Abstract
Because quantum critical systems are very sensitive to the variation of parameters around the quantum phase transition (QPT), quantum criticality has been presented as an efficient resource for metrology. In this paper, we address the issue whether the divergent feature of the inverted variance is realizable in the presence of noise when approaching the QPT. Taking the quantum Rabi model (QRM) as an example, we obtain the analytical result for the inverted variance with single-photon relaxation. We show that the inverted variance may be convergent in time due to the noise. Since the precision of the metrology is very sensitive to the noise, as a remedy, we propose squeezing the initial state to improve the precision under decoherence. In addition, we also investigate the criticality-based metrology under the influence of the two-photon relaxation. Strikingly, although the maximum inverted variance still manifests a power-law dependence on the energy gap, the exponent is positive and depends on the dimensionless coupling strength. This observation implies that the criticality may not enhance but weaken the precision in the presence of two-photon relaxation, due to the non-linearity introduced by the two-photon relaxation.
Similar content being viewed by others
References
T. L. Heugel, M. Biondi, O. Zilberberg, and R. Chitra, Quantum transducer using a parametric driven-dissipative phase transition, Phys. Rev. Lett. 123(17), 173601 (2019)
Y. Chu, S. Zhang, B. Yu, and J. Cai, Dynamic framework for criticality-enhanced quantum sensing, Phys. Rev. Lett. 126(1), 010502 (2021)
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(2), 021022 (2018)
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(12), 120504 (2020)
S. Felicetti and A. Le Boité, Universal spectral features of ultrastrongly coupled systems, Phys. Rev. Lett. 124(4), 040404 (2020)
T. Ilias, D. Yang, S. F. Huelga, and M. B. Plenio, Criticality-enhanced quantum sensing via continuous measurement, PRX Quantum 3(1), 010354 (2022)
P. Zanardi, M. G. A. Paris, and L. C. Venuti, Quantum criticality as a resource for quantum estimation, Phys. Rev. A 78(4), 042105 (2008)
M. Tsang, Quantum transition-edge detectors, Phys. Rev. A 88(2), 021801 (2013)
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(1), 013817 (2017)
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 (2021)
X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems, Sci. Rep. 3(1), 2943 (2013)
S. Sachdev, Quantum Phase Transitions, Cambridge University Press, UK, 2011
H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, Decay of Loschmidt echo enhanced by quantum criticality, Phys. Rev. Lett. 96(14), 140604 (2006)
Q. Ai, Y. D. Wang, G. L. Long, and C. P. Sun, Two mode photon bunching effect as witness of quantum criticality in circuit QED, Sci. China Ser. G 52(12), 1898 (2009)
S. S. Pang and A. N. Jordan, Optimal adaptive control for quantum metrology with time-dependent Hamiltonians, Nat. Commun. 8(1), 14695 (2017)
S. Pang and T. A. Brun, Quantum metrology for a general Hamiltonian parameter, Phys. Rev. A 90(2), 022117 (2014)
M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge University Press, UK, 1997
M. J. Hwang, R. Puebla, and M. B. Plenio, Quantum phase transition and universal dynamics in the Rabi model, Phys. Rev. Lett. 115(18), 180404 (2015)
R. Puebla, M. J. Hwang, J. Casanova, and M. B. Plenio, Probing the dynamics of a superradiant quantum phase transition with a single trapped ion, Phys. Rev. Lett. 118(7), 073001 (2017)
J. S. Pedernales, I. Lizuain, S. Felicetti, G. Romero, L. Lamata, and E. Solano, Quantum Rabi model with trapped ions, Sci. Rep. 5(1), 15472 (2015)
D. Lv, S. An, Z. Liu, J. N. Zhang, J. S. Pedernales, L. Lamata, E. Solano, and K. Kim, Quantum simulation of the quantum Rabi model in a trapped ion, Phys. Rev. X 8(2), 021027 (2018)
A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nat. Rev. Phys. 1(1), 19 (2019)
W. Salmon, C. Gustin, A. Settineri, O. Di Stefano, D. Zueco, S. Savasta, F. Nori, and S. Hughes, Gauge-independent emission spectra and quantum correlations in the ultrastrong coupling regime of open system cavity-QED, Nanophotonics 11(8), 1573 (2022)
S. Hughes, A. Settineri, S. Savasta, and F. Nori, Resonant Raman scattering of single molecules under simultaneous strong cavity coupling and ultrastrong optomechanical coupling in plasmonic resonators: Phonon-dressed polaritons, Phys. Rev. B 104(4), 045431 (2021)
A. Mercurio, V. Macrì, C. Gustin, S. Hughes, S. Savasta, and F. Nori, Regimes of cavity QED under incoherent excitation: From weak to deep strong coupling, Phys. Rev. Res. 4(2), 023048 (2022)
Y. H. Chen, A. Miranowicz, X. Chen, Y. Xia, and F. Nori, Enhanced-fidelity ultrafast geometric quantum computation using strong classical drives, Phys. Rev. Appl. 18(6), 064059 (2022)
V. Macrì, A. Mercurio, F. Nori, S. Savasta, and C. Sánchez Muñoz, Spontaneous scattering of Raman photons from cavity-QED systems in the ultrastrong coupling regime, Phys. Rev. Lett. 129(27), 273602 (2022)
D. J. Zhang and D. M. Tong, Approaching Heisenberg scalable thermometry with built-in robustness against noise, npj Quantum Inf. 8, 81 (2022)
S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency standards with quantum entanglement, Phys. Rev. Lett. 79(20), 3865 (1997)
A. W. Chin, S. F. Huelga, and M. B. Plenio, Quantum metrology in non-Markovian environments, Phys. Rev. Lett. 109(23), 233601 (2012)
J. Ma, X. Wang, C. P. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep. 509(2–3), 89 (2011)
Z. P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, and Y. Liu, Metrology with PT-symmetric cavities: Enhanced sensitivity near the PT-phase transition, Phys. Rev. Lett. 117(11), 110802 (2016)
K. Xu, Y. R. Zhang, Z. H. Sun, H. Li, P. Song, Z. Xiang, K. Huang, H. Li, Y. H. Shi, C. T. Chen, X. Song, D. Zheng, F. Nori, H. Wang, and H. Fan, Metrological characterization of non-Gaussian entangled states of superconducting qubits, Phys. Rev. Lett. 128(15), 150501 (2022)
A. G. Kofman, S. Ashhab, and F. Nori, Nonperturbative theory of weak pre- and post-selected measurements, Phys. Rep. 520(2), 43 (2012)
Y. Matsuzaki, S. C. Benjamin, and J. Fitzsimons, Magnetic field sensing beyond the standard quantum limit under the effect of decoherence, Phys. Rev. A 84(1), 012103 (2011)
Q. Ai, Y. Li, H. Zheng, and C. P. Sun, Quantum antiZeno effect without rotating wave approximation, Phys. Rev. A 81(4), 042116 (2010)
Q. Ai, D. Xu, S. Yi, A. G. Kofman, C. P. Sun, and F. Nori, Quantum anti-zeno effect without wave function reduction, Sci. Rep. 3(1), 1752 (2013)
P. M. Harrington, J. T. Monroe, and K. W. Murch, Quantum Zeno effects from measurement controlled qubit-bath interactions, Phys. Rev. Lett. 118(24), 240401 (2017)
X. Y. Long, W. T. He, N. N. Zhang, K. Tang, Z. D. Lin, H. F. Liu, X. F. Nie, G. R. Feng, J. Li, T. Xin, Q. Ai, and D. W. Lu, Entanglement-enhanced quantum metrology in colored noise by quantum Zeno effect, Phys. Rev. Lett. 129(7), 070502 (2022)
I. Buluta and F. Nori, Quantum simulators, Science 326(5949), 108 (2009)
I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86(1), 153 (2014)
N. N. Zhang, M. J. Tao, W. T. He, X. Y. Chen, X. Y. Kong, F. G. Deng, N. Lambert, and Q. Ai, Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities, Front. Phys. 16(5), 51501 (2021)
B. X. Wang, M. J. Tao, Q. Ai, T. Xin, N. Lambert, D. Ruan, Y. C. Cheng, F. Nori, F. G. Deng, and G. L. Long, Efficient quantum simulation of photosynthetic light harvesting, npj Quantum Inf. 4, 52 (2018)
X. Y. Chen, N. N. Zhang, W. T. He, X. Y. Kong, M. J. Tao, F. G. Deng, Q. Ai, and G. L. Long, Global correlation and local information flows in controllable non-Markovian open quantum dynamics, npj Quantum Inf. 8, 22 (2022)
Y. N. Lu, Y. R. Zhang, G. Q. Liu, F. Nori, H. Fan, and X. Y. Pan, Observing information backflow from controllable non-Markovian multichannels in diamond, Phys. Rev. Lett. 124(21), 210502 (2020)
Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlastakis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar, M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Confining the state of light to a quantum manifold by engineered two-photon loss, Science 347(6224), 853 (2015)
M. Malekakhlagh and A. W. Rodriguez, Quantum Rabi model with two-photon relaxation, Phys. Rev. Lett. 122(4), 043601 (2019)
R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93(1), 99 (1954)
J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149(2), 491 (1966)
H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, New York: Oxford University Press, 2002
J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183(8), 1760 (2012)
H. J. Carmichael, An Open Systems Approach to Quantum Optics, Berlin: Springer, 1993
C. W. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, Berlin: Springer, 2004
M. J. Hwang, P. Rabl, and M. B. Plenio, Dissipative phase transition in the open quantum Rabi model, Phys. Rev. A 97(1), 013825 (2018)
Q. Ai, P. B. Li, W. Qin, J. X. Zhao, C. P. Sun, and F. Nori, The NV netamaterial: Tunable quantum hyperbolic metamaterial using nitrogen vacancy centers in diamond, Phys. Rev. B 104(1), 014109 (2021)
H. Dong, D. Z. Xu, J. F. Huang, and C. P. Sun, Coherent excitation transfer via the dark-state channel in a bionic system, Light Sci. Appl. 1(3), e2 (2012)
Acknowledgements
This work was supported by Beijing Natural Science Foundation under Grant No. 1202017 and the National Natural Science Foundation of China under Grant Nos. 11674033 and 11505007, and Beijing Normal University under Grant No. 2022129.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, WT., Lu, CW., Yao, YX. et al. Criticality-based quantum metrology in the presence of decoherence. Front. Phys. 18, 31304 (2023). https://doi.org/10.1007/s11467-023-1278-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11467-023-1278-2