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Dark Soliton of Polariton Condensates under Nonresonant $\mathcal{P}\mathcal{T}$-Symmetric Pumping |
| Chun-Yu Jia, Zhao-Xin Liang** |
Department of Physics, Zhejiang Normal University, Jinhua 321004
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| Cite this article: |
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Chun-Yu Jia, Zhao-Xin Liang 2020 Chin. Phys. Lett. 37 040502 |
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Abstract A quantum system in complex potentials obeying parity-time ($\mathcal{P}\mathcal{T}$) symmetry could exhibit all real spectra, starting out in non-Hermitian quantum mechanics. The key physics behind a $\mathcal{P}\mathcal{T}$-symmetric system consists of the balanced gain and loss of the complex potential. We plan to include the nonequilibrium nature (i.e., the intrinsic kinds of gain and loss of a system) to a $\mathcal{P}\mathcal{T}$-symmetric many-body quantum system, with an emphasis on the combined effects of non-Hermitian due to nonequilibrium nature and $\mathcal{P}\mathcal{T}$ symmetry in determining the properties of a system. To this end, we investigate the static and dynamical properties of a dark soliton of a polariton Bose–Einstein condensate under the $\mathcal{P}\mathcal{T}$-symmetric non-resonant pumping by solving the driven-dissipative Gross–Pitaevskii equation both analytically and numerically. We derive the equation of motion for the center of mass of the dark soliton's center analytically with the help of the Hamiltonian approach. The resulting equation captures how the combination of the open-dissipative character and $\mathcal{P}\mathcal{T}$-symmetry affects the properties of the dark soliton; i.e., the soliton relaxes by blending with the background at a finite time. Further numerical solutions are in excellent agreement with the analytical results.
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Received: 08 January 2020
Published: 24 March 2020
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| PACS: |
05.45.Yv
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(Solitons)
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42.65.Tg
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(Optical solitons; nonlinear guided waves)
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67.85.Hj
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(Bose-Einstein condensates in optical potentials)
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| Fund: Supported by the National Natural Science Foundation of China under Grant No. 11835011. |
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| [1] | Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 | | [2] | Bender C M 2007 Rep. Prog. Phys. 70 947 | | [3] | Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A and Christodoulides D N 2009 Phys. Rev. Lett. 103 093902 | | [4] | Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192 | | [5] | Li J M, Harter A K, Liu J, Melo L D, Joglekar Y N and Luo L 2019 Nat. Commun. 10 855 | | [6] | Makris K G, El-Ganainy R, Christodoulides D N and Musslimani Z H 2011 Int. J. Theor. Phys. 50 1019 | | [7] | Hodaei H, Miri M A, Heinrich M, Christodoulides D N and Khajavikhan M 2014 Science 346 975 | | [8] | Peng B, Ozdemir S K, Rotter S, Yilmaz H, Liertzer M, Monifi F, Bender C M, Nori F and Yang L 2014 Science 346 328 | | [9] | Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E B, Almeida V R, Chen Y F and Scherer A 2013 Nat. Mater. 12 108 | | [10] | Bender C M, Berntson B K, Parker D and Samuel E 2013 Am. J. Phys. 81 173 | | [11] | Regensburger A, Bersch C, Miri M, Onishchukov G, Christodoulides D N and Peschel U 2012 Nature 488 167 | | [12] | Xu H, Mason D, Jiang L Y and Harris J G E 2016 Nature 537 80 | | [13] | Carusotto I and Ciuti C 2013 Rev. Mod. Phys. 85 299 | | [14] | Shelykh I A, Kavokin A V, Rubo Y G, Liew T C H and Malpuech G 2010 Semicond. Sci. Technol. 25 013001 | | [15] | Deng H, Haug H and Yamamoto Y 2010 Rev. Mod. Phys. 82 1489 | | [16] | Byrnes T, Kim N Y and Yamamoto Y 2014 Nat. Phys. 10 803 | | [17] | Xue Y and Matuszewski M 2014 Phys. Rev. Lett. 112 216401 | | [18] | Smirnov L A, Smirnova D A, Ostrovskaya E A and Kivshar Y S 2014 Phys. Rev. B 89 235310 | | [19] | Pinsker F and Flayac H 2014 Phys. Rev. Lett. 112 140405 | | [20] | Pinsker F 2015 Ann. Phys. 362 726 | | [21] | Pinsker F and Flayac H 2016 Proc. R. Soc. A 472 20150592 | | [22] | Ma X K, Egorov O A and Schumacher S 2017 Phys. Rev. Lett. 118 157401 | | [23] | Ma X K and Schumacher S 2018 Phys. Rev. Lett. 121 227404 | | [24] | Xu X R, Chen L, Zhang Z D and Liang Z X 2019 J. Phys. B: At. Mol. Opt. Phys. 52 025303 | | [25] | Amo A, Pigeon S, Sanvitto D, Sala V G, Hivet R, Carusotto I, Pisanello F, Leménager G, Houdré R, Giacobino E, Ciuti C and Bramati A 2011 Science 332 1167 | | [26] | Cilibrizzi P, Ohadi H, Ostatnicky T, Askitopoulos A, Langbein W and Lagoudakis P 2014 Phys. Rev. Lett. 113 103901 | | [27] | Walker P M, Tinkler L, Royall B, Skryabin D V, Farrer I, Ritchie D A, Skolnick M S and Krizhanovskii D N 2017 Phys. Rev. Lett. 119 097403 | | [28] | Gao T, Estrecho E, Bliokh K Y, Liew T C H, Fraser M D, Brodbeck S, Kamp M, Schneider C, Höfling S, Yamamoto Y, Nori F, Kivshar Y S, Truscott A G, Dall R G and Ostrovskaya E A 2015 Nature 526 554 | | [29] | Gao T, Li G, Estrecho E, Liew T C H, ComberTodd D, Nalitov A, Steger M, West K, Pfeiffer L, Snok D W, Kavokin A V, Truscott A G and Ostrovskaya E A 2018 Phys. Rev. Lett. 120 065301 | | [30] | Wertz E, Ferrier L, Solnyshkov D D, Johne R, Sanvitto D, Lemaître A, Sagnes I, Grousson R, Kavokin A V, Senellart P, Malpuech G and Bloch J 2010 Nat. Phys. 6 860 | | [31] | Qi W, Li H F and Liang Z X 2019 Chin. Phys. Lett. 36 040501 | | [32] | Musslimani Z H, Makris K G, El-Ganainy R and Christodoulides D N 2008 Phys. Rev. Lett. 100 030402 | | [33] | Lumer Y, Plotnik Y, Rechtsman M C and Segev M 2013 Phys. Rev. Lett. 111 263901 |
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