旋量玻色—爱因斯坦凝聚中的理论物理问题研究
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摘要
简并量子气体的基本性质取决于原子间相互作用的量程、强度及对称性。在旋量玻色—爱因斯坦凝聚体中不仅可以通过Feshbach共振技术来调节原子间的短程相互作用而且可以考虑各向异性的长程相互作用带来的效应。本论文主要研究旋量玻色一爱因斯坦凝聚体中自旋交换相互作用和磁偶极一偶极相互作用对凝聚体超流性、隧穿动力学及量子纠缠特性的影响,研究涉及旋量玻色一爱因斯坦凝聚体的玻色一哈伯德模型,量子隧穿模型和量子相变等物理问题。
第二章从自旋1的玻色一哈伯德模型出发,用波戈留波夫变换方法得到了光晶格中超冷玻色原子的激发谱,研究了旋量玻色一爱因斯坦凝聚体中不同的相互作用特别是自旋交换相互作用对超流性质的影响。超流临界速度与自旋组分的相关性及其可操控性,为实验探测超流相及光晶格中旋量玻色一爱因斯坦凝聚体的组分分离提供了可能。
第三章对偶极旋量玻色—爱因斯坦凝聚体的隧穿动力学进行了半经典研究,导出经典运动方程。自旋交换相互作用与磁偶极—偶极相互作用的共同影响将导致旋量玻色—爱因斯坦凝聚体的等效两组分间出现自发磁化现象和著名的“宏观量子自俘获”现象。
量子纠缠是量子力学世界最基本和最具诱惑力的特质,由此我们研究了多分量玻色—爱因斯坦凝聚体——多粒子与多模系统的纠缠特性。第四章着重讨论在有梯度的磁场作用下反铁磁相互作用的旋量玻色—爱因斯坦凝聚体中纠缠原子态的产生和操控及纠缠的动力学问题;第五章则对最简单的量子隧穿模型——两弱耦合的玻色—爱因斯坦凝聚体的本征问题及纠缠性质进行了详细的研究。
本论文研究属于凝聚态物理,理论物理和原子分子物理的交叉学科。
The essential properties of degenerate quantum gases depend on the range, strength and symmetry of atomic interactions. In spinor Bose-Einstein condensates (BEC), one can not only tune the short-range contact interaction using Feshbach resonances but also investigate effects of the long-range and anisotropic interaction. In this thesis we mainly study the properties of spinor Bose-Einstein condensates, including superfluidity, tunneling dynamics and quantum entanglement. The work relates mainly to Bose-Hubbard model, quantum tunneling model, quantum phase transition in spinor Bose-Einstein condensates.In Chapter 2, we start from spin-1 Bose-Hubbard model and derive the energy spectra in terms of Bogoliubov transformation for cold bosons in optical lattices, which indicate the dependence of superfluidity on the spin-exchange interaction. Our observation is that the critical velocities of the superfluid flow are spin-component dependent and can be controlled by adjusting the laser lights that form the optical lattice. Possible experiments to detect the superfluid phase and component separation of spinor BEC are also discussed.In Chapter 3, we describe a semiclassical treatment of the dynamics of dipolar spinor condensates. As a result of the conservation of atom numbers and total hyperfine spin of the condensates, the classical equations of motion are derived. The interplay of spin-exchange and magnetic dipole-dipole interaction leads to the phenomena of spontaneous magnetization and the novel "macroscopic quantum self-trapping".Quantum entanglement is one of the most essential and fascinating features of quantum mechanics. We study the entanglement characteristics of
multi-component Bose-Einstein condensates ------ multipartite andmultimodal systems. Chapter 4 is devoted to proposing generation and manipulation of entangled atom states in an antiferromagnetic spin-1 BEC under magnetic field with gradient and also investigating the dynamics of the entropy of entanglement. Chapter 5 pays attention to the simplest quantumtunneling model------two tunnel-coupled BEC. We study the eigen problemand entanglement characteristics with perturbation method for both weak and strong tunnel couplings, from which some new features are explored.The research in this thesis attributes to the crossover of theoretical physics, condensed matter physics and atom physics.
第二章从自旋1的玻色一哈伯德模型出发,用波戈留波夫变换方法得到了光晶格中超冷玻色原子的激发谱,研究了旋量玻色一爱因斯坦凝聚体中不同的相互作用特别是自旋交换相互作用对超流性质的影响。超流临界速度与自旋组分的相关性及其可操控性,为实验探测超流相及光晶格中旋量玻色一爱因斯坦凝聚体的组分分离提供了可能。
第三章对偶极旋量玻色—爱因斯坦凝聚体的隧穿动力学进行了半经典研究,导出经典运动方程。自旋交换相互作用与磁偶极—偶极相互作用的共同影响将导致旋量玻色—爱因斯坦凝聚体的等效两组分间出现自发磁化现象和著名的“宏观量子自俘获”现象。
量子纠缠是量子力学世界最基本和最具诱惑力的特质,由此我们研究了多分量玻色—爱因斯坦凝聚体——多粒子与多模系统的纠缠特性。第四章着重讨论在有梯度的磁场作用下反铁磁相互作用的旋量玻色—爱因斯坦凝聚体中纠缠原子态的产生和操控及纠缠的动力学问题;第五章则对最简单的量子隧穿模型——两弱耦合的玻色—爱因斯坦凝聚体的本征问题及纠缠性质进行了详细的研究。
本论文研究属于凝聚态物理,理论物理和原子分子物理的交叉学科。
The essential properties of degenerate quantum gases depend on the range, strength and symmetry of atomic interactions. In spinor Bose-Einstein condensates (BEC), one can not only tune the short-range contact interaction using Feshbach resonances but also investigate effects of the long-range and anisotropic interaction. In this thesis we mainly study the properties of spinor Bose-Einstein condensates, including superfluidity, tunneling dynamics and quantum entanglement. The work relates mainly to Bose-Hubbard model, quantum tunneling model, quantum phase transition in spinor Bose-Einstein condensates.In Chapter 2, we start from spin-1 Bose-Hubbard model and derive the energy spectra in terms of Bogoliubov transformation for cold bosons in optical lattices, which indicate the dependence of superfluidity on the spin-exchange interaction. Our observation is that the critical velocities of the superfluid flow are spin-component dependent and can be controlled by adjusting the laser lights that form the optical lattice. Possible experiments to detect the superfluid phase and component separation of spinor BEC are also discussed.In Chapter 3, we describe a semiclassical treatment of the dynamics of dipolar spinor condensates. As a result of the conservation of atom numbers and total hyperfine spin of the condensates, the classical equations of motion are derived. The interplay of spin-exchange and magnetic dipole-dipole interaction leads to the phenomena of spontaneous magnetization and the novel "macroscopic quantum self-trapping".Quantum entanglement is one of the most essential and fascinating features of quantum mechanics. We study the entanglement characteristics of
multi-component Bose-Einstein condensates ------ multipartite andmultimodal systems. Chapter 4 is devoted to proposing generation and manipulation of entangled atom states in an antiferromagnetic spin-1 BEC under magnetic field with gradient and also investigating the dynamics of the entropy of entanglement. Chapter 5 pays attention to the simplest quantumtunneling model------two tunnel-coupled BEC. We study the eigen problemand entanglement characteristics with perturbation method for both weak and strong tunnel couplings, from which some new features are explored.The research in this thesis attributes to the crossover of theoretical physics, condensed matter physics and atom physics.
引文
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