耦合Bose-Einstein凝聚体系与强激光场中原子分子体系的非线性现象
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摘要
激光与原子分子的相互作用导致了许多新颖现象,已成为近年来原子分子物理的一个研究热点。基于激光冷却与囚禁中性原子的实现和强激光技术的应用,本文研究了耦合Bose-Einstein凝聚体系和强激光场中的原子分子体系的相关非线性现象。
对耦合Bose-Einstein凝聚体系,从耦合的非线性Schr?dinger方程——Gross-Pitaevskii方程出发,我们着重分析了两耦合Bose-Einstein凝聚体系中由平均场的非线性以及体系内在的相干性导致的宏观量子现象,同时精确分析了有关多耦合Bose-Einstein凝聚体系中超流——绝缘相变以及物质波孤子链的传播、塌缩和恢复等现象。主要工作有:
(1)两耦合Bose-Einstein凝聚体系间宏观量子隧穿的准自旋模型。我们将两耦合Bose-Einstein凝聚体系间宏观量子隧穿映射为非轴向自旋体系在外加磁场中的隧穿,并推导了相应的Bloch方程。发现凝聚体系的平均场作用、组份之间的耦合与非对称性(或耦合激光的失谐)分别对应着体系的各向异性、横向磁场与轴向磁场。在低势垒情形下,用虚时间路径积分法计算了隧穿指数,得到了隧穿指数对系统参数的依赖性,同时估计了从量子机制向热机制过渡的交叉温度。
(2)激光耦合两组份Bose-Einstein凝聚体系的条件自发自旋极化与分岔滞后。我们发现激光脉冲耦合下的两组份Bose-Einstein凝聚体系的分岔和自发自旋极化不仅依赖于系统参数,而且依赖于两组份间的相对相位。这些现象不同于那些只依赖于系统参数的分岔和自发自旋极化现象,是条件分岔和条件自发自旋极化。通过分岔,系统从Rabi机制进入自发自旋极化机制。另外,当参数缓慢地扫过静态分岔点时,我们发现系统中存在分岔滞后现象。
(3)耗散及非耗散情形下的两耦合Bose-Einstein凝聚体系间的非线性布居数振荡。通过对含时非对称的双阱势中两耦合Bose-Einstein凝聚体系的研究,我们发现了混沌的及频率锁定的布居数振荡。决定性微扰下,系统在分界解附近的解是Melnikov混沌的。数值模拟表明:在非耗散机制下,随着非对称性的增加,规则振荡逐渐变为混沌振荡,长期的局域化消失;在耗散机制下,稳态混沌消失,系统经过渐态混沌进入规则的稳定的频率锁定的振荡,适当强度的阻尼可以保持长期的局域化。
对强激光场中的原子分子体系,我们从其非线性的经典Hamilton方程出发,用经典轨道Monte-Carlo法模拟了氢原子及氢分子离子在强激光场中的高次谐波产生过程。通过引入天体力学中的规则化方法消除了二体及三体库仑问题的奇点,
Laser-atom interaction induces a lot of novel phenomena and has become one of the hotspots in the field of atomic and molecular physics. Based upon the realization of laser cooling and trapping and the application of technology of intense laser in atomic and molecular physics, we have analyzed the nonlinear phenomena in coupled Bose-Einstein condensates and atomic & molecular systems in intense laser fields.
For the coupled Bose-Einstein condensates, with the coupled nonlinear Schr?dinger equations (Gross-Pitaevskii equations), we focus our investigation on the macroscopic quantum phenomena induced by the mean-field nonlinearity and the inherent coherence in Bose-Einstein condensates, we have also analyzed some related phenomena in coupled multiple Bose-Einstein condensates. The following works are enclosed in this dissertation.
(I) Quasi-spin Model for Macroscopic Quantum Tunnelling between Two Coupled Bose-Einstein Condensates: The system of two coupled Bose-Einstein condensates is mapped onto an uniaxial spin with an applied magnetic field. The mean-field interaction, the coupling and the asymmetry or the detuning correspond to the anisotropy, the transverse field and the longitudinal field, respectively. The generalized Bloch's equation is derived. In the limit of low barrier, the tunneling exponent is calculated with an imaginary-time path-integral method. The dependence of the tunneling exponent on the system parameters is obtained. The crossover temperature TC from thermal regime to quantum regime is estimated. Below TC , the quantum phenomenon dominates the tunnelling, otherwise, the thermal activation dominates.
(II) Conditional Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates: We find that the bifurcation and the spontaneous spin polarization depend not only on the system parameters, but also on the relative phase between two components. These phenomena are different from those only are determined by the parameters, we name them as conditional bifurcation and conditional spontaneous spin polarization. Through bifurcations, the system enters into the spontaneous spin polarization regime from the Rabi regime. We also find that bifurcation delay appears when the parameter is swept through the static bifurcation point.
(III) Nonlinear Population Oscillation between two Coupled Bose-Einstein Condensates: We have investigated the chaotic and frequency-locked population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric potential. Under the deterministic perturbation, there exist stable oscillations close to the separatrix solution, which are Melnikov chaotic. Numerical results reveal that, in the nondissipative regime, regular
对耦合Bose-Einstein凝聚体系,从耦合的非线性Schr?dinger方程——Gross-Pitaevskii方程出发,我们着重分析了两耦合Bose-Einstein凝聚体系中由平均场的非线性以及体系内在的相干性导致的宏观量子现象,同时精确分析了有关多耦合Bose-Einstein凝聚体系中超流——绝缘相变以及物质波孤子链的传播、塌缩和恢复等现象。主要工作有:
(1)两耦合Bose-Einstein凝聚体系间宏观量子隧穿的准自旋模型。我们将两耦合Bose-Einstein凝聚体系间宏观量子隧穿映射为非轴向自旋体系在外加磁场中的隧穿,并推导了相应的Bloch方程。发现凝聚体系的平均场作用、组份之间的耦合与非对称性(或耦合激光的失谐)分别对应着体系的各向异性、横向磁场与轴向磁场。在低势垒情形下,用虚时间路径积分法计算了隧穿指数,得到了隧穿指数对系统参数的依赖性,同时估计了从量子机制向热机制过渡的交叉温度。
(2)激光耦合两组份Bose-Einstein凝聚体系的条件自发自旋极化与分岔滞后。我们发现激光脉冲耦合下的两组份Bose-Einstein凝聚体系的分岔和自发自旋极化不仅依赖于系统参数,而且依赖于两组份间的相对相位。这些现象不同于那些只依赖于系统参数的分岔和自发自旋极化现象,是条件分岔和条件自发自旋极化。通过分岔,系统从Rabi机制进入自发自旋极化机制。另外,当参数缓慢地扫过静态分岔点时,我们发现系统中存在分岔滞后现象。
(3)耗散及非耗散情形下的两耦合Bose-Einstein凝聚体系间的非线性布居数振荡。通过对含时非对称的双阱势中两耦合Bose-Einstein凝聚体系的研究,我们发现了混沌的及频率锁定的布居数振荡。决定性微扰下,系统在分界解附近的解是Melnikov混沌的。数值模拟表明:在非耗散机制下,随着非对称性的增加,规则振荡逐渐变为混沌振荡,长期的局域化消失;在耗散机制下,稳态混沌消失,系统经过渐态混沌进入规则的稳定的频率锁定的振荡,适当强度的阻尼可以保持长期的局域化。
对强激光场中的原子分子体系,我们从其非线性的经典Hamilton方程出发,用经典轨道Monte-Carlo法模拟了氢原子及氢分子离子在强激光场中的高次谐波产生过程。通过引入天体力学中的规则化方法消除了二体及三体库仑问题的奇点,
Laser-atom interaction induces a lot of novel phenomena and has become one of the hotspots in the field of atomic and molecular physics. Based upon the realization of laser cooling and trapping and the application of technology of intense laser in atomic and molecular physics, we have analyzed the nonlinear phenomena in coupled Bose-Einstein condensates and atomic & molecular systems in intense laser fields.
For the coupled Bose-Einstein condensates, with the coupled nonlinear Schr?dinger equations (Gross-Pitaevskii equations), we focus our investigation on the macroscopic quantum phenomena induced by the mean-field nonlinearity and the inherent coherence in Bose-Einstein condensates, we have also analyzed some related phenomena in coupled multiple Bose-Einstein condensates. The following works are enclosed in this dissertation.
(I) Quasi-spin Model for Macroscopic Quantum Tunnelling between Two Coupled Bose-Einstein Condensates: The system of two coupled Bose-Einstein condensates is mapped onto an uniaxial spin with an applied magnetic field. The mean-field interaction, the coupling and the asymmetry or the detuning correspond to the anisotropy, the transverse field and the longitudinal field, respectively. The generalized Bloch's equation is derived. In the limit of low barrier, the tunneling exponent is calculated with an imaginary-time path-integral method. The dependence of the tunneling exponent on the system parameters is obtained. The crossover temperature TC from thermal regime to quantum regime is estimated. Below TC , the quantum phenomenon dominates the tunnelling, otherwise, the thermal activation dominates.
(II) Conditional Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates: We find that the bifurcation and the spontaneous spin polarization depend not only on the system parameters, but also on the relative phase between two components. These phenomena are different from those only are determined by the parameters, we name them as conditional bifurcation and conditional spontaneous spin polarization. Through bifurcations, the system enters into the spontaneous spin polarization regime from the Rabi regime. We also find that bifurcation delay appears when the parameter is swept through the static bifurcation point.
(III) Nonlinear Population Oscillation between two Coupled Bose-Einstein Condensates: We have investigated the chaotic and frequency-locked population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric potential. Under the deterministic perturbation, there exist stable oscillations close to the separatrix solution, which are Melnikov chaotic. Numerical results reveal that, in the nondissipative regime, regular
引文
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