Abstract
We theoretically investigate the optical second-order sideband generation (OSSG) in an optical parity-time (PT) symmetric system, which consists of a passive cavity trapping the atomic ensemble and an active cavity. Compared with the double-passive system, it is found that near the exceptional point (EP), the efficiency of the OSSG increases sharply not only for the blue probepump detuning resonant case but also for the red one. Using experimentally achievable parameters, we study the effect of the atomic ensemble on the efficiency of the OSSG in the PT-symmetric system. The numerical results show that the efficiency of the OSSG is 30% higher than that of the first-order sideband, which is realized easily by simultaneously modulating the atom-cavity coupling strength and detuning. Moreover, the efficiency of the OSSG can also be tuned effectively by the pump power, and the efficiency is robust when the pump power is strong enough. This study may have some guidance for modulating the nonlinear optical properties and controlling light propagation, which may stimulate further applications in optical communications.
Similar content being viewed by others
References
M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014), arXiv: 1303.0733.
T. J. Kippenberg, and K. J. Vahala, Science 321, 1172 (2008).
E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, Nature 482, 63 (2012), arXiv: 1107.3761.
L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, Nat. Commun. 6, 5850 (2015), arXiv: 1412.2084.
A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawa-mura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, Science 256, 325 (1992).
P. Rabl, Phys. Rev. Lett. 107, 063601 (2011), arXiv: 1102.0278.
R. Huang, A. Miranowicz, J. Q. Liao, F. Nori, and H. Jing, Phys. Rev. Lett. 121, 153601 (2018), arXiv: 1807.10084.
A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, Nat. Photon. 6, 768 (2012), arXiv: 1203.5730.
J. Liu, and K.-D. Zhu, Photon. Res. 6, 867 (2018).
Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, Phys. Rev. A 91, 063827 (2015), arXiv: 1506.00812.
F. C. Lei, M. Gao, C. Du, Q. L. Jing, and G. L. Long, Opt. Express 23, 11508 (2015).
X. Y. Zhang, Y. H. Zhou, Y. Q. Guo, and X. X. Yi, Phys. Rev. A 98, 033832 (2018).
W. Nie, A. Chen, and Y. Lan, Opt. Express 25, 32931 (2017).
B. P. Hou, L. F. Wei, and S. J. Wang, Phys. Rev. A 92, 033829 (2015).
Y. Guo, K. Li, W. Nie, and Y. Li, Phys. Rev. A 90, 053841 (2014), arXiv: 1407.5202.
Z. X. Liu, B. Wang, H. Xiong, and Y. Wu, Opt. Lett. 43, 3698 (2018), arXiv: 1806.08289.
C. Cao, S. C. Mi, Y. P. Gao, L. Y. He, D. Yang, T. J. Wang, R. Zhang, and C. Wang, Sci. Rep. 6, 22920 (2016).
H. Xiong, L. G. Si, X. Y. Lü, X. Yang, and Y. Wu, Opt. Lett. 38, 353 (2013).
J. Li, J. Li, Q. Xiao, and Y. Wu, Phys. Rev. A 93, 063814 (2016).
L. Li, W. X. Yang, Y. Zhang, T. Shui, A. X. Chen, and Z. Jiang, Phys. Rev. A 98, 063840 (2018).
L. Y. He, Phys. Rev. A 99, 033843 (2019).
B. Chen, L. Shang, X. F. Wang, J. B. Chen, H. B. Xue, X. Liu, and J. Zhang, Phys. Rev. A 99, 063810 (2019).
H. Xiong, and Y. Wu, Appl. Phys. Rev. 5, 031305 (2018).
P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
W. X. Yang, A. X. Chen, X. T. Xie, and L. Ni, Phys. Rev. A 96, 013802 (2017).
Y. Louyer, D. Meschede, and A. Rauschenbeutel, Phys. Rev. A 72, 031801 (2005), arXiv: quant-ph/0501002.
K. J. Vahala, Nature 424, 839 (2003).
Z. Z. Hao, L. Zhang, A. Gao, W. B. Mao, X. D. Lyu, X. M. Gao, F. Bo, F. Gao, G. Q. Zhang, and J. J. Xu, Sci. China-Phys. Mech. Astron. 61, 114211 (2018).
Q. H. Song, Sci. China-Phys. Mech. Astron. 62, 074231 (2019).
C. M. Bender, and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998), arXiv: physics/9712001.
C. M. Bender, Rep. Prog. Phys. 70, 947 (2007), arXiv: hep-th/0703096.
A. Mostafazadeh, J. Math. Phys. 43, 205 (2002), arXiv: math-ph/0107001.
Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011), arXiv: 1108.2493.
H. F. Jones, J. Phys. A-Math. Theor. 45, 135306 (2012), arXiv: 1111.2041.
H. Benisty, A. Degiron, A. Lupu, A. de Lustrac, S. Chénais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, and G. Lérondel, Opt. Express 19, 18004 (2011).
C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
S. Bittner, B. Dietz, U. Günther, H. L. Harney, M. Miski-Oglu, A. Richter, and F. Schäfer, Phys. Rev. Lett. 108, 024101 (2012), arXiv: 1107.4256.
A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
B. Peng, K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Nat. Phys. 10, 394 (2014), arXiv: 1308.4564.
L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
X. Y. Lü, H. Jing, J. Y. Ma, and Y. Wu, Phys. Rev. Lett. 114, 253601 (2015), arXiv: 1506.08917.
H. Jing, S. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, Phys. Rev. Lett. 113, 053604 (2014), arXiv: 1403.0657.
J. Li, X. Zhan, C. Ding, D. Zhang, and Y. Wu, Phys. Rev. A 92, 043830 (2015).
R. W. Boyd, Nonlinear Optics (Elsevier, New York, 2003).
Y. F. Jiao, T. X. Lu, and H. Jing, Phys. Rev. A 97, 013843 (2018), arXiv: 1801.08669.
C. Jiang, X. Bian, Y. Cui, and G. Chen, J. Opt. Soc. Am. B 33, 2099 (2016).
S. Liu, W. X. Yang, Z. Zhu, T. Shui, and L. Li, Opt. Lett. 43, 9 (2018).
S. Weis, R. Riviére, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, Science 330, 1520 (2010), arXiv: 1007.0565.
H. Xiong, L. G. Si, A. S. Zheng, X. Yang, and Y. Wu, Phys. Rev. A 86, 013815 (2012).
S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006), arXiv: quant-ph/0607068.
O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006), arXiv: quant-ph/0607205.
C. Genes, D. Vitali, and P. Tombesi, Phys. Rev. A 77, 050307 (2008), arXiv: 0801.2266.
Z. P. Liu, J. Zhang, K. Özdemir, B. Peng, H. Jing, X. Y. Lü, C. W. Li, L. Yang, F. Nori, and Y. Liu, Phys. Rev. Lett. 117, 110802 (2016), arXiv: 1510.05249.
J. Zhang, B. Peng, K. Özdemir, Y. Liu, H. Jing, X. Lü, Y. Liu, L. Yang, and F. Nori, Phys. Rev. B 92, 115407 (2015), arXiv: 1510.07343.
Author information
Authors and Affiliations
Corresponding authors
Additional information
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61368002, 91736106, 11674390, and 91836302), the Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (Grant No. KF201711), the Foundation for Distinguished Young Scientists of Jiangxi Province (Grant No. 20162BCB23009), and the Graduate Innovation Special Fund of Jiangxi Province (Grant No. YC2019-S102).
Rights and permissions
About this article
Cite this article
Xiao, X., Liao, Q., Zhou, N. et al. Tunable optical second-order sideband effects in a parity-time symmetric optomechanical system. Sci. China Phys. Mech. Astron. 63, 114211 (2020). https://doi.org/10.1007/s11433-020-1559-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11433-020-1559-4