熱原子團激發之雙光子態

Spectrally entangled biphoton state of cascade emissions from Doppler-broadened atomic ensembles

張子軒(Tzu-Hsuan Chang)

指導教授 ： 林俊達

共同指導教授 ： 任祥華

國立臺灣大學/理學院/物理學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901418

摘要

本篇論文針對熱原子團激發之雙光子態的頻譜糾纏性質進行理論研究。雙光子來自於受兩道脈衝激發之熱原子團的級聯發射。在四波混頻的情況下，可以分別從較高能階轉換以及較低能階轉換產生信號光子和游離光子。藉由施密特分解，我們從較低能階轉換的超幅射衰退率、激發脈衝期和環境溫度等三個參數研究雙光 子頻譜的糾纏性質。透過頻移的多路複用，發現在正相關與反相關的頻移多路複用中，增加原子團數量可以產生具有更高糾纏性質的雙光子態。此外，在頻移多路複 用中，施密特基底下的特徵值有簡併的現象，對應的施密特值甚至可以高於多路複用的熱原子團數目，說明在連續的頻率基底中具有更高的糾纏性質與更多互相關聯的特徵模式。最後，我們研究從多路複用的熱原子團中可得到的最低糾纏雙光子態。

關鍵字

雙光子 ； 糾纏 ； 熱原子團 ； 多路複用

並列摘要

We theoretically investigate the spectral property of a biphoton state from multi- plexed thermal atomic ensembles. This biphoton state originates from the cascade emissions, which can be generated by two weak pump fields under four-wave mixing condition. Under this condition, a signal photon from the upper transition, chosen in a telecommunication bandwidth, can be generated along with a correlated idler photon from the lower infrared transition. We obtain the spectral property under different superradiant decay rates of the lower transition, excitation pulse du- rations, and temperature of the medium. We can spectrally shape the biphoton state by multiplexing the atomic ensembles with frequency-shifted emissions, where the entropy of entanglement can be analyzed via Schmidt decompositions. We find that this spectral entanglement increases when more vapor cells are multiplexed with correlated or anti-correlated signal and idler fields. The eigenvalues in Schmidt bases approach degenerate under this multiplexing scheme, and corresponding Schmidt numbers can be larger than the number of the multiplexed vapor cells, showing the enlarged entropy of entanglement and excess correlated modes in con- tinuous frequency spaces. We also investigate the lowest entropy of entanglement allowed in the multiplexing scheme, which is preferential for generating a pure single photon source. This shows the potentiality to spectrally shape the bipho- ton source, where high-capacity spectral modes can be applied in long-distance quantum communication and multimode quantum information processing.

並列關鍵字

biphoton ； entanglement ； thermal atomic ensemble ； cascade emission ； multiplexing

參考文獻

[1] M. O. Scully and M. S. Zubairy, Quantum Optics. Cambridge University Press, 1997.

[2] C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: Effective finite hilbert space and entropy control,” Phys. Rev. Lett., vol. 84, pp. 5304–5307, Jun 2000.

[3] T. Chang, G.-D. Lin, and H. Jen, “Spectral shaping of the biphoton state from multiplexed thermal atomic ensembles,” arXiv preprint arXiv:1905.09482, 2019.

[4] A. Ac ́ın, I. Bloch, H. Buhrman, T. Calarco, C. Eichler, J. Eisert, D. Esteve, N. Gisin, S. J. Glaser, F. Jelezko, S. Kuhr, M. Lewenstein, M. F. Riedel, P. O. Schmidt, R. Thew, A. Wallraff, I. Walmsley, and F. K. Wilhelm, “The quantum technologies roadmap: a european community view,” New Journal of Physics, no. 8, p. 080201, aug 2018.

[5] H. J. Kimble, “The quantum internet,” Nature, vol. 453, pp. 1023 EP –, 06 2008.