Non-Hermitian phonon quantization controlled through different phases of Eu<sup>3+</sup>: BiPO<sub>4</sub>

Non-Hermitian phonon quantization controlled through different phases of Eu³⁺: BiPO₄

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Muhammad Qasim Khan^a, Iqbal Hussain^a, Faisal Nadeem^a, Nadir Khan^a, Mudassir^a, Huanrong Fan^a^,^b^,^*, Changbiao Li^a^,^**, Yanpeng Zhang^a^,^***

Progress in Natural Science: Materials International | 2026, 36(1) : 65 - 75

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Progress in Natural Science: Materials International | 2026, 36(1): 65-75

• Research Article •

Non-Hermitian phonon quantization controlled through different phases of Eu³⁺: BiPO₄

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Muhammad Qasim Khan^a, Iqbal Hussain^a, Faisal Nadeem^a, Nadir Khan^a, Mudassir^a, Huanrong Fan^a^,^b^,^*, Changbiao Li^a^,^**, Yanpeng Zhang^a^,^***

Affiliations

^aKey Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an, 710049, China

^bCollege of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, 412007, China

Published: 2026-02-22 doi: 10.1016/j.pnsc.2025.09.007

Outline

Abstract

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This study investigates a novel phenomenon of non-Hermitian phonon quantization in Eu³⁺: BiPO₄ crystals controlled by different phases. The hexagonal (H) -phase (0.5:1) with low symmetry has strongest destructive gamma phonon quantization as compare to high symmetry phases H-Monoclinic (M) phases (12:1, 1:1) in fluorescence (FL) region, while strong constructive dominant dressing quantization exhibits due to higher phonon density of states in spontaneous four wave mixing (SFWM) region. Strong Spectral Autler-Townes (SAT) is observed in (6:1) phase at small angle and time gate position (GP = 500 ns), while, strong Temporal Autler-Townes (TAT) is studied at GP = 1ns. Also, (6:1) exhibits angle destructive quantization in FL region. Comparison between the H-M (12:1) phase and H = M (6:1) phases reveals that the H-M phase exhibits stronger destructive gamma quantization in FL region due to larger gamma phonon in (12:1) phase. Moreover, H-phase (0.5:1) exhibits large number of phonon density and shows strong constructive quantization as compare to M-phase (7:1) in SWFM region. Additionally, two destructive dressing quantization are observed in fluorescence region where gamma quantization is affected by additional laser. This work establishes a deterministic relation between non-Hermitian phonon quantization and different phases of Eu³⁺: BiPO₄, enabling applications in quantum memory and tunable bandpass filters. The Band pass filter control through phonon quantization with different phases of Eu³⁺: BiPO₄.

Key words

Destructive/constructive quantization / Phonon quantization / Different phases / Temporal autler townes splitting

Cite this Article

Muhammad Qasim Khan, Iqbal Hussain, Faisal Nadeem, Nadir Khan, Mudassir, Huanrong Fan, Changbiao Li, Yanpeng Zhang. Non-Hermitian phonon quantization controlled through different phases of Eu³⁺: BiPO₄[J]. Progress in Natural Science: Materials International, 2026 , 36 (1) : 65 -75 . DOI: 10.1016/j.pnsc.2025.09.007

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Funding

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National Natural Science Foundation of China(62475208; 62475209; 12474392)

Appendix

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Year 2026 volume 36 Issue 1

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Article Info

doi: 10.1016/j.pnsc.2025.09.007

Receive Date：2025-06-28
Online Date：2026-06-03
Published：2026-02-22

Article Data

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History

Received：2025-06-28
Revised：2025-09-11
Accepted：2025-09-25

Funding

National Natural Science Foundation of China(62475208; 62475209; 12474392)

Affiliations

^aKey Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an, 710049, China

^bCollege of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, 412007, China

Corresponding:

^* College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, 412007, China. E-mail addresses: fanhuanrong001@stu.xjtu.edu.cn (H. Fan)

^** E-mail addresses: cbli@mail.xjtu.edu.cn (C. Li)

^*** E-mail addresses: ypzhang@mail.xjtu.edu.cn (Y. Zhang).

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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