\lambda^2$. In all regimes one can consider static and dynamical properties of the system, except for the ultraweak coupling regime. That one is a purely dynamical regime in which time is coarse grained to the value $\tau = \lambda^2 t$. In the current paper we focus on the ultrastrong coupling regime $\lambda \to \infty$. We show that it gives rise to a nonselective measurement of the system followed by a quantum Zeno dynamics.

Popular summary

We study the dynamics of a small quantum system strongly interacting with an infinite reservoir. We show that the reservoir effectively acts as a measuring apparatus, performing repeated measurements on the system with a frequency that is larger for large coupling. In the limit of infinite coupling the dynamics is strongly constrained, and in some cases it is completely frozen. This effect is usually called the quantum Zeno effect, in analogy with the paradox of the motionless arrow proposed by the ancient philosopher Zeno. We can extend our results to the case of a small system interacting with many reservoirs when one of the couplings is much stronger than the others. In this case, the strongly coupled reservoir produces a Zeno effect on the system and the other reservoirs together, so that the dynamics of the small system alone can still be quite complex.

► BibTeX data

@article{Marcantoni2025ultrastrong,
  doi = {10.22331/q-2025-03-06-1656},
  url = {https://doi.org/10.22331/q-2025-03-06-1656},
  title = {Ultrastrong coupling, nonselective measurement and quantum {Z}eno dynamics},
  author = {Marcantoni, Stefano and Merkli, Marco},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1656},
  month = mar,
  year = {2025}
}

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Cited by

[1] Sakil Khan and Bijay Kumar Agarwalla, "Emergence of distinct relaxation behavior and the quantum regression theorem in the ultrastrong-coupling limit", Physical Review A 113 1, L010203 (2026).

[2] Michele Fantechi and Marco Merkli, "Bosonization of Noise Effects in Nonlocal Quantum Dynamics", Physical Review Letters 136 6, 060402 (2026).

[3] Alessandro Prositto, Carlos Ramon-Escandell, and Dvira Segal, "Collisional model with dissipative and dephasing baths: nonadditive effects at strong coupling", New Journal of Physics 28 1, 014502 (2026).

[4] Nirmalendu Acharyya, Martin Richter, and Benjamin P. Fingerhut, "Coherent dynamics of the spin-boson model in the ultra-strong coupling regime", The Journal of Chemical Physics 165 4, 044114 (2026).

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