Entropy evolution law of general quadratic state in a laser channel

Abstract

Using the integration within ordered products, we obtain the analytical density-operator evolution of the general quadratic state {\rho }_0 in a laser channel, which always maintains the same form as the initial density operator {\rho }_0. Introducing the differential representation of the von-Neumann entropy and two important resemble formulas, we analytically and numerically investigate the entropy evolution of the state {\rho }_0 in a laser channel, which is determined by not only the competition of the gain and loss of the laser channel, but also the coefficients \alpha, \beta of the initial quadratic state {\rho }_0.

Graphical abstract

Keywords

general quadratic state / laser channel / quantum entropy / operator ordering / integration within ordered product

References

[1] X. L. Ruan, S. C. Rand, and M. Kaviany, Entropy and efficiency in laser cooling of solids, Phys. Rev. B 75(21), 214304 (2007)

[2] H. Metcalf, Entropy exchange in laser cooling, Phys. Rev. A 77(6), 061401(R) (2008)

[3] G. Gour and M. M. Wilde, Entropy of a quantum channel, Phys. Rev. Res. 3(2), 023096 (2021)

[4] Y. J. Chu, F. Huang, M. X. Li, and Z. J. Zheng, An entropy function of a quantum channel, Quantum Inform. Process. 22(1), 27 (2022)

[5] M.O. ScullyM. S. Zubairy, Quantum Optics, Cambridge: Cambridge University Press, 1997

[6] H. Y. Fan and Y. Fan, New representation of thermal states in thermal field dynamics, Phys. Lett. A 246(3−4), 242 (1998)

[7] H. Y. Fan and Y. Fan, New representation for thermo excitation and de-excitation in thermofield dynamics, Phys. Lett. A 282(4−5), 269 (2001)

[8] J. H. Chen and H. Y. Fan, Entropy evolution law in a laser process, Ann. Phys. 334, 272 (2013)

[9] H. Y. Fan, Entangled states, squeezed states gained via the route of developing Dirac’s symbolic method and their applications, Int. J. Mod. Phys. B 18(10−11), 1387 (2004)

[10] A. Vesperini, G. Bel-Hadj-Aissa, L. Capra, and R. Franzosi, Unveiling the geometric meaning of quantum entanglement: Discrete and continuous variable systems, Front. Phys. 19(5), 51204 (2024)

[11] P. S. Yan, L. Zhou, W. Zhong, and Y. B. Sheng, Measurement-based entanglement purification for entangled coherent states, Front. Phys. 17(2), 21501 (2022)

[12] X. G. Meng, K. C. Li, J. S. Wang, Z. S. Yang, X. Y. Zhang, Z. T. Zhang, and B. L. Liang, Multi-variable special polynomials using an operator ordering method, Front. Phys. 15(5), 52501 (2020)

[13] X. G. Meng, J. S. Wang, B. L. Liang, and C. X. Han, Evolution of a two-mode squeezed vacuum for amplitude decay via continuous-variable entangled state approach, Front. Phys. 13(5), 130322 (2018)

[14] T. Liu, B. Q. Guo, Y. H. Zhou, J. L. Zhao, Y. L. Fang, Q. C. Wu, and C. P. Yang, Transfer of quantum entangled states between superconducting qubits and microwave field qubits, Front. Phys. 17(6), 61502 (2022)

[15] L. Y. Cheng, F. Ming, F. Zhao, L. Ye, and D. Wang, The uncertainty and quantum correlation of measurement in double quantum-dot systems, Front. Phys. 17(6), 61504 (2022)

[16] X. G. Meng, J. S. Wang, X. Y. Zhang, Z. S. Yang, B. L. Liang, and Z. T. Zhang, Nonclassicality via the superpositions of photon addition and subtraction and quantum decoherence for thermal noise, Ann. Phys. 532(12), 2000219 (2020)

[17] X. G. Meng, K. C. Li, J. S. Wang, X. Y. Zhang, X. T. Zhang, X. S. Yang, and B. L. Liang, Continuous variable entanglement and Wigner-function negativity via adding or subtracting photons, Ann. Phys. 532(5), 1900585 (2020)

Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11347026), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2020MA085 and ZR2020MF113), and the Science and Technology Plan Project of Weifang (Grant No. 2023GX031).

RIGHTS & PERMISSIONS

2024 Higher Education Press