多分量凝聚体的隧穿动力学研究
摘要
在玻色-爱因斯坦凝聚体(BEC)实现后,相关的量子隧穿问题一直以来都是研究的焦点问题之一。本文主要对多分量BEC的量子隧穿问题进行了研究,研究的问题主要有两个,一是BEC在双势阱间的外部隧穿问题；二是旋量BEC的内部隧穿问题。
第一章中我们对冷原子领域作了基本的简要介绍。主要是介绍了所研究的体系相关的一些基本概念与相关理论。
第二章用Bogliubov Backreaction方法,我们讨论了一阶的量子涨落对于约瑟夫森振荡到自囚禁的动力学相变所产生的影响。研究发现量子涨落会使原有的相变的临界行为消失,并且动力学相变点产生了偏移。
第三章我们讨论了双阱中两分量凝聚体的隧穿动力学中的动力学相变行为。发现当逐渐增大两分量间的散射强度时,系统的隧穿行为得到了加强,并且随着两分量间的散射强度增加到一个阈值时,量子隧穿会发生一个动力学的相变,并且这一动力学的相变遵从指数率。最后通过Poincare截面的分析我们发现这一动力学的相变对应着相空间分割线的穿越行为。
第四章我们对两分量的双阱问题同样用Bogoliubov backreaction method(BBR)方法计算了量子修正对于平均场的修正,研究了一阶的量子修正下对平均场下双阱中两分量凝聚体的隧穿动力学相变的影响。
第五章我们研究了考虑分畴效应后的铁磁性旋量凝聚体的内部隧穿动力学。在两畴模型下,研究了两个磁畴的磁性隧穿问题,研究发现在磁畴形成过程中磁化强度是振荡增加的,这种振荡现象正是玻色-爱因斯坦凝聚体相干性的直接体现。另外还发现振荡的幅度起先是随着能量耗散逐步增加的,表明热耗散增强了量子相干性。而弛豫较长一段时间之后,量子振荡仍然会趋于衰减；磁畴随之逐步稳定下来。并且在考虑磁畴动力学后,分量MF=0所占的比率会因为分畴效应而被抑制。
第六章对本文的主要内容作了总结。
The experimental realization of Bose-Einstein condensate has attract lots of interest in investigating various quantum phenomena within, quan-tum tunneling effect is one of the hot topic in the last decades. This thesis is devoted to study quantum tunneling problem in multicomponent Bose-Einstein condensates(BEC). Their are two systems we deal with, one is a binary mixtures of BEC trapped in double well, the other is a spin-1 Bose-Einstein condesates. Both system show interesting tunneling phenomena, one is tunneling between different wells, while the other show internal tun-neling. We first introduce the basic knowledge of Bose-Einstein condensate, then the models in our context of investigation.
In chapter II, we disscussed the dynamical phase transition in sys-tem of double well trapped one-species BEC. Considering the first order quantum correction by using'Bogoliubov backreaction method" (BBR), we find the effect of quantum fluctuation would change behavior of the transition from Josephson oscillation to self-trapping. First, it is not a critical phenomena anymore. Second, the phase transition point has been shifted. Third, we find the Von Neumann entropy will reach its maximum at the original dynamical phase transition point.
In chapter III, we disscussed the dynamical phase transition in sys-tem of double well trapped two-species BEC. We find that by gradually increasing the interspecies interaction strength, there exists a dynamical phase transition which involves logarithmic singularity. This dynamical phase transition is the direct consequence of separatrix crossing in phase space as we revealed by using the poincare section analysis, this is quite similar to the Josephson oscillation to self-trapping transition found in one species double well problem.
In chapter IV, we extended the "Bogoliubov backreaction method" (BBR) to the problem of double well trapped two-species BEC, and we disscussed the first order quantum correction on dynamical phase transition behavior described in previous chapter.
In chapter V, considering the domain formation influences, we diss-cussed internal tunneling behavior of a spin-1 BEC system. We demon-strate that the domain formationis a co-effect of the quantum coherence and the thermal relaxation. Also, a thermally enhanced quantum-oscillation is observed during the dynamical process of the domain formation, and it is found the spatial separation of domains leads to significant decay of the MF= 0 component fraction in an initial MF=0 condensate.
A summary was made in the last chapter.
第一章中我们对冷原子领域作了基本的简要介绍。主要是介绍了所研究的体系相关的一些基本概念与相关理论。
第二章用Bogliubov Backreaction方法,我们讨论了一阶的量子涨落对于约瑟夫森振荡到自囚禁的动力学相变所产生的影响。研究发现量子涨落会使原有的相变的临界行为消失,并且动力学相变点产生了偏移。
第三章我们讨论了双阱中两分量凝聚体的隧穿动力学中的动力学相变行为。发现当逐渐增大两分量间的散射强度时,系统的隧穿行为得到了加强,并且随着两分量间的散射强度增加到一个阈值时,量子隧穿会发生一个动力学的相变,并且这一动力学的相变遵从指数率。最后通过Poincare截面的分析我们发现这一动力学的相变对应着相空间分割线的穿越行为。
第四章我们对两分量的双阱问题同样用Bogoliubov backreaction method(BBR)方法计算了量子修正对于平均场的修正,研究了一阶的量子修正下对平均场下双阱中两分量凝聚体的隧穿动力学相变的影响。
第五章我们研究了考虑分畴效应后的铁磁性旋量凝聚体的内部隧穿动力学。在两畴模型下,研究了两个磁畴的磁性隧穿问题,研究发现在磁畴形成过程中磁化强度是振荡增加的,这种振荡现象正是玻色-爱因斯坦凝聚体相干性的直接体现。另外还发现振荡的幅度起先是随着能量耗散逐步增加的,表明热耗散增强了量子相干性。而弛豫较长一段时间之后,量子振荡仍然会趋于衰减；磁畴随之逐步稳定下来。并且在考虑磁畴动力学后,分量MF=0所占的比率会因为分畴效应而被抑制。
第六章对本文的主要内容作了总结。
The experimental realization of Bose-Einstein condensate has attract lots of interest in investigating various quantum phenomena within, quan-tum tunneling effect is one of the hot topic in the last decades. This thesis is devoted to study quantum tunneling problem in multicomponent Bose-Einstein condensates(BEC). Their are two systems we deal with, one is a binary mixtures of BEC trapped in double well, the other is a spin-1 Bose-Einstein condesates. Both system show interesting tunneling phenomena, one is tunneling between different wells, while the other show internal tun-neling. We first introduce the basic knowledge of Bose-Einstein condensate, then the models in our context of investigation.
In chapter II, we disscussed the dynamical phase transition in sys-tem of double well trapped one-species BEC. Considering the first order quantum correction by using'Bogoliubov backreaction method" (BBR), we find the effect of quantum fluctuation would change behavior of the transition from Josephson oscillation to self-trapping. First, it is not a critical phenomena anymore. Second, the phase transition point has been shifted. Third, we find the Von Neumann entropy will reach its maximum at the original dynamical phase transition point.
In chapter III, we disscussed the dynamical phase transition in sys-tem of double well trapped two-species BEC. We find that by gradually increasing the interspecies interaction strength, there exists a dynamical phase transition which involves logarithmic singularity. This dynamical phase transition is the direct consequence of separatrix crossing in phase space as we revealed by using the poincare section analysis, this is quite similar to the Josephson oscillation to self-trapping transition found in one species double well problem.
In chapter IV, we extended the "Bogoliubov backreaction method" (BBR) to the problem of double well trapped two-species BEC, and we disscussed the first order quantum correction on dynamical phase transition behavior described in previous chapter.
In chapter V, considering the domain formation influences, we diss-cussed internal tunneling behavior of a spin-1 BEC system. We demon-strate that the domain formationis a co-effect of the quantum coherence and the thermal relaxation. Also, a thermally enhanced quantum-oscillation is observed during the dynamical process of the domain formation, and it is found the spatial separation of domains leads to significant decay of the MF= 0 component fraction in an initial MF=0 condensate.
A summary was made in the last chapter.
引文
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