二维激子极化激元凝聚中涡旋叠加态稳态及动力学特性研究
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摘要
利用分步Crank-Nicolson方案的虚时和实时有限差分方法求解耗散系统的Gross-Pitaevskii(GP)方程,研究了二维激子极化激元凝聚(exciton-polariton condensates)体系中正反涡旋叠加态的稳态结构并直观地验证这种稳态结构在半导体微腔旋转下的稳定性和动力学特性.通过虚时和实时演化相结合的方法求解出几种角动量情况下所对应的稳定涡旋叠加态.然后利用实时演化方法研究在半导体微腔旋转的情况下,正反涡旋叠加态的稳定性及其旋转角速率和半导体微腔旋转角速率之间的定量关系.最后研究了单涡旋态在半导体微腔旋转时形成涡旋阵列的动力学过程,并给出了泵浦光宽度和增益项对涡旋阵列结构的影响.研究表明,系统的泵浦,损耗和增益对稳定性和动力学特性有重要影响.
The Gross-Pitaevskii(GP) equation of the dissipative system is solved by using the algorithm involving real-and imaginary-time propagation based on a split-step Crank-Nicolson method. The steady-state structure of the vortex and antivortex superposed state in a two-dimensional exciton-polariton condensates is studied, and the stability and dynamic characteristics of the steady state structure under the semiconductor micro-cavity rotation are intuitively verified. The stable vortex superposition states corresponding to several angular momentum conditions are solved by combining real-and imaginary-time propagation. Then the quantitative relationship of the rotational angular velocity between vortex and antivortex superposed state and the semiconductor microcavity is studied by using the real-time propagation method, and the rotational stability of the inverse vortex superposition state is investigated. Finally, the dynamic process of the vortex array formed by the rotation of a single vortex in a semiconductor micro cavity is studied, and the influence of the width of pumping light and gain on the structure of the vortex array is given. The results show that the pump, loss and gain of the system have important influence on the stability and dynamic characteristics.
The Gross-Pitaevskii(GP) equation of the dissipative system is solved by using the algorithm involving real-and imaginary-time propagation based on a split-step Crank-Nicolson method. The steady-state structure of the vortex and antivortex superposed state in a two-dimensional exciton-polariton condensates is studied, and the stability and dynamic characteristics of the steady state structure under the semiconductor micro-cavity rotation are intuitively verified. The stable vortex superposition states corresponding to several angular momentum conditions are solved by combining real-and imaginary-time propagation. Then the quantitative relationship of the rotational angular velocity between vortex and antivortex superposed state and the semiconductor microcavity is studied by using the real-time propagation method, and the rotational stability of the inverse vortex superposition state is investigated. Finally, the dynamic process of the vortex array formed by the rotation of a single vortex in a semiconductor micro cavity is studied, and the influence of the width of pumping light and gain on the structure of the vortex array is given. The results show that the pump, loss and gain of the system have important influence on the stability and dynamic characteristics.
引文
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[21] Ma X K,Egorov O A,Schumacher S.Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates[J].Phys.Rev.Lett.,2017,118:157401.
[22] Thanvanthri S,Kapale K T,Dowling J P,et al.Arbitrary coherent superpositions of quantized vortices in Bose-Einstein condensates via orbital angular momentum of light[J].Phys.Rev.A,2008,77:053825.
[2] Adhikari S K,Muruganandam P.Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation [J].J.Phys.B:At.,Mol.Opt.Phys.,2002,35:409.
[3] Chen G P,Hao J B.Nonlinear dynamics of vorices in a Bose-Einstein condendsate with dipole-dipole [J].J.At.Mol.Phys.,2017,34:1175 (in Chinese) [陈光平,郝加波.偶极-偶极相互作用下玻色-爱因斯坦凝聚体中涡旋的非线性动力学研究[J].原子与分子物理学报,2017,34:1175]
[4] Li Y S.Corrections on thermodynamics of rotating ideal Bose gases confined in a two dimensional harmonic trap [J].J.At.Mol.Phys.,2017,34:973 (in Chinese) [李玉山.二维简谐势阱中旋转理想玻色气体热力学性质的修正[J].原子与分子物理学报,2017,34:973]
[5] He Z M.The controlling of rogue wave in Bose-Einstein condensates [J].J.At.Mol.Phys.,2017,34:511 (in Chinese) [何章明.玻色-爱因斯坦凝聚体中的怪波操控[J].原子与分子物理学报,2017,34:511]
[6] Deng H,Haug H,Yamamoto Y.Exciton-polariton Bose-Einstein condensation[J].Rev.Mod.Phys.,2010,82:1489.
[7] Bobrovska N,Ostrovskaya E A,Matuszewski M.Stability and spatial coherence of nonresonantly pumped exciton-polariton condensates[J].Phys.Rev.B,2014,90:205304.
[8] Liu X Y,Su Y P,Xu Z J.Detection of quantum vortex by interference of Bose-condensed gas in a double-well trap [J].Chin.J.Quant.Elect.,2011,28:313 (in Chinese) [刘夏吟,苏艳平,徐志君.双磁阱中玻色凝聚气体干涉演化探测量子涡旋[J].量子电子学报,2011,28:313]
[9] Liu M,Wen L H,Xiong H W,et al.Structure and generation of the vortex-antivortex superposed state in Bose-Einstein condensates[J].Phys.Rev.A,2006,73:063620.
[10] Thanvanthri S,Kapale K T,Dowling J P.Ultra-stable matter-wave gyroscopy with counterrotating vortex superpositions in Bose-Einstein condensates[J].J.Mod.Opt.,2012,59:1180.
[11] Padhi B,Duboscq R,Niranjan A,et al.Vortex dynamics of rotating bose-einstein condensate of microcavity polaritons[J].J.Phys.B:At,Mol.Opt.Phys.,2015,88:116.
[12] Frederick Ira Moxley III,Dowling J P,Dai W D,et al.Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates[J].Phys.Rev.A,2016,93:053603.
[13] Muruganandam P,Adhikari S K.Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap[J].Comput.Phys.Commun.,2009,180:1888.
[14] Gargoubi H,Guillet T,Jaziri S,et al.Polariton condensation threshold investigation through the numerical resolution of the generalized Gross-Pitaevskii equation[J].Phys.Rev.E,2016,94:043310.
[15] Wouters M,Carusotto I,Ciuti C.Spatial and spectral shape of inhomogeneous nonequilibrium exciton-polariton condensates[J].Phys.Rev.B,2008,77:115340.
[16] Balili R,Hartwell V,Snoke D,et al.Bose-Einstein condensation of microcavity polaritons in a trap[J].Science,2007,316:1007.
[17] Kato A,Nakano Y,Kasamatsu K,et al.Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice[J].Phys.Rev.A,2011,84:053623.
[18] Wang H,Wen L H,Yang H,et al.Vortex states and spin textures of rotating spin-orbit-coupled Bose-Einstein condensates in a toroidal trap[J].J.Phys.B:At.Mol.Opt.Phys.,2017,50:155301.
[19] Borgh M O,Franchetti G,Keeling J,et al.Robustness and observability of rotating vortex lattices in an exciton-polariton condensate[J].Phys.Rev.B,2012,86:035307.
[20] Wouters M,Carusotto I.Superfluidity and critical velocities in nonequilibrium Bose-Einstein condensates.Phys.Rev.Lett.,2010,105:020602.
[21] Ma X K,Egorov O A,Schumacher S.Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates[J].Phys.Rev.Lett.,2017,118:157401.
[22] Thanvanthri S,Kapale K T,Dowling J P,et al.Arbitrary coherent superpositions of quantized vortices in Bose-Einstein condensates via orbital angular momentum of light[J].Phys.Rev.A,2008,77:053825.