Abstract The strongly coupled system composed of atoms, molecules, molecule aggregates, and semiconductor quantum dots embedded within an optical microcavity/nanocavity with high quality factor and/or low modal volume has become an excellent platform to study cavity quantum electrodynamics (CQED), where a prominent quantum effect called Rabi splitting can occur due to strong interaction of cavity-mode single-photon with the two-level atomic states. In this paper, we build a new quantum model that can describe the optical response of the strongly-coupled system under the action of an external probing light and the spectral lineshape. We take the Hamiltonian for the strongly-coupled photon-atom system as the unperturbed Hamiltonian 0 and the interaction Hamiltonian of the probe light upon the coupled-system quantum states as the perturbed Hamiltonian . The theory yields a double Lorentzian lineshape for the permittivity function, which agrees well with experimental observation of Rabi splitting in terms of spectral splitting. This quantum theory will pave the way to construct a complete understanding for the microscopic strongly-coupled system that will become an important element for quantum information processing, nano-optical integrated circuits, and polariton chemistry.
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2018YFA0306200), the National Natural Science Foundation of China (Grant No. 11974119), and Guangdong Provincial Innovative and Entrepreneurial Research Team Program, China.
Corresponding Authors:
Zhi-Yuan Li
E-mail: phzyli@scut.edu.cn
Cite this article:
Jian Zeng(曾健) and Zhi-Yuan Li(李志远) Quantum mechanical solution to spectral lineshape in strongly-coupled atom-nanocavity system 2022 Chin. Phys. B 31 043202
[1] Chen W, Beck K M, Bucker R, Gullans M, Lukin M D, Tanji-Suzuki H and Vuletic V 2013 Science341 768 [2] Tiecke T, Thompson J D, de Leon N P, Liu L, Vuletić V and Lukin M D 2014 Nature508 241 [3] Hacker B, Welte S, Rempe G and Ritter S 2016 Nature536 193 [4] Daiss S, Langenfeld S, Welte S, Distante E, Thomas P, Hartung L, Morin O and Rempe G 2021 Science371 614 [5] Kalb N, Reiserer A, Ritter S and Rempe G 2015 Phys. Rev. Lett. 114 220501 [6] Bennett A, Lee J, Ellis D, Farrer I, Ritchie D and Shields A 2016 Nat. Nanotechnology11 857 [7] Han Y H, Cao C, Fan L and Zhang R 2021 Opt. Express29 20045 [8] Fan L and Cao C 2021 JOSA B38 1593 [9] Cao C, Han Y H, Zhang L, Fan L, Duan Y W and Zhang R 2019 Advanced Quantum Technologies2 1900081 [10] Xia B Y, Cao C, Han Y H and Zhang R 2018 Laser Phys. 28 095201 [11] Scully M O and Zubairy M S 1997 Quantum Optics (United Kingdom:Cambridge University Press) [12] Wang B, Zeng X Z and Li Z Y 2020 Photon. Res. 8 343 [13] Purcell E M, Torrey H C and Pound R V 1946 Phys. Rev. 69 37 [14] Pelton M 2015 Nat. Photon. 9 427 [15] Novotny L and van Hulst N 2011 Nat. Photon. 5 83 [16] Russell K J, Liu T L, Cui S and Hu E L 2012 Nat. Photon. 6 459 [17] Dovzhenko D S, Ryabchuk S V, Rakovich Y P and Nabiev I R 2018 Nanoscale10 3589 [18] Jaynes E T and Cummings F W 1963 Proc. IEEE51 89 [19] Hertzog M, Wang M, Mony J and Borjesson K 2019 Chem. Soc. Rev. 48 937 [20] Sato Y, Tanaka Y, Upham J, Takahashi Y, Asano T and Noda S 2012 Nat. Photon. 6 56 [21] Thompson J D, Tiecke T, de Leon N P, Feist J, Akimov A, Gullans M, Zibrov A S, Vuletić V and Lukin M D 2013 Science340 1202 [22] McKeever J, Boca A, Boozer A D, Buck J R and Kimble H J 2003 Nature425 268 [23] Thomas A, Jayachandran A, Lethuillier-Karl L, Vergauwe R M A, Nagarajan K, Devaux E, Genet C, Moran J and Ebbesen T W 2020 Nanophotonics9 249 [24] Hertzog M, Rudquist P, Hutchison J A, George J, Ebbesen T W and Borjesson K 2017 Chemistry-a European Journal23 18166 [25] Khitrova G, Gibbs H M, Kira M, Koch S W and Scherer A 2006 Nat. Phys. 2 81 [26] Thompson R J, Rempe G and Kimble H J 1992 Phys. Rev. Lett. 68 1132 [27] Agarwal G S 1984 Phys. Rev. Lett. 53 1732 [28] Boca A, Miller R, Birnbaum K M, Boozer A D, McKeever J and Kimble H J 2004 Phys. Rev. Lett. 93 233603 [29] Weisbuch C, Nishioka M, Ishikawa A and Arakawa Y 1992 Phys. Rev. Lett. 69 3314 [30] Khitrova G, Gibbs H M, Jahnke F, Kira M and Koch S W 1999 Rev. Mod. Phys. 71 1591 [31] Hennessy K, Badolato A, Winger M, Gerace D, Atatüre M, Gulde S, Fält S, Hu E L and Imamoglu A 2007 Nature445 896 [32] Peter E, Senellart P, Martrou D, Lemaître A, Hours J, Gérard J M and Bloch J 2005 Phys. Rev. Lett. 95 067401 [33] Reithmaier J P, Sȩk G, Löffler A, Hofmann C, Kuhn S, Reitzenstein S, Keldysh L V, Kulakovskii V D, Reinecke T L and Forchel A 2004 Nature432 197 [34] Yoshle T, Scherer A, Hendrickson J, Khitrova G, Gibbs H M, Rupper G, Ell C, Shchekin O B and Deppe D G 2004 Nature432 200 [35] Kleemann M E, Chikkaraddy R, Alexeev E M, Kos D, Carnegie C, Deacon W, De Pury A C, Große C, De Nijs B, Mertens J, Tartakovskii A I and Baumberg J J 2017 Nat. Commun. 8 1296 [36] Liu R, Zhou Z K, Yu Y C, Zhang T, Wang H, Liu G, Wei Y, Chen H and Wang X H 2017 Phys. Rev. Lett. 118 237401 [37] Chikkaraddy R, de Nijs B, Benz F, Barrow S J, Scherman O A, Rosta E, Demetriadou A, Fox P, Hess O and Baumberg J J 2016 Nature535 127 [38] Zengin G, Wersall M, Nilsson S, Antosiewicz T J, Käll M and Shegai T 2015 Phys. Rev. Lett. 114 157401 [39] Hakala T K, Toppari J J, Kuzyk A, Pettersson M, Tikkanen H, Kunttu H, and Törmä P 2009 Phys. Rev. Lett. 103 053602 [40] Hertzog M and Borjesson K 2020 Chemphotochem4 612 [41] Ribeiro R F, Martinez-Martinez L A, Du M, Campos-Gonzalez-Angulo J and Yuen-Zhou J 2018 Chem. Sci. 9 6325 [42] Vurgaftman I, Simpkins B S, Dunkelberger A D and Owrutsky J C 2020 J. Phys. Chem. Lett. 11 3557 [43] Xiang B, Ribeiro R F, Du M, Chen L, Yang Z, Wang J, Yuen-Zhou J and Xiong W 2020 Science368 665 [44] Dunkelberger A D, Spann B T, Fears K P, Simpkins B S and Owrutsky J C 2016 Nat. Commun. 7 13504 [45] Born M and Wolf E 1999 Principles of Optics:Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edn. (United Kingdom:ECambridge University Press) p. 366 [46] Memmi H, Benson O, Sadofev S and Kalusniak S 2017 Phys. Rev. Lett. 118 126802 [47] Agrawal A, Singh A, Yazdi S, Singh A, Ong G K, Bustillo K, Johns R W, Ringe E and Milliron D J 2017 Nano Lett. 17 2611 [48] Gramotnev D K and Bozhevolnyi S I 2010 Nat. Photon. 4 83 [49] Bužavaitė-Vertelienė E, Vertelis V and Balevičius Z 2021 Nanophotonics10 1565 [50] Fox M 2006 Quantum optics:an introduction (USA:Oxford University Press) [51] Carmichael H J 2008 Statistical Methods in Quantum Optics 2:Non-Classical Fields (Germany:Springer)
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