Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

Karol Gietka, Friederike Metz, Tim Keller, and Jing Li

Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore $regular$ quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.

Critical metrology, which relies on the extreme sensitivity of critical ground states to small changes of Hamiltonian parameters, is believed to give rise to an enhanced precision compared to regular quantum metrology. However, the required time resources for preparing the critical ground state are usually not considered and will result in critical quantum metrology protocols which will inevitably operate on time scales beyond the decoherence times of an experiment. In order to decrease the time of an adiabatic protocol one could harness shortcuts-to-adiabaticity and, in principle, overcome the Heisenberg limit of precision. However, in our article we show that not only the adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision but also argue that even though shortcuts-to-adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology.

► BibTeX data

► References

[1] V. Giovannetti, S. Lloyd, and L. Maccone. Quantum metrology. Phys. Rev. Lett., 96: 010401, 2006. 10.1103/​PhysRevLett.96.010401.
https:/​/​doi.org/​10.1103/​PhysRevLett.96.010401

[2] V. Giovannetti, S. Lloyd, and L. Maccone. Quantum-enhanced measurements: beating the standard quantum limit. Science, 306 (5700): 1330–1336, 2004a. 10.1126/​science.1104149.
https:/​/​doi.org/​10.1126/​science.1104149

[3] V. Giovannetti, S. Lloyd, and L. Maccone. Quantum-enhanced measurements: beating the standard quantum limit. Science, 306 (5700): 1330–1336, 2004b. 10.1126/​science.1104149.
https:/​/​doi.org/​10.1126/​science.1104149

[4] R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă. The elusive heisenberg limit in quantum-enhanced metrology. Nat. Commun, 3 (1): 1–8, 2012. 10.1038/​ncomms2067.
https:/​/​doi.org/​10.1038/​ncomms2067

[5] R. Demkowicz-Dobrzański, M. Jarzyna, and J. Kołodyński. Chapter four - quantum limits in optical interferometry. In E. Wolf, editor, Progress in Optics, volume 60, pages 345 – 435. Elsevier, 2015. 10.1016/​bs.po.2015.02.003.
https:/​/​doi.org/​10.1016/​bs.po.2015.02.003

[6] E. Polino, M. Valeri, N. Spagnolo, and F. Sciarrino. Photonic quantum metrology. AVS Quantum Science, 2 (2): 024703, 2020. 10.1116/​5.0007577.
https:/​/​doi.org/​10.1116/​5.0007577

[7] 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, 2018a. 10.1103/​RevModPhys.90.035005.
https:/​/​doi.org/​10.1103/​RevModPhys.90.035005

[8] BM Escher, RL de Matos Filho, and L. Davidovich. General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nat. Phys., 7 (5): 406–411, 2011. 10.1038/​nphys1958.
https:/​/​doi.org/​10.1038/​nphys1958

[9] R. Chaves, J. B. Brask, M. Markiewicz, J. Kołodyński, and A. Acín. Noisy metrology beyond the standard quantum limit. Phys. Rev. Lett., 111: 120401, 2013. 10.1103/​PhysRevLett.111.120401.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.120401

[10] 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. 10.1103/​RevModPhys.90.035006.
https:/​/​doi.org/​10.1103/​RevModPhys.90.035006

[11] 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. 10.1103/​PhysRevA.78.042106.
https:/​/​doi.org/​10.1103/​PhysRevA.78.042106

[12] P. Zanardi, M. G. A. Paris, and L. Campos Venuti. Quantum criticality as a resource for quantum estimation. Phys. Rev. A, 78: 042105, 2008a. 10.1103/​PhysRevA.78.042105.
https:/​/​doi.org/​10.1103/​PhysRevA.78.042105

[13] P. A. Ivanov and D. Porras. Adiabatic quantum metrology with strongly correlated quantum optical systems. Phys. Rev. A, 88: 023803, 2013. 10.1103/​PhysRevA.88.023803.
https:/​/​doi.org/​10.1103/​PhysRevA.88.023803

[14] M. Tsang. Quantum transition-edge detectors. Phys. Rev. A, 88: 021801, 2013. 10.1103/​PhysRevA.88.021801.
https:/​/​doi.org/​10.1103/​PhysRevA.88.021801

[15] G. Salvatori, A. Mandarino, and M. G. A. Paris. Quantum metrology in lipkin-meshkov-glick critical systems. Phys. Rev. A, 90: 022111, 2014. 10.1103/​PhysRevA.90.022111.
https:/​/​doi.org/​10.1103/​PhysRevA.90.022111

[16] K. Macieszczak, Guţă, M., I. Lesanovsky, and J. P. Garrahan. Dynamical phase transitions as a resource for quantum enhanced metrology. Phys. Rev. A, 93: 022103, 2016. 10.1103/​PhysRevA.93.022103.
https:/​/​doi.org/​10.1103/​PhysRevA.93.022103

[17] 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. 10.1103/​PhysRevE.93.052118.
https:/​/​doi.org/​10.1103/​PhysRevE.93.052118

[18] 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. 10.1103/​PhysRevA.96.013817.
https:/​/​doi.org/​10.1103/​PhysRevA.96.013817

[19] 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. 10.1103/​PhysRevLett.123.173601.
https:/​/​doi.org/​10.1103/​PhysRevLett.123.173601

[20] 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. 10.1103/​PhysRevLett.124.120504.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.120504

[21] Y. Chu, S. Zhang, B. Yu, and J. Cai. Dynamic framework for criticality-enhanced quantum sensing. Phys. Rev. Lett., 126: 010502, 2021. 10.1103/​PhysRevLett.126.010502.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.010502

[22] P. Zanardi, M. G. A. Paris, and L. Campos Venuti. Quantum criticality as a resource for quantum estimation. Phys. Rev. A, 78: 042105, 2008b. 10.1103/​PhysRevA.78.042105.
https:/​/​doi.org/​10.1103/​PhysRevA.78.042105

[23] 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. 10.1103/​PhysRevX.8.021022.
https:/​/​doi.org/​10.1103/​PhysRevX.8.021022

[24] O. Abah, R. Puebla, A. Kiely, G. De Chiara, M. Paternostro, and S. Campbell. Energetic cost of quantum control protocols. New J. Phys., 21 (10): 103048, 2019. 10.1088/​1367-2630/​ab4c8c.
https:/​/​doi.org/​10.1088/​1367-2630/​ab4c8c

[25] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 91: 045001, 2019. 10.1103/​RevModPhys.91.045001.
https:/​/​doi.org/​10.1103/​RevModPhys.91.045001

[26] Busch P. Time in Quantum Mechanics. Lecture Notes in Physics, volume 72, chapter The Time-Energy Uncertainty Relation. Springer, Berlin, Heidelberg, 2002. doi.org/​10.1007/​3-540-45846-8_3.
https:/​/​doi.org/​10.1007/​3-540-45846-8_3

[27] H. R. Lewis and PGL Leach. A direct approach to finding exact invariants for one-dimensional time-dependent classical hamiltonians. J. Math. Phys., 23 (12): 2371–2374, 1982. 10.1063/​1.525329.
https:/​/​doi.org/​10.1063/​1.525329

[28] M. V. Berry. Transitionless quantum driving. J. Phys. A Math. Theor., 42 (36): 365303, 2009. 10.1088/​1751-8113/​42/​36/​365303.
https:/​/​doi.org/​10.1088/​1751-8113/​42/​36/​365303

[29] M. Demirplak and S. A. Rice. Adiabatic population transfer with control fields. J. Phys. Chem. A, 107 (46): 9937–9945, 2003. 10.1021/​jp030708a.
https:/​/​doi.org/​10.1021/​jp030708a

[30] S. Masuda and K. Nakamura. Fast-forward of adiabatic dynamics in quantum mechanics. Proc. R. Soc. A, 466 (2116): 1135–1154, 2010. 10.1098/​rspa.2009.0446.
https:/​/​doi.org/​10.1098/​rspa.2009.0446

[31] X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga. Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity. Phys. Rev. Lett., 104: 063002, 2010a. 10.1103/​PhysRevLett.104.063002.
https:/​/​doi.org/​10.1103/​PhysRevLett.104.063002

[32] E. Torrontegui, S. Ibáñez, Xi Chen, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga. Fast atomic transport without vibrational heating. Phys. Rev. A, 83: 013415, 2011. 10.1103/​PhysRevA.83.013415.
https:/​/​doi.org/​10.1103/​PhysRevA.83.013415

[33] Xi Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga. Shortcut to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett., 105: 123003, 2010b. 10.1103/​PhysRevLett.105.123003.
https:/​/​doi.org/​10.1103/​PhysRevLett.105.123003

[34] E. Torrontegui, S. Ibánez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga. Shortcuts to adiabaticity. In Advances in atomic, molecular, and optical physics, volume 62, pages 117–169. Elsevier, 2013. 10.1016/​B978-0-12-408090-4.00002-5.
https:/​/​doi.org/​10.1016/​B978-0-12-408090-4.00002-5

[35] C. Jarzynski. Generating shortcuts to adiabaticity in quantum and classical dynamics. Phys. Rev. A, 88: 040101, 2013. 10.1103/​PhysRevA.88.040101.
https:/​/​doi.org/​10.1103/​PhysRevA.88.040101

[36] A. del Campo. Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett., 111: 100502, 2013. 10.1103/​PhysRevLett.111.100502.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.100502

[37] S. Pang and A. N Jordan. Optimal adaptive control for quantum metrology with time-dependent hamiltonians. Nat. Commun, 8 (1): 1–9, 2017. 10.1038/​ncomms14695.
https:/​/​doi.org/​10.1038/​ncomms14695

[38] M. Cabedo-Olaya, J. G. Muga, and S. Martínez-Garaot. Shortcut-to-adiabaticity-like techniques for parameter estimation in quantum metrology. Entropy, 22 (11): 1251, 2020. doi.org/​10.3390/​e22111251.
https:/​/​doi.org/​10.3390/​e22111251

[39] 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. 10.1103/​PhysRevLett.126.070503.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.070503

[40] J. Yang, S. Pang, and A. N. Jordan. Quantum parameter estimation with the landau-zener transition. Phys. Rev. A, 96: 020301, 2017. 10.1103/​PhysRevA.96.020301.
https:/​/​doi.org/​10.1103/​PhysRevA.96.020301

[41] S. Campbell and S. Deffner. Trade-off between speed and cost in shortcuts to adiabaticity. Phys. Rev. Lett., 118: 100601, 2017. 10.1103/​PhysRevLett.118.100601.
https:/​/​doi.org/​10.1103/​PhysRevLett.118.100601

[42] Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori. Shortcuts to adiabaticity for the quantum rabi model: Efficient generation of giant entangled cat states via parametric amplification. Phys. Rev. Lett., 126: 023602, 2021. 10.1103/​PhysRevLett.126.023602.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.023602

[43] C. W. Helstrom. Quantum detection and estimation theory. J. Stat. Phys., 1: 231–252, 1969. 10.1007/​BF01007479.
https:/​/​doi.org/​10.1007/​BF01007479

[44] S. L. Braunstein and C. M. Caves. Statistical distance and the geometry of quantum states. Phys. Rev. Lett., 72: 3439–3443, 1994. 10.1103/​PhysRevLett.72.3439.
https:/​/​doi.org/​10.1103/​PhysRevLett.72.3439

[45] S. Boixo, S. T. Flammia, C. M. Caves, and JM Geremia. Generalized limits for single-parameter quantum estimation. Phys. Rev. Lett., 98: 090401, 2007. 10.1103/​PhysRevLett.98.090401.
https:/​/​doi.org/​10.1103/​PhysRevLett.98.090401

[46] 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, 2018b. 10.1103/​RevModPhys.90.035005.
https:/​/​doi.org/​10.1103/​RevModPhys.90.035005

[47] W. Hyllus, P.and Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi. Fisher information and multiparticle entanglement. Phys. Rev. A, 85: 022321, 2012. 10.1103/​PhysRevA.85.022321.
https:/​/​doi.org/​10.1103/​PhysRevA.85.022321

[48] G. Tóth. Multipartite entanglement and high-precision metrology. Phys. Rev. A, 85: 022322, 2012. 10.1103/​PhysRevA.85.022322.
https:/​/​doi.org/​10.1103/​PhysRevA.85.022322

[49] H. Strobel, W. Muessel, D. Linnemann, T. Zibold, D. B. Hume, L. Pezzè, A. Smerzi, and M. K. Oberthaler. Fisher information and entanglement of non-gaussian spin states. Science, 345 (6195): 424–427, 2014. 10.1126/​science.1250147.
https:/​/​doi.org/​10.1126/​science.1250147

[50] S. Sachdev. Quantum phase transitions. Handbook of Magnetism and Advanced Magnetic Materials, 2007. 10.1002/​9780470022184.
https:/​/​doi.org/​10.1002/​9780470022184

[51] 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. 10.1103/​PhysRevE.76.022101.
https:/​/​doi.org/​10.1103/​PhysRevE.76.022101

[52] L. Campos Venuti and P. Zanardi. Quantum critical scaling of the geometric tensors. Phys. Rev. Lett., 99: 095701, 2007. 10.1103/​PhysRevLett.99.095701.
https:/​/​doi.org/​10.1103/​PhysRevLett.99.095701

[53] A. C. Santos and M. S. Sarandy. Generalized shortcuts to adiabaticity and enhanced robustness against decoherence. J. Phys. A, 51 (2): 025301, 2017. 10.1088/​1751-8121/​aa96f1.
https:/​/​doi.org/​10.1088/​1751-8121/​aa96f1

[54] J. G. Muga, X. Chen, S. Ibáñez, I. Lizuain, and A. Ruschhaupt. Transitionless quantum drivings for the harmonic oscillator. J. Phys. B, 43 (8): 085509, 2010. 10.1088/​0953-4075/​43/​8/​085509.
https:/​/​doi.org/​10.1088/​0953-4075/​43/​8/​085509

[55] A. del Campo, M. M. Rams, and W. H. Zurek. Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum ising model. Phys. Rev. Lett., 109: 115703, 2012. 10.1103/​PhysRevLett.109.115703.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.115703

[56] S. Deffner and S. Campbell. Quantum speed limits: from heisenberg’s uncertainty principle to optimal quantum control. J. Phys. A, 50 (45): 453001, 2017. 10.1088/​1751-8121/​aa86c6.
https:/​/​doi.org/​10.1088/​1751-8121/​aa86c6

[57] V. Giovannetti, S. Lloyd, and L. Maccone. Quantum limits to dynamical evolution. Phys. Rev. A, 67: 052109, 2003. 10.1103/​PhysRevA.67.052109.
https:/​/​doi.org/​10.1103/​PhysRevA.67.052109

[58] C. Zener. Non-adiabatic crossing of energy levels. Proc. Math. Phys. Eng., 137 (833): 696–702, 1932. 10.1098/​rspa.1932.0165.
https:/​/​doi.org/​10.1098/​rspa.1932.0165

[59] L. Innocenti, G. De Chiara, M. Paternostro, and R. Puebla. Ultrafast critical ground state preparation via bang–bang protocols. New J. Phys., 22 (9): 093050, 2020. 10.1088/​1367-2630/​abb1df.
https:/​/​doi.org/​10.1088/​1367-2630/​abb1df

[60] J. Zhang, F. M. Cucchietti, C. M. Chandrashekar, M. Laforest, C. A. Ryan, M. Ditty, A. Hubbard, J. K. Gamble, and R. Laflamme. Direct observation of quantum criticality in ising spin chains. Phys. Rev. A, 79: 012305, 2009. 10.1103/​PhysRevA.79.012305.
https:/​/​doi.org/​10.1103/​PhysRevA.79.012305

[61] M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch. High-fidelity quantum driving. Nat. Phys, 8 (2): 147–152, 2012. 10.1038/​nphys2170.
https:/​/​doi.org/​10.1038/​nphys2170

[62] G. C. Hegerfeldt. Driving at the quantum speed limit: Optimal control of a two-level system. Phys. Rev. Lett., 111: 260501, 2013. 10.1103/​PhysRevLett.111.260501.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.260501

[63] 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. 10.1103/​PhysRevLett.115.180404.
https:/​/​doi.org/​10.1103/​PhysRevLett.115.180404

[64] H. Zhong, Q. Xie, M. T. Batchelor, and C. Lee. Analytical eigenstates for the quantum rabi model. J. Phys. A, 46 (41): 415302, 2013. 10.1088/​1751-8113/​46/​41/​415302.
https:/​/​doi.org/​10.1088/​1751-8113/​46/​41/​415302

[65] Z.-J. Ying, M. Liu, H.-G. Luo, H.-Q. Lin, and J. Q. You. Ground-state phase diagram of the quantum rabi model. Phys. Rev. A, 92: 053823, 2015. 10.1103/​PhysRevA.92.053823.
https:/​/​doi.org/​10.1103/​PhysRevA.92.053823

[66] A. Monras. Optimal phase measurements with pure gaussian states. Phys. Rev. A, 73: 033821, 2006. 10.1103/​PhysRevA.73.033821.
https:/​/​doi.org/​10.1103/​PhysRevA.73.033821

[67] I. Frérot and T. Roscilde. Quantum critical metrology. Phys. Rev. Lett., 121: 020402, 2018. 10.1103/​PhysRevLett.121.020402.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.020402

[68] T. Hatomura. Shortcuts to adiabatic cat-state generation in bosonic josephson junctions. New J. Phys., 20 (1): 015010, 2018. 10.1088/​1367-2630/​aaa117.
https:/​/​doi.org/​10.1088/​1367-2630/​aaa117

[69] S. S. Mirkhalaf, E. Witkowska, and L. Lepori. Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate. Phys. Rev. A, 101: 043609, 2020. 10.1103/​PhysRevA.101.043609.
https:/​/​doi.org/​10.1103/​PhysRevA.101.043609

[70] S. Krämer, D. Plankensteiner, L. Ostermann, and H. Ritsch. QuantumOptics.jl: A julia framework for simulating open quantum systems. Comput. Phys. Commun, 227: 109–116, 2018. 10.1016/​j.cpc.2018.02.004.
https:/​/​doi.org/​10.1016/​j.cpc.2018.02.004

[71] K. Husimi. Some formal properties of the density matrix. Soc. Jpn, 22 (4): 264–314, 1940. 10.11429/​ppmsj1919.22.4_264.
https:/​/​doi.org/​10.11429/​ppmsj1919.22.4_264

Cited by

[1] Theodoros Ilias, Dayou Yang, Susana F. Huelga, and Martin B. Plenio, "Criticality-Enhanced Quantum Sensing via Continuous Measurement", PRX Quantum 3 1, 010354 (2022).

[2] Laurin Ostermann and Karol Gietka, "Temperature-enhanced critical quantum metrology", Physical Review A 109 5, L050601 (2024).

[3] Takuya Hatomura, Atsuki Yoshinaga, Yuichiro Matsuzaki, and Mamiko Tatsuta, "Quantum metrology based on symmetry-protected adiabatic transformation: imperfection, finite time duration, and dephasing", New Journal of Physics 24 3, 033005 (2022).

[4] Hai-Long Shi, Xi-Wen Guan, and Jing Yang, "Universal Shot-Noise Limit for Quantum Metrology with Local Hamiltonians", Physical Review Letters 132 10, 100803 (2024).

[5] Karol Gietka, Christoph Hotter, and Helmut Ritsch, "Unique Steady-State Squeezing in a Driven Quantum Rabi Model", Physical Review Letters 131 22, 223604 (2023).

[6] Wan-Ting He, Cong-Wei Lu, Yi-Xuan Yao, Hai-Yuan Zhu, and Qing Ai, "Criticality-based quantum metrology in the presence of decoherence", Frontiers of Physics 18 3, 31304 (2023).

[7] Lin Jiao, Wei Wu, Si‐Yuan Bai, and Jun‐Hong An, "Quantum Metrology in the Noisy Intermediate‐Scale Quantum Era", Advanced Quantum Technologies 2300218 (2023).

[8] Enes Aybar, Artur Niezgoda, Safoura S. Mirkhalaf, Morgan W. Mitchell, Daniel Benedicto Orenes, and Emilia Witkowska, "Critical quantum thermometry and its feasibility in spin systems", Quantum 6, 808 (2022).

[9] 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).

[10] Ayan Sahoo, Utkarsh Mishra, and Debraj Rakshit, "Localization-driven quantum sensing", Physical Review A 109 3, L030601 (2024).

[11] Ye Xia, Weiming Guo, and Zibo Miao, "Time-Varying Engineered Reservoir for the Improved Estimation of Atom-Cavity Coupling Strength", Photonics 10 2, 157 (2023).

[12] 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).

[13] R. Di Candia, F. Minganti, K. V. Petrovnin, G. S. Paraoanu, and S. Felicetti, "Critical parametric quantum sensing", npj Quantum Information 9 1, 23 (2023).

[14] Venelin P Pavlov, Diego Porras, and Peter A Ivanov, "Quantum metrology with critical driven-dissipative collective spin system", Physica Scripta 98 9, 095103 (2023).

[15] Karol Gietka, Lewis Ruks, and Thomas Busch, "Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point", Quantum 6, 700 (2022).

[16] Karol Gietka and Helmut Ritsch, "Squeezing and Overcoming the Heisenberg Scaling with Spin-Orbit Coupled Quantum Gases", Physical Review Letters 130 9, 090802 (2023).

[17] Christoph Hotter, Helmut Ritsch, and Karol Gietka, "Combining Critical and Quantum Metrology", Physical Review Letters 132 6, 060801 (2024).

[18] Raffaele Salvia, Mohammad Mehboudi, and Martí Perarnau-Llobet, "Critical Quantum Metrology Assisted by Real-Time Feedback Control", Physical Review Letters 130 24, 240803 (2023).

[19] Karol Gietka, "Squeezing by critical speeding up: Applications in quantum metrology", Physical Review A 105 4, 042620 (2022).

[20] 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).

[21] 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).

[22] Karol Gietka, "Harnessing center-of-mass excitations in quantum metrology", Physical Review Research 4 4, 043074 (2022).

[23] George Mihailescu, Abolfazl Bayat, Steve Campbell, and Andrew K. Mitchell, "Multiparameter critical quantum metrology with impurity probes", Quantum Science and Technology 9 3, 035033 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-15 20:39:32) and SAO/NASA ADS (last updated successfully 2024-07-15 20:39:33). The list may be incomplete as not all publishers provide suitable and complete citation data.