Quantum parameter estimation and initial state optimization based on the Jaynes-Cummings model

doi:10.3969/j.issn.1000-5641.2024.03.014

Abstract

Abstract:

Quantum parameter estimation is a powerful theoretical tool for inferring unknown parameters in physical models from experimental data. The Jaynes-Cummings model is widely used in quantum optics, and describes the interaction between a two-level atom and a single-mode quantum optical field. Systematic research was performed on the estimation precision of atom-light coupling strength “g” in this model and the initial state was identified by which the estimation can achieve the best precision. Our results can improve the precision of quantum measurement with the Jaynes-Cummings model, and can be used for quantum metrology with other hybrid quantum systems.

Key words: quantum Fisher information, Jaynes–Cummings model, parameter estimation theory

CLC Number:

O413

Liwen QIAO, Jiaxin PENG, Baiqiang ZHU, Keye ZHANG. Quantum parameter estimation and initial state optimization based on the Jaynes-Cummings model[J]. Journal of East China Normal University(Natural Science), 2024, 2024(3): 128-135.

Figures/Tables 3

References 26

1	DEGEN C L, REINHARD F, CAPPELLARO P.. Quantum sensing. Reviews of Modern Physics, 2017, 89 (3): 035002.
2	GIOVANNETTI V, LLOYD S, MACCONE L.. Advances in quantum metrology. Nature Photonics, 2011, 5 (4): 222- 229.
3	LIU J, YUAN H, LU X-M, et al.. Quantum Fisher information matrix and multiparameter estimation. Journal of Physics A, 2020, 53 (2): 023001.
4	FISHER R A. Theory of statistical estimation[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1925, 22(5): 700-725.
5	HELSTROM C W.. Quantum detection and estimation theory. Journal of Statistical Physics, 1969, 1 (2): 231- 252.
6	HOLEVO A. Probabilistic and Statistical Aspects of Quantum Theory [M]. Pisa: Edizioni Della Normale Pisa, 2011.
7	PARIS M G.. Quantum estimation for quantum technology. International Journal of Quantum Information, 2009, 7 (supp01): 125- 137.
8	DEMKOWICZ-DOBRZAŃSKI R, JARZYNA M, KOŁODYŃSKI J. Quantum limits in optical interferometry [G]// Progress in Optics. [S.l.]: Elsevier Ltd., 2015, 60: 345-435.
9	JING X X, LIU J, ZHONG W, et al.. Quantum Fisher information of entangled coherent states in a lossy Mach-Zehnder interferometer. Communications in Theoretical Physics, 2014, 61 (1): 115- 120.
10	PANG S, BRUN T A.. Quantum metrology for a general Hamiltonian parameter. Physical Review A, 2014, 90 (2): 022117.
11	VOGEL W, WELSCH D G. Quantum Optics [M]. [S.l.]: John Wiley & Sons, 2006.
12	MEYSTRE P, SARGENT M. Elements of Quantum Optics [M]. [S.l.]: Springer Science & Business Media, 2007.
13	YÖNAÇ M, YU T, EBERLY J.. Sudden death of entanglement of two Jaynes-Cummings atoms. Journal of Physics B, 2006, 39 (15): S621.
14	RAJAGOPAL A, JENSEN K, CUMMINGS F.. Quantum entangled supercorrelated states in the Jaynes–Cummings model. Physics Letters A, 1999, 259 (3/4): 285- 90.
15	AKHTARSHENAS S J, FARSI M.. Negativity as entanglement degree of the Jaynes-Cummings model. Physica Scripta, 2007, 75 (5): 608.
16	GEA-BANACLOCHE J.. Collapse and revival of the state vector in the Jaynes-Cummings model: An example of state preparation by a quantum apparatus. Physical Review Letters, 1990, 65 (27): 3385- 3388.
17	METWALLY N, ABDELATY M, OBADA A S.. Quantum teleportation via entangled states generated by the Jaynes-Cummings model. Chaos, Solitons & Fractals, 2004, 22 (3): 529- 535.
18	LIU J M, WENG B.. Approximate teleportation of an unknown atomic state in the two-photon Jaynes-Cummings model. Physica A: Statistical Mechanics and its Applications, 2006, 367, 215- 219.
19	MIRMASOUDI F, AHADPOUR S.. Dynamics super quantum discord and quantum discord teleportation in the Jaynes-Cummings model. Journal of Modern Optics, 2018, 65 (5-6): 730- 736.
20	GENONI M G, INVERNIZZI C.. Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction. The European Physical Journal Special Topics, 2012, 203 (1): 49- 60.
21	EL ANOUZ K, EL ALLATI A, SALAH A, et al.. Quantum fisher information: Probe to measure fractional evolution. International Journal of Theoretical Physics, 2020, 59, 1460- 1474.
22	GIOVANNETTI V, LLOYD S, MACCONE L.. Quantum metrology. Physical Review Letters, 2006, 96 (1): 010401.
23	BRODY D C, GRAEFE E M.. Information geometry of complex hamiltonians and exceptional points. Entropy, 2013, 15 (9): 3361- 3378.
24	BRAUNSTEIN S L, CAVES C M, MILBURN G J.. Generalized uncertainty relations: Theory, examples, and Lorentz invariance. Annals of Physics, 1996, 247 (1): 135- 173.
25	MERZBACHER E. Quantum Mechanics [M]. [S.l.]: John Wiley & Sons, 1998.
26	SCHWABL F. Quantum Mechanics [M]. [S.l.]: Springer Science & Business Media, 2007.

[1]	Yijun LIAN, Jinming LIU. Protecting quantum Fisher information of a qubit-qutrit system near the horizon of the Garfinkle-Horowitz-Strominger dilation space-time [J]. Journal of East China Normal University(Natural Science), 2022, 2022(4): 120-130.
[2]	WANG Qiang, ZENG Jie, JIAO Gaofeng, YUAN Chunhua. Limit of multi-parameter phase estimation in an actively correlated Mach-Zehnder interferometer [J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 135-142.