Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point
Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| Published: | 2022-04-27, volume 6, page 700 |
| Eprint: | arXiv:2110.04048v3 |
| Doi: | https://doi.org/10.22331/q-2022-04-27-700 |
| Citation: | Quantum 6, 700 (2022). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms $N$ in the cavity, even in the absence of $N$-body coupling terms.
Featured image: The schematic represents a toy model for a quantum phase transition ($g/g_c>1$ is the superradiant phase), with the black line being the effective potential that is felt by a quantum state (dashed-gray line). Driving the system close to the critical point ($g/g_c \sim 1)$ creates the correlated (squeezed) excitations at a very slow rate (critical slowing down), since the effective potential is still of trapping form. However, if the system is quenched beyond the critical point ($g/g_c > 1$), the same number of correlated excitations can be generated much faster since the initial state will behave as if it was placed in an inverted harmonic oscillator potential. The purple ellipses represent the phase space picture of the state.
Popular summary
Systems exhibiting quantum phase transitions have been the recent subject of intense focus due to their extreme sensitivity in the vicinity of the critical point. However, preparation of the critical ground state must be performed over long time scales in order to avoid excitations, which has so far resulted in sub-optimal scaling of sensitivity with time accounted for as a resource.
In our work, we depart from the traditional notion of metrology near a critical point, instead showing that sensitivity can be enhanced exponentially in a dynamical protocol by quenching past the critical point. We mathematically prove in the paradigmatic setting of cavity QED that a sensitivity exponentially growing in time can be obtained by quenching through a superradiant phase transition. We show that this is associated with a macroscopic occupation of the photonic mode, and that a basic homodyne detection scheme then yields the optimal measurement. Our result offers an exponential speed-up in time over existing protocols acting near the critical point in a general class of superradiant systems, and opens a new avenue for dynamical quantum metrology in critical systems.
► BibTeX data
► References
[1] K. Hammerer, A. S. Sørensen, and E. S. Polzik, Quantum interface between light and atomic ensembles, Rev. Mod. Phys. 82, 1041 (2010).
https://doi.org/10.1103/RevModPhys.82.1041
[2] H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys. 85, 553 (2013).
https://doi.org/10.1103/RevModPhys.85.553
[3] F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, Cavity QED with quantum gases: new paradigms in many-body physics, Advances in Physics 70, 1 (2021).
https://doi.org/10.1080/00018732.2021.1969727
[4] D. Vitali, S. Kuhr, M. Brune, and J.-M. Raimond, A cavity-QED scheme for Heisenberg-limited interferometry, J. Mod. Opt. 54, 1551 (2007).
https://doi.org/10.1080/09500340600741124
[5] S. Gammelmark and K. Mølmer, Phase transitions and Heisenberg limited metrology in an Ising chain interacting with a single-mode cavity field, New J. Phys. 13, 053035 (2011).
https://doi.org/10.1088/1367-2630/13/5/053035
[6] Z.-P. Liu, J. Zhang, B. Özdemir, Ş. K.and Peng, H. Jing, X.-Y. Lü, C.-W. Li, L. Yang, F. Nori, and Y.-x. Liu, Metrology with $\mathcal{PT}$-Symmetric Cavities: Enhanced Sensitivity near the $\mathcal{PT}$-Phase Transition, Phys. Rev. Lett. 117, 110802 (2016).
https://doi.org/10.1103/PhysRevLett.117.110802
[7] K. Gietka, T. Wasak, J. Chwedeńczuk, F. Piazza, and H. Ritsch, Quantum-enhanced interferometry with cavity QED-generated non-classical light, Eur. Phys. J. D 71, 273 (2017).
https://doi.org/10.1140/epjd/e2017-80235-2
[8] W. Cheng, S. C. Hou, Z. Wang, and X. X. Yi, Quantum metrology enhanced by coherence-induced driving in a cavity-QED setup, Phys. Rev. A 100, 053825 (2019).
https://doi.org/10.1103/PhysRevA.100.053825
[9] K. Gietka, F. Mivehvar, and H. Ritsch, Supersolid-Based Gravimeter in a Ring Cavity, Phys. Rev. Lett. 122, 190801 (2019).
https://doi.org/10.1103/PhysRevLett.122.190801
[10] R. J. Lewis-Swan, D. Barberena, J. A. Muniz, J. R. K. Cline, D. Young, J. K. Thompson, and A. M. Rey, Protocol for Precise Field Sensing in the Optical Domain with Cold Atoms in a Cavity, Phys. Rev. Lett. 124, 193602 (2020).
https://doi.org/10.1103/PhysRevLett.124.193602
[11] K. Gietka, F. Mivehvar, and T. Busch, Cavity-enhanced magnetometer with a spinor Bose–Einstein condensate, New J. Phys. 23, 043020 (2021a).
https://doi.org/10.1088/1367-2630/abedff
[12] 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 (2021a).
https://doi.org/10.1103/PhysRevLett.127.210401
[13] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum-enhanced measurements: beating the standard quantum limit, Science 306, 1330 (2004).
https://doi.org/10.1126/science.1104149
[14] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Metrology, Phys. Rev. Lett. 96, 010401 (2006).
https://doi.org/10.1103/PhysRevLett.96.010401
[15] O. Pinel, P. Jian, N. Treps, C. Fabre, and D. Braun, Quantum parameter estimation using general single-mode Gaussian states, Phys. Rev. A 88, 040102 (2013).
https://doi.org/10.1103/PhysRevA.88.040102
[16] L. Pezzé and A. Smerzi, Entanglement, Nonlinear Dynamics, and the Heisenberg Limit, Phys. Rev. Lett. 102, 100401 (2009).
https://doi.org/10.1103/PhysRevLett.102.100401
[17] S. Boixo, S. T. Flammia, C. M. Caves, and J. M. Geremia, Generalized Limits for Single-Parameter Quantum Estimation, Phys. Rev. Lett. 98, 090401 (2007).
https://doi.org/10.1103/PhysRevLett.98.090401
[18] S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
https://doi.org/10.1103/PhysRevLett.72.3439
[19] 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).
https://doi.org/10.1103/RevModPhys.90.035005
[20] E. Polino, M. Valeri, N. Spagnolo, and F. Sciarrino, Photonic quantum metrology, AVS Quantum Science 2, 024703 (2020).
https://doi.org/10.1116/5.0007577
[21] S. Pang and A. N. Jordan, Optimal adaptive control for quantum metrology with time-dependent Hamiltonians, Nat. Commun. 8, 14695 (2017).
https://doi.org/10.1038/ncomms14695
[22] Z. Hou, Y. Jin, H. Chen, J.-F. Tang, C.-J. Huang, H. Yuan, G.-Y. Xiang, C.-F. Li, and G.-C. Guo, ``super-Heisenberg'' and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field, Phys. Rev. Lett. 126, 070503 (2021).
https://doi.org/10.1103/PhysRevLett.126.070503
[23] S. M. Roy and S. L. Braunstein, Exponentially Enhanced Quantum Metrology, Phys. Rev. Lett. 100, 220501 (2008).
https://doi.org/10.1103/PhysRevLett.100.220501
[24] C. D. Marciniak, T. Feldker, I. Pogorelov, R. Kaubruegger, D. V. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, and T. Monz, Optimal metrology with programmable quantum sensors, Nature 603, 604 (2022).
https://doi.org/10.1038/s41586-022-04435-4
[25] M. A. C. Rossi, F. Albarelli, D. Tamascelli, and M. G. Genoni, Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement, Phys. Rev. Lett. 125, 200505 (2020).
https://doi.org/10.1103/PhysRevLett.125.200505
[26] K. Gietka, F. Metz, T. Keller, and J. Li, Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied, Quantum 5, 489 (2021b).
https://doi.org/10.22331/q-2021-07-01-489
[27] D. Braun, G. Adesso, F. Benatti, R. Floreanini, U. Marzolino, M. W. Mitchell, and S. Pirandola, Quantum-enhanced measurements without entanglement, Rev. Mod. Phys. 90, 035006 (2018).
https://doi.org/10.1103/RevModPhys.90.035006
[28] P. Zanardi, M. G. A. Paris, and L. Campos Venuti, Quantum criticality as a resource for quantum estimation, Phys. Rev. A 78, 042105 (2008).
https://doi.org/10.1103/PhysRevA.78.042105
[29] C. Invernizzi, M. Korbman, L. Campos Venuti, and M. G. A. Paris, Optimal quantum estimation in spin systems at criticality, Phys. Rev. A 78, 042106 (2008).
https://doi.org/10.1103/PhysRevA.78.042106
[30] P. A. Ivanov and D. Porras, Adiabatic quantum metrology with strongly correlated quantum optical systems, Phys. Rev. A 88, 023803 (2013).
https://doi.org/10.1103/PhysRevA.88.023803
[31] M. Tsang, Quantum transition-edge detectors, Phys. Rev. A 88, 021801 (2013).
https://doi.org/10.1103/PhysRevA.88.021801
[32] G. Salvatori, A. Mandarino, and M. G. A. Paris, Quantum metrology in Lipkin-Meshkov-Glick critical systems, Phys. Rev. A 90, 022111 (2014).
https://doi.org/10.1103/PhysRevA.90.022111
[33] K. Macieszczak, M. Guţă, I. Lesanovsky, and J. P. Garrahan, Dynamical phase transitions as a resource for quantum enhanced metrology, Phys. Rev. A 93, 022103 (2016).
https://doi.org/10.1103/PhysRevA.93.022103
[34] M. Bina, I. Amelio, and M. G. A. Paris, Dicke coupling by feasible local measurements at the superradiant quantum phase transition, Phys. Rev. E 93, 052118 (2016).
https://doi.org/10.1103/PhysRevE.93.052118
[35] S. Fernández-Lorenzo and D. Porras, Quantum sensing close to a dissipative phase transition: Symmetry breaking and criticality as metrological resources, Phys. Rev. A 96, 013817 (2017).
https://doi.org/10.1103/PhysRevA.96.013817
[36] T. L. Heugel, M. Biondi, O. Zilberberg, and R. Chitra, Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition, Phys. Rev. Lett. 123, 173601 (2019).
https://doi.org/10.1103/PhysRevLett.123.173601
[37] L. Garbe, M. Bina, A. Keller, M. G. A. Paris, and S. Felicetti, Critical Quantum Metrology with a Finite-Component Quantum Phase Transition, Phys. Rev. Lett. 124, 120504 (2020).
https://doi.org/10.1103/PhysRevLett.124.120504
[38] M. Salado-Mejía, R. Román-Ancheyta, F. Soto-Eguibar, and H. M. Moya-Cessa, Spectroscopy and critical quantum thermometry in the ultrastrong coupling regime, Quantum Sci. Technol. 6, 025010 (2021).
https://doi.org/10.1088/2058-9565/abdca5
[39] T. Hatomura, A. Yoshinaga, Y. Matsuzaki, and M. Tatsuta, Quantum metrology based on symmetry-protected adiabatic transformation: imperfection, finite time duration, and dephasing, New J. Phys. 24, 033005 (2022).
https://doi.org/10.1088/1367-2630/ac5375
[40] T. Ilias, D. Yang, S. F. Huelga, and M. B. Plenio, Criticality-Enhanced Quantum Sensing via Continuous Measurement, PRX Quantum 3, 010354 (2022).
https://doi.org/10.1103/PRXQuantum.3.010354
[41] L. Garbe, O. Abah, S. Felicetti, and R. Puebla, Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling (2021), arXiv:2110.04144 [quant-ph].
https://doi.org/10.48550/arXiv.2110.04144
arXiv:2110.04144
[42] K. Gietka, Squeezing by Critical Speeding-up: Applications in Quantum Metrology (2021), arXiv:2111.12206 [quant-ph].
https://doi.org/10.48550/arXiv.2111.12206
arXiv:2111.12206
[43] S. Sachdev, Quantum phase transitions, Handbook of Magnetism and Advanced Magnetic Materials 10.1002/9780470022184 (2007).
https://doi.org/10.1002/9780470022184
[44] W.-L. You, Y.-W. Li, and S.-J. Gu, Fidelity, dynamic structure factor, and susceptibility in critical phenomena, Phys. Rev. E 76, 022101 (2007).
https://doi.org/10.1103/PhysRevE.76.022101
[45] M. Born and V. Fock, Beweis des Adiabatensatzes, Z. Phys. 51, 165 (1928).
https://doi.org/10.1007/BF01343193
[46] M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, and J. Zakrzewski, At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited, Phys. Rev. X 8, 021022 (2018).
https://doi.org/10.1103/PhysRevX.8.021022
[47] Y. Chu, S. Zhang, B. Yu, and J. Cai, Dynamic Framework for Criticality-Enhanced Quantum Sensing, Phys. Rev. Lett. 126, 010502 (2021b).
https://doi.org/10.1103/PhysRevLett.126.010502
[48] K. Gietka and T. Busch, Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model, Phys. Rev. E 104, 034132 (2021).
https://doi.org/10.1103/PhysRevE.104.034132
[49] M. Perarnau-Llobet, D. Malz, and J. I. Cirac, Weakly invasive metrology: quantum advantage and physical implementations, Quantum 5, 446 (2021).
https://doi.org/10.22331/q-2021-04-28-446
[50] S. Felicetti and A. Le Boité, Universal Spectral Features of Ultrastrongly Coupled Systems, Phys. Rev. Lett. 124, 040404 (2020).
https://doi.org/10.1103/PhysRevLett.124.040404
[51] J. Larson and E. K. Irish, Some remarks on `superradiant' phase transitions in light-matter systems, J. Phys. A Math 50, 174002 (2017).
https://doi.org/10.1088/1751-8121/aa65dc
[52] J. Peng, E. Rico, J. Zhong, E. Solano, and I. L. Egusquiza, Unified superradiant phase transitions, Phys. Rev. A 100, 063820 (2019).
https://doi.org/10.1103/PhysRevA.100.063820
[53] M.-J. Hwang, R. Puebla, and M. B. Plenio, Quantum Phase Transition and Universal Dynamics in the Rabi Model, Phys. Rev. Lett. 115, 180404 (2015).
https://doi.org/10.1103/PhysRevLett.115.180404
[54] S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Ann. Physics 326, 2793 (2011).
https://doi.org/10.1016/j.aop.2011.06.004
[55] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).
https://doi.org/10.1103/RevModPhys.84.621
[56] D. F. Walls, Squeezed states of light, Nature 306, 141 (1983).
https://doi.org/10.1038/306141a0
[57] S. Pang and T. A. Brun, Quantum metrology for a general Hamiltonian parameter, Phys. Rev. A 90, 022117 (2014).
https://doi.org/10.1103/PhysRevA.90.022117
[58] A. Monras, Optimal phase measurements with pure Gaussian states, Phys. Rev. A 73, 033821 (2006).
https://doi.org/10.1103/PhysRevA.73.033821
[59] C. Oh, C. Lee, C. Rockstuhl, H. Jeong, J. Kim, H. Nha, and S.-Y. Lee, Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology, npj Quantum Inf. 5, 10 (2019).
https://doi.org/10.1038/s41534-019-0124-4
[60] A. A. Berni, T. Gehring, B. M. Nielsen, V. Händchen, M. G. A. Paris, and U. L. Andersen, Ab initio quantum-enhanced optical phase estimation using real-time feedback control, Nat. Photonics 9, 577 (2015).
https://doi.org/10.1038/nphoton.2015.139
[61] H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, 2009).
https://doi.org/10.1017/CBO9780511813948
[62] A. Hentschel and B. C. Sanders, Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes, Phys. Rev. Lett. 107, 233601 (2011).
https://doi.org/10.1103/PhysRevLett.107.233601
[63] R. Demkowicz-Dobrzański, J. Czajkowski, and P. Sekatski, Adaptive Quantum Metrology under General Markovian Noise, Phys. Rev. X 7, 041009 (2017).
https://doi.org/10.1103/PhysRevX.7.041009
[64] L. Pezzè and A. Smerzi, Quantum Phase Estimation Algorithm with Gaussian Spin States, PRX Quantum 2, 040301 (2021).
https://doi.org/10.1103/PRXQuantum.2.040301
[65] D. Šafránek, Estimation of Gaussian quantum states, J. Phys. A Math 52, 035304 (2018).
https://doi.org/10.1088/1751-8121/aaf068
[66] L. Bakmou, M. Daoud, and R. ahl laamara, Multiparameter quantum estimation theory in quantum Gaussian states, J. Phys. A Math 53, 385301 (2020).
https://doi.org/10.1088/1751-8121/aba770
[67] A. T. Black, H. W. Chan, and V. Vuletić, Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering, Phys. Rev. Lett. 91, 203001 (2003).
https://doi.org/10.1103/PhysRevLett.91.203001
[68] K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature 464, 1301 (2010).
https://doi.org/10.1038/nature09009
[69] D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, Dicke-Model Phase Transition in the Quantum Motion of a Bose-Einstein Condensate in an Optical Cavity, Phys. Rev. Lett. 104, 130401 (2010).
https://doi.org/10.1103/PhysRevLett.104.130401
[70] P. Domokos and H. Ritsch, Collective Cooling and Self-Organization of Atoms in a Cavity, Phys. Rev. Lett. 89, 253003 (2002).
https://doi.org/10.1103/PhysRevLett.89.253003
[71] J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, Dynamical phase transition in the open Dicke model, PNAS 112, 3290 (2015).
https://doi.org/10.1073/pnas.1417132112
[72] M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, Realization of the Dicke Model Using Cavity-Assisted Raman Transitions, Phys. Rev. Lett. 113, 020408 (2014).
https://doi.org/10.1103/PhysRevLett.113.020408
[73] R. M. Kroeze, Y. Guo, V. D. Vaidya, J. Keeling, and B. L. Lev, Spinor Self-Ordering of a Quantum Gas in a Cavity, Phys. Rev. Lett. 121, 163601 (2018).
https://doi.org/10.1103/PhysRevLett.121.163601
[74] H. Keßler, P. Kongkhambut, C. Georges, L. Mathey, J. G. Cosme, and A. Hemmerich, Observation of a Dissipative Time Crystal, Phys. Rev. Lett. 127, 043602 (2021).
https://doi.org/10.1103/PhysRevLett.127.043602
[75] A. Dareau, Y. Meng, P. Schneeweiss, and A. Rauschenbeutel, Observation of Ultrastrong Spin-Motion Coupling for Cold Atoms in Optical Microtraps, Phys. Rev. Lett. 121, 253603 (2018).
https://doi.org/10.1103/PhysRevLett.121.253603
[76] P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Ultrastrong coupling regimes of light-matter interaction, Rev. Mod. Phys. 91, 025005 (2019).
https://doi.org/10.1103/RevModPhys.91.025005
[77] A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nat. Rev. Phys 1, 19 (2019).
https://doi.org/10.1038/s42254-018-0006-2
[78] C. Hamner, C. Qu, Y. Zhang, J. Chang, M. Gong, C. Zhang, and P. Engels, Dicke-type phase transition in a spin-orbit-coupled Bose–Einstein condensate, Nat. Commun. 5, 4023 (2014).
https://doi.org/10.1038/ncomms5023
[79] A. Safavi-Naini, R. J. Lewis-Swan, J. G. Bohnet, M. Gärttner, K. A. Gilmore, J. E. Jordan, J. Cohn, J. K. Freericks, A. M. Rey, and J. J. Bollinger, Verification of a Many-Ion Simulator of the Dicke Model Through Slow Quenches across a Phase Transition, Phys. Rev. Lett. 121, 040503 (2018).
https://doi.org/10.1103/PhysRevLett.121.040503
[80] F. M. Gambetta, I. Lesanovsky, and W. Li, Exploring nonequilibrium phases of the generalized Dicke model with a trapped Rydberg-ion quantum simulator, Phys. Rev. A 100, 022513 (2019).
https://doi.org/10.1103/PhysRevA.100.022513
[81] K. M. Yunusova, D. Konstantinov, H. Bouchiat, and A. D. Chepelianskii, Coupling between Rydberg States and Landau levels of Electrons Trapped on Liquid Helium, Phys. Rev. Lett. 122, 176802 (2019).
https://doi.org/10.1103/PhysRevLett.122.176802
[82] S. Krämer, D. Plankensteiner, L. Ostermann, and H. Ritsch, QuantumOptics.jl: A Julia framework for simulating open quantum systems, Comput. Phys. Commun 227, 109 (2018).
https://doi.org/10.1016/j.cpc.2018.02.004
Cited by
[1] Lu Zhou, Jia Kong, Zhihao Lan, and Weiping Zhang, "Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing", Physical Review Research 5 1, 013087 (2023).
[2] Karol Gietka, "Harnessing center-of-mass excitations in quantum metrology", Physical Review Research 4 4, 043074 (2022).
[3] Anton Bölian, Phatthamon Kongkhambut, Christoph Georges, Roy D. Jara, José Vargas, Jens Klinder, Jayson G. Cosme, Hans Keßler, and Andreas Hemmerich, "Observation of a zero-energy excitation mode in the open Dicke model", Physical Review Research 7 3, L032056 (2025).
[4] Ming Xue, Lu Zhou, Guang-Ming Huang, and Gao-xiang Li, "Quantum Fisher information decomposition for optimal sensing in the quantum Rabi model", Physical Review A 113 1, 013736 (2026).
[5] Wen Huang, Ying Wu, and Xin-You Lü, "Superradiant phase transition induced by the indirect Rabi interaction", Physical Review A 107 3, 033702 (2023).
[6] Guillaume Beaulieu, Fabrizio Minganti, Simone Frasca, Vincenzo Savona, Simone Felicetti, Roberto Di Candia, and Pasquale Scarlino, "Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator", Nature Communications 16 1, 1954 (2025).
[7] Ricard Puig, Pavel Sekatski, Paolo Andrea Erdman, Paolo Abiuso, John Calsamiglia, and Martí Perarnau-Llobet, "From Dynamical to Steady-State Many-Body Metrology: Precision Limits and Their Attainability with Two-Body Interactions", PRX Quantum 6 3, 030309 (2025).
[8] Deng‐Kui Jiang, Rui Zhang, Ying Liu, and Le‐Man Kuang, "Photon‐Assisted Quantum Phase Transitions in a Cavity Optomechanical System with Two Nonlinear Mechanical Modes", Annalen der Physik 536 11, 2400179 (2024).
[9] Shao-Bo Tang, Hao Qin, Bing-Bing Liu, D.-Y. Wang, Kaifeng Cui, S.-L. Su, L.-L. Yan, and Gang Chen, "Enhancement of quantum sensing in a cavity-optomechanical system around the quantum critical point", Physical Review A 108 5, 053514 (2023).
[10] Wei Qin, Anton Frisk Kockum, Carlos Sánchez Muñoz, Adam Miranowicz, and Franco Nori, "Quantum amplification and simulation of strong and ultrastrong coupling of light and matter", Physics Reports 1078, 1 (2024).
[11] Ju-Yeon Gyhm, Hyukjoon Kwon, and Myung-Joong Hwang, "Fundamental scaling limit in critical quantum metrology", Physical Review Research 8 3, 033004 (2026).
[12] Robert Mattes, Albert Cabot, Federico Carollo, and Igor Lesanovsky, "Designing Open Quantum Systems for Enabling Quantum-Enhanced Sensing through Classical Measurements", Physical Review Letters 135 23, 230402 (2025).
[13] Kahan Dare, Jannek J. Hansen, Iurie Coroli, Aisling Johnson, Markus Aspelmeyer, and Uroš Delić, "Ultrastrong linear optomechanical interaction", Physical Review Research 6 4, L042025 (2024).
[14] Raffaele Salvia, Mohammad Mehboudi, and Martí Perarnau-Llobet, "Critical Quantum Metrology Assisted by Real-Time Feedback Control", Physical Review Letters 130 24, 240803 (2023).
[15] Ting-Ting Ma, Jian Tang, Yun-Lan Zuo, Ran Huang, Adam Miranowicz, Franco Nori, and Hui Jing, "Two-Polariton Blockade via Ultrastrong Light-Matter Coupling", Physical Review Letters 136 3, 033601 (2026).
[16] Rui Zhang, Wenkui Ding, Zhucheng Zhang, Lei Shao, Yuyu Zhang, and Xiaoguang Wang, "Relations between quantum metrology and criticality in general su(1,1) systems", Physical Review A 110 1, 012413 (2024).
[17] Christoph Hotter, Helmut Ritsch, and Karol Gietka, "Combining Critical and Quantum Metrology", Physical Review Letters 132 6, 060801 (2024).
[18] Zu‐Jian Ying, Hang‐Hang Han, Bo‐Jian Li, Simone Felicetti, and Daniel Braak, "Critical Quantum Metrology in a Stabilized Two‐Photon Rabi Model", Advanced Quantum Technologies 8 11, e00263 (2025).
[19] Simone Cavazzoni, Berihu Teklu, and Matteo G. A. Paris, "Frequency estimation by frequency jumps", npj Quantum Information 11 1, 174 (2025).
[20] Louis Garbe, Obinna Abah, Simone Felicetti, and Ricardo Puebla, "Exponential time-scaling of estimation precision by reaching a quantum critical point", Physical Review Research 4 4, 043061 (2022).
[21] Lu Zhou, Zheng-Chun Li, Keye Zhang, Zhihao Lan, Alessio Celi, and Weiping Zhang, "Moiré superradiance in cavity quantum electrodynamics with quantum atom gas", Physical Review A 112 4, 043718 (2025).
[22] George Mihailescu, Uesli Alushi, Roberto Di Candia, Simone Felicetti, and Karol Gietka, "Critical Quantum Sensing: A Tutorial on Parameter Estimation Near Quantum Phase Transitions", PRX Quantum 7 2, 020201 (2026).
[23] Yaoming Chu, Xiangbei Li, and Jianming Cai, "Quantum Delocalization on Correlation Landscape: The Key to Exponentially Fast Multipartite Entanglement Generation", Physical Review Letters 133 11, 110201 (2024).
[24] Keshav Das Agarwal, Sayan Mondal, Ayan Sahoo, Debraj Rakshit, Aditi Sen(De), and Ujjwal Sen, "Quantum sensing with ultracold simulators in lattice and ensemble systems: A review", International Journal of Modern Physics C 2543006 (2025).
[25] Dingwei Zhao, Abolfazl Bayat, and Victor Montenegro, "Near-ultimate quantum-enhanced sensitivity in dissipative critical sensing with partial access", Physical Review Research 8 2, 023241 (2026).
[26] Karol Gietka, Christoph Hotter, and Helmut Ritsch, "Unique Steady-State Squeezing in a Driven Quantum Rabi Model", Physical Review Letters 131 22, 223604 (2023).
[27] George Mihailescu, Steve Campbell, and Karol Gietka, "Uncertain quantum critical metrology: From single- to multiparameter sensing", Physical Review A 111 5, 052621 (2025).
[28] Jia-Ming Cheng, Yong-Chang Zhang, Xiang-Fa Zhou, and Zheng-Wei Zhou, "Super-Heisenberg Scaling in a Triple-Point Criticality", Physical Review Letters 134 19, 190802 (2025).
[29] Jim Skulte, Jayson G. Cosme, and Ludwig Mathey, "Rotation sensor based on an atom-cavity system", Physical Review Research 8 2, L022057 (2026).
[30] Jose Carlos Pelayo, Karol Gietka, and Thomas Busch, "Distributed quantum sensing with optical lattices", Physical Review A 107 3, 033318 (2023).
[31] Fabrizio Minganti, Louis Garbe, Alexandre Le Boité, and Simone Felicetti, "Non-Gaussian superradiant transition via three-body ultrastrong coupling", Physical Review A 107 1, 013715 (2023).
[32] U. Alushi, W. Górecki, S. Felicetti, and R. Di Candia, "Optimality and Noise Resilience of Critical Quantum Sensing", Physical Review Letters 133 4, 040801 (2024).
[33] Wojciech Górecki, Francesco Albarelli, Simone Felicetti, Roberto Di Candia, and Lorenzo Maccone, "Interplay Between Time and Energy in Bosonic Noisy Quantum Metrology", PRX Quantum 6 2, 020351 (2025).
[34] Zu-Jian Ying, Simone Felicetti, Gang Liu, and Daniel Braak, "Critical Quantum Metrology in the Non-Linear Quantum Rabi Model", Entropy 24 8, 1015 (2022).
[35] Venelin P Pavlov, Diego Porras, and Peter A Ivanov, "Quantum metrology with critical driven-dissipative collective spin system", Physica Scripta 98 9, 095103 (2023).
[36] Guillaume Beaulieu, Fabrizio Minganti, Simone Frasca, Marco Scigliuzzo, Simone Felicetti, Roberto Di Candia, and Pasquale Scarlino, "Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator", PRX Quantum 6 2, 020301 (2025).
[37] Zhen-Xia Niu and Qian Wang, "Role of interaction range in critical quantum metrology for long-range Kitaev chain", New Journal of Physics 28 1, 014504 (2026).
[38] Victor Montenegro, Chiranjib Mukhopadhyay, Rozhin Yousefjani, Saubhik Sarkar, Utkarsh Mishra, Matteo G.A. Paris, and Abolfazl Bayat, "Review: Quantum metrology and sensing with many-body systems", Physics Reports 1134, 1 (2025).
[39] Yan Li and Zhihong Ren, "Quantum Fisher information of an N-qubit maximal sliced state in decoherence channels and Ising-type interacting model", Chaos, Solitons & Fractals 177, 114289 (2023).
[40] Yan Li and Zhi-Hong Ren, "Quantum Fisher information of multi-qubit WV entangled state under Lipkin-Meshkov-Glick model", Acta Physica Sinica 72 22, 220302 (2023).
[41] Uesli Alushi, Alessandro Coppo, Valentina Brosco, Roberto Di Candia, and Simone Felicetti, "Collective quantum enhancement in critical quantum sensing", Communications Physics 8 1, 74 (2025).
[42] Jia-Hao Lü, Wen Ning, Fan Wu, Ri-Hua Zheng, Ken Chen, Xin Zhu, Zhen-Biao Yang, Huai-Zhi Wu, and Shi-Biao Zheng, "Critical quantum metrology robust against dissipation and nonadiabaticity", Science Advances 12 6, eady2358 (2026).
[43] Laurin Ostermann and Karol Gietka, "Temperature-enhanced critical quantum metrology", Physical Review A 109 5, L050601 (2024).
[44] Karol Gietka and Helmut Ritsch, "Squeezing and Overcoming the Heisenberg Scaling with Spin-Orbit Coupled Quantum Gases", Physical Review Letters 130 9, 090802 (2023).
[45] Louis Garbe, Obinna Abah, Simone Felicetti, and Ricardo Puebla, "Critical quantum metrology with fully-connected models: from Heisenberg to Kibble-Zurek scaling", Quantum Science and Technology 7 3, 035010 (2022).
[46] Karol Gietka, "Squeezing by critical speeding up: Applications in quantum metrology", Physical Review A 105 4, 042620 (2022).
[47] Eoin O'Connor, Victor Montenegro, Francesco Albarelli, Matteo G. A. Paris, Abolfazl Bayat, and Marco G. Genoni, "Attaining Quantum Sensing Enhancement from Monitored Dissipative Time Crystals", arXiv:2508.15448, (2025).
[48] Enrico Rinaldi, Roberto Di Candia, Simone Felicetti, and Fabrizio Minganti, "Dispersive qubit readout with machine learning", arXiv:2112.05332, (2021).
[49] Luca Previdi, Yilun Xu, Qiongyi He, and Matteo G. A. Paris, "Multi-Parameter Multi-Critical Metrology of the Dicke Model", arXiv:2603.03451, (2026).
The above citations are from Crossref's cited-by service (last updated successfully 2026-07-17 05:17:10) and SAO/NASA ADS (last updated successfully 2026-07-16 16:38:28). The list may be incomplete as not all publishers provide suitable and complete citation data.
Could not fetch ADS cited-by data during last attempt 2026-07-17 05:17:09: Cannot retrieve data from ADS due to rate limitations.
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.