Nonclassical properties of single-mode displaced Fock state

Truong Minh Duc * and Do Chinh Hap

* Corresponding author: (truongminhduc@dhsphue.edu.vn)

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Received: Jul 22, 2025
Revised: Oct 3, 2025
Accepted: Oct 6, 2025
Published: Oct 20, 2025
Title: Nonclassical properties of single-mode displaced Fock state
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How to Cite
Đức, T. M., & Hạp, Đ. C. (2025). Nonclassical properties of single-mode displaced Fock state. Journal of Science and Education, 65(02), 315-320. Retrieved from https://tckhgd.dhsphue.edu.vn/index.php/jse/article/view/85
Issue
Vol. 65 No. 02 (2025): JOURNAL OF SCIENCE AND EDUCATION
Section
Khoa học Tự nhiên – Công nghệ

Abstract

In this paper, we investigate the nonclassical properties of the single-mode displaced Fock state, specifically lower- and higher-order Hillery squeezing, Hong-Mandel squeezing, and sub-Poisson statistics. The results show that the single-mode displaced Fock state does not exhibit lower- and higher-order Hillery squeezing but does exhibit higher- order Hong-Mandel squeezing. Furthermore, this state exhibits sub-Poisson statistics at both lower and higher orders, corresponding to the number of particles in the Fock state n ≥ 1. Thus, the single-mode displaced Fock state is nonclassical, and its nonclassical properties are well demonstrated.
Keywords: Hillery squeezing, Hong–Mandel squeezing, Sub-Poissonian statistics, Photon antibunching, Single-mode displaced Fock State

Tóm tắt

Trong bài báo này, chúng tôi nghiên cứu các tính chất phi cổ điển của trạng thái dịch chuyển Fock đơn mode, đó là tính chất nén Hillery, tính chất nén Hong-Mandel, và tính thống kê sub-Poisson bậc thấp và bậc cao. Kết quả khảo sát cho thấy trạng thái dịch chuyển Fock đơn mode không thể hiện tính chất nén Hillery bậc thấp và bậc cao nhưng lại thể hiện tính chất nén Hong-Mandel bậc cao. Hơn nữa, trạng thái này thể hiện tính chất thống kê sub-Poisson cả ở bậc thấp và bậc cao tương ứng với số hạt trong trạng thái Fock n ≥ 1. Như vậy, trạng thái dịch chuyển Fock đơn mode là một trạng thái phi cổ điển và các tính chất phi cổ điển của chúng được thể hiện tương đối rõ ràng.
Từ khóa: Nén Hillery, Nén Hong-Mandel, Thống kê sub-Poisson, Trạng thái dịch chuyển Fock đơn mode

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References

Daniel, E., Vyas, R., & Surendra, S. (2002). Higher-order sub-Poissonian photon statistics in terms of factorial moments. Journal of the Optical Society of America B, 19(6), 1471–1476.

Deepak and Chatterjee A. (2024), “Analyzing performance of f-deformed displaced Fock state in continuous-variable quantum teleportation”, Physica Scripta, 99, 095124.

Faghihi, M. J. (2020). Generalized photon-added and subtracted f-deformed displaced Fock states. Annalen der Physik, 532(12), 2000215. https://doi.org/10.1002/andp.202000215

Glauber, R. J. (1963). Coherent and incoherent states of the radiation field. Physical Review, 131(6), 2766–2788. https://doi.org/10.1103/PhysRev.131.2766

Hillery, M. (1987). Squeezing of the square of the field amplitude in second harmonic generation. Optics Communications, 62(2), 135–138. https://doi.org/10.1016/0030-4018(87)90117-1

Hollenhorst, J. N. (1979). Quantum limits on resonant-mass gravitational radiation detectors. Physical Review D, 19(6), 1669–1679. https://doi.org/10.1103/PhysRevD.19.1669

Hong, C. K., & Mandel, L. (1985). Higher-order squeezing of a quantum field. Physical Review Letters, 54(4), 323–325. https://doi.org/10.1103/PhysRevLett.54.323

Karimi, A. (2017). Construction of the superposition of displaced Fock states and entangled displaced Fock states. International Journal of Theoretical Physics, 56(9), 2703–2715. https://doi.org/10.1007/s10773-017-3436-2

Malpani, P., Alam, N., Thapliyal, K., Narayanan, V., & Banerjee, S. (2019). Lower- and higher-order nonclassical properties of photon-added and subtracted displaced Fock states. Annalen der Physik, 531(2), 1800318. https://doi.org/10.1002/andp.201800318

Malpani, P., Thapliyal, K., Alam, N., Pathak, A., Narayanan, V., & Banerjee, S. (2020). Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state. Optics Communications, 459, 124964. https://doi.org/10.1016/j.optcom.2019.124964

Malpani, P., Thapliyal, K., Banerji, J., & Pathak, A. (2023). Enhancement of non-Gaussianity and nonclassicality of photon-added displaced Fock state: A quantitative approach. Annalen der Physik, 535(1), 2200261. https://doi.org/10.1002/andp.202200261

Mandel, L. (1986). Non-classical states of the electromagnetic field. Physica Scripta, T12, 34–42. https://doi.org/10.1088/0031-8949/1986/T12/005

Miry S. R., Faghihi M. J. and Mahmoudi H. (2023), “Nonclassicality of entangled Schr¨odinger cat states associated to generalized displaced Fock states”, Physica Scripta, 98, 125109.

Phan, T. D. N., Le, T. T. H., & Truong, D. M. (2024). Nonclassical properties of two-mode displaced Fock state. Dalat University Journal of Science, 14(3S), 3–12.

Shijie D., Renzhi Y., Chuang Y., and Mugen P. (2025), “Estimation of displacement operations based on Fock states considering thermal noise in preparing probes”, Optics Letters, 50 (7), 2413.

Stoler, D. (1970). Equivalence classes of minimum uncertainty packets. Physical Review D, 1(12), 3217–3219. https://doi.org/10.1103/PhysRevD.1.3217

Sudarshan, E. C. G. (1963). Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Physical Review Letters, 10(7), 277–279. https://doi.org/10.1103/PhysRevLett.10.277

Wünsche, A. (1991). Displaced Fock states and their connection to quasiprobabilities. Quantum Optics: Journal of the European Optical Society Part B, 3, 359–383.