- Open Access
Reconfigurable Dissipative Entanglement between Many Spin Ensembles: From Robust Quantum Sensing to Many-Body State Engineering
Phys. Rev. X 16, 021047 – Published 1 June, 2026
DOI: https://doi.org/10.1103/qdh9-2pc7
Abstract
An attractive approach for stabilizing entangled many-body spin states is to employ engineered dissipation. Most existing proposals either target relatively simple collective spin states or require numerous independent and complex dissipative processes. Here, we show a surprisingly versatile scheme for many-body reservoir engineering that relies solely on fully collective single-excitation decay, augmented with local Hamiltonian terms. Crucially, all these ingredients are readily available in cavity QED setups. Our method is based on splitting the spin system into groups of subensembles and provides an easily tunable setup for stabilizing a broad family of pure, highly entangled states with closed-form analytic descriptions. Our results have immediate application to multiensemble quantum metrology, enabling Heisenberg-limited sensing of field gradients and curvatures. Notably, our approach solves an important challenge in differential quantum sensing by providing an example of Heisenberg-limited differential sensing immune to common-mode noise and accessible with only simple one-body measurements. The same setup also allows the stabilization of an entire family of entangled states in a one-dimensional chain of spin ensembles with symmetry-protected topological order and has a direct connection to the outputs of sequential unitary circuits. A special case of our protocol efficiently stabilizes the celebrated Affleck-Kennedy-Lieb-Tasaki state.
Physics Subject Headings (PhySH)
Popular Summary
Stabilizing complex entangled states against decoherence remains a central challenge in quantum science, often requiring intricate and specialized dissipative processes. We introduce a versatile framework that overcomes this complexity by utilizing a single collective decay process—ubiquitous in cavity QED systems—augmented with easily tunable laser detunings and spin interactions. By breaking permutation symmetry, we dissipatively stabilize a broad family of noncollective many-body states with exact analytical descriptions. Our approach enables multiensemble quantum sensors that achieve Heisenberg-limited sensitivity to field gradients and curvatures while remaining robust to common-mode noise. Furthermore, we demonstrate the stabilization of symmetry-protected topological order, including the celebrated Affleck-Kennedy-Lieb-Tasaki state. These results indicate that simple, naturally occurring dissipation can be reimagined as a reconfigurable tool for engineering both metrological resources and exotic phases of quantum matter.
Article Text
References (90)
- L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
- F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, Cavity QED with quantum gases: New paradigms in many-body physics, Adv. Phys. 70, 1 (2021).
- R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
- M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301 (1982).
- R. Puri and S. Lawande, Exact steady-state density operator for a collective atomic system in an external field, Phys. Lett. 72A, 200 (1979).
- H. J. Carmichael, Analytical and numerical results for the steady state in cooperative resonance fluorescence, J. Phys. B 13, 3551 (1980).
- F. Iemini, A. Russomanno, J. Keeling, M. Schirò, M. Dalmonte, and R. Fazio, Boundary time crystals, Phys. Rev. Lett. 121, 035301 (2018).
- G. S. Agarwal and R. R. Puri, Cooperative behavior of atoms irradiated by broadband squeezed light, Phys. Rev. A 41, 3782 (1990).
- E. G. Dalla Torre, J. Otterbach, E. Demler, V. Vuletic, and M. D. Lukin, Dissipative preparation of spin squeezed atomic ensembles in a steady state, Phys. Rev. Lett. 110, 120402 (2013).
- S.-Y. Bai and J.-H. An, Generating stable spin squeezing by squeezed-reservoir engineering, Phys. Rev. Lett. 127, 083602 (2021).
- P. Groszkowski, M. Koppenhöfer, H.-K. Lau, and A. A. Clerk, Reservoir-engineered spin squeezing: Macroscopic even-odd effects and hybrid-systems implementations, Phys. Rev. X 12, 011015 (2022).
- R. Gutiérrez-Jáuregui, A. Asenjo-Garcia, and G. S. Agarwal, Dissipative stabilization of dark quantum dimers via squeezed vacuum, Phys. Rev. Res. 5, 013127 (2023).
- A. S. Parkins, E. Solano, and J. I. Cirac, Unconditional two-mode squeezing of separated atomic ensembles, Phys. Rev. Lett. 96, 053602 (2006).
- H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, Entanglement generated by dissipation and steady state entanglement of two macroscopic objects, Phys. Rev. Lett. 107, 080503 (2011).
- M. Mamaev, M. Koppenhöfer, A. Pocklington, and A. A. Clerk, Non-Gaussian generalized two-mode squeezing: Applications to two-ensemble spin squeezing and beyond, Phys. Rev. Lett. 134, 073603 (2025).
- R. Kaubruegger, D. F. Padilla, A. Shankar, C. Hotter, S. R. Muleady, J. Bringewatt, Y. Baamara, E. Abbasgholinejad, A. V. Gorshkov, K. Mølmer, J. K. Thompson, and A. M. Rey, Lieb-Mattis states for robust entangled differential phase sensing, arXiv:2506.10151 [Phys. Rev. X (to be published)].
- J. F. Poyatos, J. I. Cirac, and P. Zoller, Quantum reservoir engineering with laser cooled trapped ions, Phys. Rev. Lett. 77, 4728 (1996).
- T. Rakovszky, S. Gopalakrishnan, and C. von Keyserlingk, Defining stable phases of open quantum systems, Phys. Rev. X 14, 041031 (2024).
- S. Sang, Y. Zou, and T. H. Hsieh, Mixed-state quantum phases: Renormalization and quantum error correction, Phys. Rev. X 14, 031044 (2024).
- P. M. Harrington, E. J. Mueller, and K. W. Murch, Engineered dissipation for quantum information science, Nat. Rev. Phys. 4, 660 (2022).
- K. Stannigel, P. Rabl, and P. Zoller, Driven-dissipative preparation of entangled states in cascaded quantum-optical networks, New J. Phys. 14, 063014 (2012).
- T. Ramos, H. Pichler, A. J. Daley, and P. Zoller, Quantum spin dimers from chiral dissipation in cold-atom chains, Phys. Rev. Lett. 113, 237203 (2014).
- H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, Quantum optics of chiral spin networks, Phys. Rev. A 91, 042116 (2015).
- A. Periwal, E. S. Cooper, P. Kunkel, J. F. Wienand, E. J. Davis, and M. Schleier-Smith, Programmable interactions and emergent geometry in an array of atom clouds, Nature (London) 600, 630 (2021).
- B. K. Malia, Y. Wu, J. Martínez-Rincón, and M. A. Kasevich, Distributed quantum sensing with mode-entangled spin-squeezed atomic states, Nature (London) 612, 661 (2022).
- E. S. Cooper, P. Kunkel, A. Periwal, and M. Schleier-Smith, Graph states of atomic ensembles engineered by photon-mediated entanglement, Nat. Phys. 20, 770 (2024).
- D. J. Young, A. Chu, E. Y. Song, D. Barberena, D. Wellnitz, Z. Niu, V. M. Schäfer, R. J. Lewis-Swan, A. M. Rey, and J. K. Thompson, Observing dynamical phases of BCS superconductors in a cavity QED simulator, Nature (London) 625, 679 (2024).
- R. Corgier, M. Malitesta, L. A. Sidorenkov, F. P. Dos Santos, G. Rosi, G. M. Tino, A. Smerzi, L. Salvi, and L. Pezzè, Optimized squeezing for accurate differential sensing under large phase noise, Quantum Sci. Technol. 10, 045016 (2025).
- X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems, Phys. Rev. B 83, 035107 (2011).
- F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, Symmetry protection of topological phases in one-dimensional quantum spin systems, Phys. Rev. B 85, 075125 (2012).
- X. Chen, A. Dua, M. Hermele, D. T. Stephen, N. Tantivasadakarn, R. Vanhove, and J.-Y. Zhao, Sequential quantum circuits as maps between gapped phases, Phys. Rev. B 109, 075116 (2024).
- I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59, 799 (1987).
- I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Valence bond ground states in isotropic quantum antiferromagnets, Commun. Math. Phys. 115, 477 (1988).
- T. E. Lee, C.-K. Chan, and S. F. Yelin, Dissipative phase transitions: Independent versus collective decay and spin squeezing, Phys. Rev. A 90, 052109 (2014).
- D. Barberena, R. J. Lewis-Swan, J. K. Thompson, and A. M. Rey, Driven-dissipative quantum dynamics in ultra-long-lived dipoles in an optical cavity, Phys. Rev. A 99, 053411 (2019).
- D. Roberts and A. A. Clerk, Exact solution of the infinite-range dissipative transverse-field ising model, Phys. Rev. Lett. 131, 190403 (2023).
- G. Ferioli, A. Glicenstein, I. Ferrier-Barbut, and A. Browaeys, A non-equilibrium superradiant phase transition in free space, Nat. Phys. 19, 1345 (2023).
- E. Y. Song, D. Barberena, D. J. Young, E. Chaparro, A. Chu, S. Agarwal, Z. Niu, J. T. Young, A. M. Rey, and J. K. Thompson, A dissipation-induced superradiant transition in a strontium cavity-QED system, Sci. Adv. 11, eadu5799 (2025).
- P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, Chiral quantum optics, Nature (London) 541, 473 (2017).
- D. G. Suárez-Forero, M. Jalali Mehrabad, C. Vega, A. González-Tudela, and M. Hafezi, Chiral quantum optics: Recent developments and future directions, PRX Quantum 6, 020101 (2025).
- C. W. Gardiner, Driving a quantum system with the output field from another driven quantum system, Phys. Rev. Lett. 70, 2269 (1993).
- H. J. Carmichael, Quantum trajectory theory for cascaded open systems, Phys. Rev. Lett. 70, 2273 (1993).
- D. Roberts, A. Lingenfelter, and A. A. Clerk, Hidden time-reversal symmetry, quantum detailed balance and exact solutions of driven-dissipative quantum systems, PRX Quantum 2, 020336 (2021).
- A. Cabot, F. Carollo, and I. Lesanovsky, Continuous sensing and parameter estimation with the boundary time crystal, Phys. Rev. Lett. 132, 050801 (2024).
- B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller, Preparation of entangled states by quantum Markov processes, Phys. Rev. A 78, 042307 (2008).
- J. Kitzinger, M. Chaudhary, M. Kondappan, V. Ivannikov, and T. Byrnes, Two-axis two-spin squeezed states, Phys. Rev. Res. 2, 033504 (2020).
- B. Sundar, D. Barberena, A. P. Orioli, A. Chu, J. K. Thompson, A. M. Rey, and R. J. Lewis-Swan, Bosonic pair production and squeezing for optical phase measurements in long-lived dipoles coupled to a cavity, Phys. Rev. Lett. 130, 113202 (2023).
- A. Pocklington and A. A. Clerk, Universal time-entanglement trade-off in open quantum systems, PRX Quantum 5, 040305 (2024).
- A. Pocklington and A. A. Clerk, Accelerating dissipative state preparation with adaptive open quantum dynamics, Phys. Rev. Lett. 134, 050603 (2025).
- M. B. Plenio and P. L. Knight, The quantum-jump approach to dissipative dynamics in quantum optics, Rev. Mod. Phys. 70, 101 (1998).
- M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138 (1993).
- M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, Squeezing the collective spin of a dilute atomic ensemble by cavity feedback, Phys. Rev. A 81, 021804(R) (2010).
- A. Chu, P. He, J. K. Thompson, and A. M. Rey, Quantum enhanced cavity QED interferometer with partially delocalized atoms in lattices, Phys. Rev. Lett. 127, 210401 (2021).
- D. Barberena, A. Chu, J. K. Thompson, and A. M. Rey, Trade-offs between unitary and measurement induced spin squeezing in cavity QED, Phys. Rev. Res. 6, L032037 (2024).
- G. E. Marti, R. B. Hutson, A. Goban, S. L. Campbell, N. Poli, and J. Ye, Imaging optical frequencies with precision and resolution, Phys. Rev. Lett. 120, 103201 (2018).
- X. Zheng, J. Dolde, and S. Kolkowitz, Reducing the instability of an optical lattice clock using multiple atomic ensembles, Phys. Rev. X 14, 011006 (2024).
- K. Kim, A. Aeppli, W. Warfield, A. Chu, A. M. Rey, and J. Ye, Atomic coherence of 2 minutes and instability of at 1 s in a wannier-stark lattice clock, Phys. Rev. Lett. 135, 103601 (2025).
- J. B. Fixler, G. T. Foster, J. M. McGuirk, and M. A. Kasevich, Atom interferometer measurement of the Newtonian constant of gravity, Science 315, 74 (2007).
- G. Rosi, L. Cacciapuoti, F. Sorrentino, M. Menchetti, M. Prevedelli, and G. M. Tino, Measurement of the gravity-field curvature by atom interferometry, Phys. Rev. Lett. 114, 013001 (2015).
- R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. Müller, Measurement of the fine-structure constant as a test of the standard model, Science 360, 191 (2018).
- G. T. Foster, J. B. Fixler, J. M. McGuirk, and M. A. Kasevich, Method of phase extraction between coupled atom interferometers using ellipse-specific fitting, Opt. Lett. 27, 951 (2002).
- Y. Li, L. Joosten, Y. Baamara, P. Colciaghi, A. Sinatra, P. Treutlein, and T. Zibold, Multiparameter estimation with an array of entangled atomic sensors, Science 391, 374 (2026).
- C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, Sequential Generation of Entangled Multiqubit States, Phys. Rev. Lett. 95, 110503 (2005).
- C. Schön, K. Hammerer, M. M. Wolf, J. I. Cirac, and E. Solano, Sequential generation of matrix-product states in cavity QED, Phys. Rev. A 75, 032311 (2007).
- M. C. Bañuls, D. Pérez-García, M. M. Wolf, F. Verstraete, and J. I. Cirac, Sequentially generated states for the study of two-dimensional systems, Phys. Rev. A 77, 052306 (2008).
- Z.-Y. Wei, D. Malz, and J. I. Cirac, Sequential generation of projected entangled-pair states, Phys. Rev. Lett. 128, 010607 (2022).
- F. D. M. Haldane, Nonlinear field theory of large-spin heisenberg antiferromagnets: Semiclassically quantized solitons of the one-dimensional easy-axis Néel state, Phys. Rev. Lett. 50, 1153 (1983).
- F. Verstraete and J. I. Cirac, Valence-bond states for quantum computation, Phys. Rev. A 70, 060302(R) (2004).
- D. Gross and J. Eisert, Novel schemes for measurement-based quantum computation, Phys. Rev. Lett. 98, 220503 (2007).
- F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys. 5, 633 (2009).
- J. I. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93, 045003 (2021).
- H.-H. Tu, G.-M. Zhang, T. Xiang, Z.-X. Liu, and T.-K. Ng, Topologically distinct classes of valence-bond solid states with their parent Hamiltonians, Phys. Rev. B 80, 014401 (2009).
- K. C. Smith, E. Crane, N. Wiebe, and S. M. Girvin, Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements, PRX Quantum 4, 020315 (2023).
- J. Agustí, X. H. H. Zhang, Y. Minoguchi, and P. Rabl, Autonomous distribution of programmable multiqubit entanglement in a dual-rail quantum network, Phys. Rev. Lett. 131, 250801 (2023).
- V. Sharma and E. J. Mueller, Driven-dissipative control of cold atoms in tilted optical lattices, Phys. Rev. A 103, 043322 (2021).
- L. Zhou, S. Choi, and M. D. Lukin, Symmetry-protected dissipative preparation of matrix product states, Phys. Rev. A 104, 032418 (2021).
- Y. Wang, K. Snizhko, A. Romito, Y. Gefen, and K. Murch, Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array, Phys. Rev. A 108, 013712 (2023).
- J. Langbehn, K. Snizhko, I. Gornyi, G. Morigi, Y. Gefen, and C. P. Koch, Dilute measurement-induced cooling into many-body ground states, PRX Quantum 5, 030301 (2024).
- M. den Nijs and K. Rommelse, Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains, Phys. Rev. B 40, 4709 (1989).
- M. Oshikawa, Hidden symmetry in quantum spin chains with arbitrary integer spin, J. Phys. Condens. Matter 4, 7469 (1992).
- K. Totsuka and M. Suzuki, Matrix formalism for the VBS-type models and hidden order, J. Phys. Condens. Matter 7, 1639 (1995).
- F. Pollmann and A. M. Turner, Detection of symmetry-protected topological phases in one dimension, Phys. Rev. B 86, 125441 (2012).
- A. K. Kolezhuk and H.-J. Mikeska, Models with exact ground states connecting smoothly the dimer and Haldane phases of one-dimensional spin chains, Phys. Rev. B 56, R11380 (1997).
- Z. Zhang and Q. Zhuang, Distributed quantum sensing, Quantum Sci. Technol. 6, 043001 (2021).
- F. Mivehvar, Conventional and unconventional dicke models: Multistabilities and nonequilibrium dynamics, Phys. Rev. Lett. 132, 073602 (2024).
- Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).
- D. M. Brink and G. R. Satchler, Angular Momentum, 2nd ed. (Oxford University Press, New York, 1968).
- R. Kubo, Generalized Cumulant Expansion Method, J. Phys. Soc. Jpn. 17, 1100 (1962).
- E. Davis, G. Bentsen, and M. Schleier-Smith, Approaching the Heisenberg limit without single-particle detection, Phys. Rev. Lett. 116, 053601 (2016).
- M. Koppenhöfer, P. Groszkowski, and A. A. Clerk, Squeezed superradiance enables robust entanglement-enhanced metrology even with highly imperfect readout, Phys. Rev. Lett. 131, 060802 (2023).
