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Entanglement growth in the dark intervals of a locally monitored free-fermion chain

Giovanni Di Fresco, Youenn Le Gal, Davide Valenti, Marco Schiró, and Angelo Carollo

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AbstractWe consider a free fermionic chain with monitoring of the particle density on a single site of the chain and study the entanglement dynamics of quantum jump trajectories. We show that the entanglement entropy grows in time towards a stationary state which display volume law scaling of the entropy, in stark contrast with both the unitary dynamics after a local quench and the no-click limit corresponding to full post-selection. We explain the extensive entanglement growth as a consequence of the peculiar distribution of quantum jumps in time, which display superpoissonian waiting time distribution characterised by a bunching of quantum jumps followed by long dark intervals where no-clicks are detected, akin to the distribution of fluorescence light in a driven atom. We show that the presence of dark intervals is the key feature to explain the effect and that by increasing the number of sites which are monitored the volume law scaling gives away to the Zeno effect and its associated area law.Popular summaryThe dynamics of quantum entanglement in monitored systems has recently attracted considerable interest. We show that continuously monitoring just one site of a quantum chain can profoundly affect the entanglement dynamics of the entire system. We find that entanglement growth is driven by long “dark” intervals, during which no jumps are recorded, interspersed with rapid bursts of bunched quantum jumps reminiscent of the fluorescence emitted by a driven atom. Although each jump tends to reduce entanglement, it also modifies the many-body state, allowing new entanglement to build up during the following dark interval. Our results reveal how monitoring a single site can generate highly nontrivial collective behaviours and could be more experimentally accessible than protocols requiring measurements over an extensive number of degrees of freedom.► BibTeX data@article{DiFresco2026entanglementgrowth, doi = {10.22331/q-2026-08-03-2183}, url = {https://doi.org/10.22331/q-2026-08-03-2183}, title = {Entanglement growth in the dark intervals of a locally monitored free-fermion chain}, author = {Di Fresco, Giovanni and Le Gal, Youenn and Valenti, Davide and Schir{\'{o}}, Marco and Carollo, Angelo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2183}, month = aug, year = {2026} }► References [1] C. Cohen-Tannoudji and J. Dalibard. ``Single-atom laser spectroscopy. looking for dark periods in fluorescence light''. Europhysics Letters 1, 441 (1986). https://doi.org/10.1209/0295-5075/1/9/004 [2] Richard J. Cook and H. J. Kimble. ``Possibility of direct observation of quantum jumps''. Phys. Rev. Lett. 54, 1023–1026 (1985). https://doi.org/10.1103/PhysRevLett.54.1023 [3] J. C. Bergquist, Randall G. Hulet, Wayne M. Itano, and D. J. Wineland. ``Observation of quantum jumps in a single atom''. Phys. Rev. Lett. 57, 1699–1702 (1986). https://doi.org/10.1103/PhysRevLett.57.1699 [4] Warren Nagourney, Jon Sandberg, and Hans Dehmelt. ``Shelved optical electron amplifier: Observation of quantum jumps''. Phys. Rev. Lett. 56, 2797–2799 (1986). https://doi.org/10.1103/PhysRevLett.56.2797 [5] Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Gutiérrez-Jáuregui, R. J. Schoelkopf, M. Mirrahimi, H. J. Carmichael, and M. H. Devoret. ``To catch and reverse a quantum jump mid-flight''. Nature 570, 200–204 (2019). https://doi.org/10.1038/s41586-019-1287-z [6] Masahito Ueda. ``Nonequilibrium open-system theory for continuous photodetection processes: A probability-density-functional description''. Phys. Rev. A 41, 3875–3890 (1990). https://doi.org/10.1103/PhysRevA.41.3875 [7] Jean Dalibard, Yvan Castin, and Klaus Mølmer. ``Wave-function approach to dissipative processes in quantum optics''. Phys. Rev. Lett. 68, 580–583 (1992). https://doi.org/10.1103/PhysRevLett.68.580 [8] C. W. Gardiner, A. S. Parkins, and P. Zoller. ``Wave-function quantum stochastic differential equations and quantum-jump simulation methods''. Phys. Rev. A 46, 4363–4381 (1992). https://doi.org/10.1103/PhysRevA.46.4363 [9] M. B. Plenio and P. L. Knight. ``The quantum-jump approach to dissipative dynamics in quantum optics''. Rev. Mod. Phys. 70, 101–144 (1998). https://doi.org/10.1103/RevModPhys.70.101 [10] Howard M. Wiseman and Gerard J. Milburn. ``Quantum measurement and control''.

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X 8, 011032 (2018). https://doi.org/10.1103/PhysRevX.8.011032 [59] B. Ravon, P. Méhaignerie, Y. Machu, A. Durán Hernández, M. Favier, J. M. Raimond, M. Brune, and C. Sayrin. ``Array of individual circular rydberg atoms trapped in optical tweezers''. Phys. Rev. Lett. 131, 093401 (2023). https://doi.org/10.1103/PhysRevLett.131.093401 [60] Antoine Browaeys and Thierry Lahaye. ``Many-body physics with individually controlled rydberg atoms''. Nature Physics 16, 132–142 (2020). https://doi.org/10.1038/s41567-019-0733-z [61] Jean-Marie Stéphan and Jérôme Dubail. ``Local quantum quenches in critical one-dimensional systems: entanglement, the loschmidt echo, and light-cone effects''. Journal of Statistical Mechanics: Theory and Experiment 2011, P08019 (2011). https://doi.org/10.1088/1742-5468/2011/08/P08019Cited by[1] Pallabi Chatterjee and Ranjan Modak, "Measurement-induced phase transition in periodically driven free-fermionic systems", Physical Review B 112 2, 024304 (2025). [2] Clemens Niederegger, Tatiana Vovk, Elias Starchl, and Lukas M. Sieberer, "Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions", Physical Review B 113 14, 144317 (2026). [3] Y. Machu, A. Durán-Hernández, G. Creutzer, A. A. Young, J. M. Raimond, M. Brune, and C. Sayrin, "Nondestructive Optical Readout and Manipulation of Circular Rydberg Atoms", Physical Review X 16 2, 021040 (2026). [4] Giuseppe Di Giulio, Xhek Turkeshi, and Sara Murciano, "Measurement-Induced Symmetry Restoration and Quantum Mpemba Effect", Entropy 27 4, 407 (2025). [5] Katha Ganguly, Preethi Gopalakrishnan, Atharva Naik, Bijay Kumar Agarwalla, and Manas Kulkarni, "Quantum trajectories and Page-curve entanglement dynamics", Journal of Statistical Mechanics: Theory and Experiment 2025 12, 123102 (2025). [6] Kazuki Yamamoto and Ryusuke Hamazaki, "Measurement-Induced Crossover of Quantum Jump Statistics in Postselection-Free Many-Body Dynamics", arXiv:2503.02418, (2025). [7] Pablo Bayona-Pena, Michele Mazzoni, and Lorenzo Piroli, "Generalized hydrodynamics of free fermions under extensive-charge monitoring", arXiv:2604.05850, (2026). [8] Kazuki Yamamoto and Ryusuke Hamazaki, "Anomalous waiting-time distributions in postselection-free quantum many-body dynamics under continuous monitoring", arXiv:2604.00358, (2026). [9] Kazuki Yamamoto and Ryusuke Hamazaki, "Measurement-Induced Crossover of Quantum Jump Statistics in Postselection-Free Many-Body Dynamics", Physical Review Letters 137 4, 040402 (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-08-03 12:18:42). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-08-03 12:18:40: Could not fetch cited-by data for 10.22331/q-2026-08-03-2183 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe consider a free fermionic chain with monitoring of the particle density on a single site of the chain and study the entanglement dynamics of quantum jump trajectories. We show that the entanglement entropy grows in time towards a stationary state which display volume law scaling of the entropy, in stark contrast with both the unitary dynamics after a local quench and the no-click limit corresponding to full post-selection. We explain the extensive entanglement growth as a consequence of the peculiar distribution of quantum jumps in time, which display superpoissonian waiting time distribution characterised by a bunching of quantum jumps followed by long dark intervals where no-clicks are detected, akin to the distribution of fluorescence light in a driven atom. We show that the presence of dark intervals is the key feature to explain the effect and that by increasing the number of sites which are monitored the volume law scaling gives away to the Zeno effect and its associated area law.Popular summaryThe dynamics of quantum entanglement in monitored systems has recently attracted considerable interest. We show that continuously monitoring just one site of a quantum chain can profoundly affect the entanglement dynamics of the entire system. We find that entanglement growth is driven by long “dark” intervals, during which no jumps are recorded, interspersed with rapid bursts of bunched quantum jumps reminiscent of the fluorescence emitted by a driven atom. Although each jump tends to reduce entanglement, it also modifies the many-body state, allowing new entanglement to build up during the following dark interval. Our results reveal how monitoring a single site can generate highly nontrivial collective behaviours and could be more experimentally accessible than protocols requiring measurements over an extensive number of degrees of freedom.► BibTeX data@article{DiFresco2026entanglementgrowth, doi = {10.22331/q-2026-08-03-2183}, url = {https://doi.org/10.22331/q-2026-08-03-2183}, title = {Entanglement growth in the dark intervals of a locally monitored free-fermion chain}, author = {Di Fresco, Giovanni and Le Gal, Youenn and Valenti, Davide and Schir{\'{o}}, Marco and Carollo, Angelo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2183}, month = aug, year = {2026} }► References [1] C. Cohen-Tannoudji and J. Dalibard. ``Single-atom laser spectroscopy. looking for dark periods in fluorescence light''. Europhysics Letters 1, 441 (1986). https://doi.org/10.1209/0295-5075/1/9/004 [2] Richard J. Cook and H. J. Kimble. ``Possibility of direct observation of quantum jumps''. Phys. Rev. Lett. 54, 1023–1026 (1985). https://doi.org/10.1103/PhysRevLett.54.1023 [3] J. C. Bergquist, Randall G. Hulet, Wayne M. Itano, and D. J. Wineland. ``Observation of quantum jumps in a single atom''. Phys. Rev. Lett. 57, 1699–1702 (1986). https://doi.org/10.1103/PhysRevLett.57.1699 [4] Warren Nagourney, Jon Sandberg, and Hans Dehmelt. ``Shelved optical electron amplifier: Observation of quantum jumps''. Phys. Rev. Lett. 56, 2797–2799 (1986). https://doi.org/10.1103/PhysRevLett.56.2797 [5] Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Gutiérrez-Jáuregui, R. J. Schoelkopf, M. Mirrahimi, H. J. Carmichael, and M. H. Devoret. ``To catch and reverse a quantum jump mid-flight''. Nature 570, 200–204 (2019). https://doi.org/10.1038/s41586-019-1287-z [6] Masahito Ueda. ``Nonequilibrium open-system theory for continuous photodetection processes: A probability-density-functional description''. Phys. Rev. A 41, 3875–3890 (1990). https://doi.org/10.1103/PhysRevA.41.3875 [7] Jean Dalibard, Yvan Castin, and Klaus Mølmer. ``Wave-function approach to dissipative processes in quantum optics''. Phys. Rev. Lett. 68, 580–583 (1992). https://doi.org/10.1103/PhysRevLett.68.580 [8] C. W. Gardiner, A. S. Parkins, and P. Zoller. ``Wave-function quantum stochastic differential equations and quantum-jump simulation methods''. Phys. Rev. A 46, 4363–4381 (1992). https://doi.org/10.1103/PhysRevA.46.4363 [9] M. B. Plenio and P. L. Knight. ``The quantum-jump approach to dissipative dynamics in quantum optics''. Rev. Mod. Phys. 70, 101–144 (1998). https://doi.org/10.1103/RevModPhys.70.101 [10] Howard M. Wiseman and Gerard J. Milburn. ``Quantum measurement and control''.

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