一维有限囚禁势中BEC的动力学特性
|
摘要
研究了一维有限囚禁势中玻色-爱因斯坦凝聚体(BEC)基态和激发态的动力学特性.利用变分法,得到了系统非线性系数g和化学势u的表达式,并且计算出系统状态发生变化的2个临界点:临界非线性系数g_(crit)和最大非线性系数g_(max).这2个临界点将系统划分为3个状态:束缚态(g 束缚态(g_(crit) g_(max)),并且系统的状态与势阱的形状紧密相关.对于有限深势阱,由于准束缚态的存在,势阱中粒子数发生明显变化的临界值为g_(crit).相对于基态,激发态的凝聚体需要更深更宽的势阱才能维持稳定.对于激发态中的亮孤子,系统不存在凝聚体向外发生遂穿的准束缚态,g_(max)成为系统从稳态到不稳态过渡时囚禁在势阱中的粒子数明显发生变化的临界点.
In this paper,the dynamical properties of ground state and excited state of Bose-Einstein condensate in one-dimensional finite confinement potential are studied. By using the variational method,the expressions of nonlinearitygand the chemical potentialuare obtained. The two critical points which are the critical nonlinearityg_(crit)and the maximum nonlinearity g_(max)are calculated. These two critical points divide the system into three states: the bound state( g < g_(crit)),the quasi-bound state( g_(crit)< g < g_(max)) and the unstable state( g> g_(max)),and the state of the system is closely related to the shape of the potential well. For the finite depth potential well,the critical value of a significant change in the number of particles in the well is g_(crit)due to the existence of a quasi-bound state. Compared with the ground state,the condensate of the excited state needs a deeper and wider potential well to maintain stability. For bright solitons in the excited state,there is no quasi-bound state in which the condensate tunnels outward,and g_(max)becomes the critical point for the obvious change of the number of particles trapped in the potential well during the transition from steady state to unsteady state.
In this paper,the dynamical properties of ground state and excited state of Bose-Einstein condensate in one-dimensional finite confinement potential are studied. By using the variational method,the expressions of nonlinearitygand the chemical potentialuare obtained. The two critical points which are the critical nonlinearityg_(crit)and the maximum nonlinearity g_(max)are calculated. These two critical points divide the system into three states: the bound state( g < g_(crit)),the quasi-bound state( g_(crit)< g < g_(max)) and the unstable state( g> g_(max)),and the state of the system is closely related to the shape of the potential well. For the finite depth potential well,the critical value of a significant change in the number of particles in the well is g_(crit)due to the existence of a quasi-bound state. Compared with the ground state,the condensate of the excited state needs a deeper and wider potential well to maintain stability. For bright solitons in the excited state,there is no quasi-bound state in which the condensate tunnels outward,and g_(max)becomes the critical point for the obvious change of the number of particles trapped in the potential well during the transition from steady state to unsteady state.
引文
[1] ANDERSON M H,ENSHER J R,MATTHEWS M R,et al.Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor[J].Science,1995,269:198-201.
[2] ALEXANDER J E Kreil,DMYTRO ABozhko,HALYNA Yu Musiienko-Shmarova,et al.From Kinetic Instability to Bose-Einstein Condensationand Magnon Supercurrent[J].Phys. Rev. Lett.,2018,121:077203.
[3] MARDONOV Sh,KONOTOP V V,MALOMEd B A,et al.Spin-orbit-coupled soliton in a random potential[J].Phys. Rev. A,2018,98:023604.
[4] WILSON Kali E,NEWMAN Zachary L,LOWNEY Joseph D,et al. In situ imaging of vortices in Bose-Einsteincondensates[J].Phys. Rev. A,2015,91:023621.
[5] JIAN Yue,ZHANG Ai-xia,HE Cai-xia,et al.Dynamics of a nonlocal discrete Gross-Pitaevskii equationwith defects[J].Phys. Rev. E,2013,87:053201.
[6] JIAN Yue,XUE Ju-Kui.Superfluid Fermi gases in an optical lattice with random defects[J].Eur. Phys. J. D,2012,66:191.
[7] WANG Tun,YELIN SF. Theory for Raman superradiance in atomic gases[J]. Phys. Rev. A,2005,72:043804.
[8] CAO Gao-qing,HE Lian-yi,ZHUANG Peng-fei.BCSBEC quantum phase transition and collective excitations in two-dimensionalFermi gases with p-and d-wave pairings[J].Phys.Rev. A,2013,87:013613.
[9] GRIFFIN A. Conserving and gapless approximations for an inhomogeneous Bose gas atfinite temperatures[J].Phys. Rev. B,1996,53:9341.
[10] HAI Wen-hua,LEE Chao-hong,CHONG Gui-shu.Propagation and breathing of matter-wave-packettrains[J].Phys. Rev. A,2004,70:053621.
[11] VICTOR MPérez-García,MICHINEL H,CIRAC J I,et al.Low Energy Excitations of a Bose-Einstein Condensate:A Time-Dependent Variational Analysis[J].Phys. Rev. Lett.,1996,77:5320.
[12] DIE go A. Alcala,GREGOR Urban,MATTHIAS Weidemüller,et al. Macroscopic quantum escape of Bose-Einstein condensates:Analysis of experimentally realizable quasi-one-dimensional traps[J]. Phys.Rev. A,2018,98:023619.
[13] ZHANG Dan-Wei,XUE Zheng-Yuan,YAN Hui,et al. Macroscopic Klein tunneling in spin-orbit-coupled Bose-Einstein condensates[J]. Phys. Rev. A. 2012,85:013628.
[14] ZHOU Xiao-yan,MU Ai-xia,XUE Ju-kui.The stability of Bose-Einstein condensatesin atwo-dimensional shallow trap[J]. Chinese Physics,2007,16:3197-3203.
[15] MICHAEL Albiez,RUDOLF Gati,JONAS F9lling,et al. Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction[J].Phys. Rev. Lett.,2005,95:010402.
[16]奚玉东,王登龙,佘彦超,等.双色光晶格势阱中玻色-爱因斯坦凝聚体的Landau-Zener隧穿行为[J].物理学报,2010,59(6):3720-3726.
[17]王冠芳,刘彬,傅立斌,等.非线性三能级体系的绝热朗道-齐纳隧穿[J].物理学报,2007,56(7):3733-3738.
[18] ADHIKARI Sadhan K.Bound states of attractive BoseEinstein condensates in shallow traps in two and three dimensions[J]. J. Phys. B:At. Mol. Opt. Phys.,2005,38,579-591.
[19] CARR L D,HOLLAND M J,MALOMED B A.Macroscopic quantum tunnelling of Bose-Einsteincondensates in a finite potential well[J]. J. Phys. B:At.Mol. Opt. Phys.,2005,38,3217-3231.
[2] ALEXANDER J E Kreil,DMYTRO ABozhko,HALYNA Yu Musiienko-Shmarova,et al.From Kinetic Instability to Bose-Einstein Condensationand Magnon Supercurrent[J].Phys. Rev. Lett.,2018,121:077203.
[3] MARDONOV Sh,KONOTOP V V,MALOMEd B A,et al.Spin-orbit-coupled soliton in a random potential[J].Phys. Rev. A,2018,98:023604.
[4] WILSON Kali E,NEWMAN Zachary L,LOWNEY Joseph D,et al. In situ imaging of vortices in Bose-Einsteincondensates[J].Phys. Rev. A,2015,91:023621.
[5] JIAN Yue,ZHANG Ai-xia,HE Cai-xia,et al.Dynamics of a nonlocal discrete Gross-Pitaevskii equationwith defects[J].Phys. Rev. E,2013,87:053201.
[6] JIAN Yue,XUE Ju-Kui.Superfluid Fermi gases in an optical lattice with random defects[J].Eur. Phys. J. D,2012,66:191.
[7] WANG Tun,YELIN SF. Theory for Raman superradiance in atomic gases[J]. Phys. Rev. A,2005,72:043804.
[8] CAO Gao-qing,HE Lian-yi,ZHUANG Peng-fei.BCSBEC quantum phase transition and collective excitations in two-dimensionalFermi gases with p-and d-wave pairings[J].Phys.Rev. A,2013,87:013613.
[9] GRIFFIN A. Conserving and gapless approximations for an inhomogeneous Bose gas atfinite temperatures[J].Phys. Rev. B,1996,53:9341.
[10] HAI Wen-hua,LEE Chao-hong,CHONG Gui-shu.Propagation and breathing of matter-wave-packettrains[J].Phys. Rev. A,2004,70:053621.
[11] VICTOR MPérez-García,MICHINEL H,CIRAC J I,et al.Low Energy Excitations of a Bose-Einstein Condensate:A Time-Dependent Variational Analysis[J].Phys. Rev. Lett.,1996,77:5320.
[12] DIE go A. Alcala,GREGOR Urban,MATTHIAS Weidemüller,et al. Macroscopic quantum escape of Bose-Einstein condensates:Analysis of experimentally realizable quasi-one-dimensional traps[J]. Phys.Rev. A,2018,98:023619.
[13] ZHANG Dan-Wei,XUE Zheng-Yuan,YAN Hui,et al. Macroscopic Klein tunneling in spin-orbit-coupled Bose-Einstein condensates[J]. Phys. Rev. A. 2012,85:013628.
[14] ZHOU Xiao-yan,MU Ai-xia,XUE Ju-kui.The stability of Bose-Einstein condensatesin atwo-dimensional shallow trap[J]. Chinese Physics,2007,16:3197-3203.
[15] MICHAEL Albiez,RUDOLF Gati,JONAS F9lling,et al. Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction[J].Phys. Rev. Lett.,2005,95:010402.
[16]奚玉东,王登龙,佘彦超,等.双色光晶格势阱中玻色-爱因斯坦凝聚体的Landau-Zener隧穿行为[J].物理学报,2010,59(6):3720-3726.
[17]王冠芳,刘彬,傅立斌,等.非线性三能级体系的绝热朗道-齐纳隧穿[J].物理学报,2007,56(7):3733-3738.
[18] ADHIKARI Sadhan K.Bound states of attractive BoseEinstein condensates in shallow traps in two and three dimensions[J]. J. Phys. B:At. Mol. Opt. Phys.,2005,38,579-591.
[19] CARR L D,HOLLAND M J,MALOMED B A.Macroscopic quantum tunnelling of Bose-Einsteincondensates in a finite potential well[J]. J. Phys. B:At.Mol. Opt. Phys.,2005,38,3217-3231.