玻色—爱因斯坦凝聚中量子化涡旋与量子反射的理论研究
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摘要
玻色-爱因斯坦凝聚体作为一种崭新的物质状态,从1995年在稀薄气体中实现以来,掀起了研究的热潮。由于玻色-爱因斯坦凝聚具有非常奇妙的性质,对其进行研究有助于人们理解和揭示量子力学中的重要基本问题。因此,在近十年内,人们在玻色-爱因斯坦凝聚的理论和实验研究方面取得了巨大的进展。本论文具体研究了玻色-爱因斯坦凝聚中量子化的涡旋以及量子反射等问题,主要工作体现在以下几个方面:
1.提出了玻色-爱因斯坦凝聚中涡旋-反涡旋相干叠加态的概念,并证明了涡旋-反涡旋相干叠加态能稳定存在于系统中。同时也研究了涡旋-反涡旋相干叠加态的相关性质及其产生方法,比如在轴对称的谐振子束缚势下涡旋-反涡旋相干叠加态呈现规则的花瓣结构,通过按照一定的时序压缩以及恢复单个涡旋的束缚势,可以产生稳定的单量子化涡旋-反涡旋相干叠加态。
2.研究了玻色-爱因斯坦凝聚中单量子化涡旋与硅固体表面之间的量子反射过程。由于涡旋的特殊性质,其量子反射有更丰富的量子特性。我们的研究表明:ⅰ)由于相干性质的存在,在涡旋与固体表面相互作用的过程中,被固体表面反射回去的部分与正在入射的部分在空间叠加后一定会产生清晰的干涉条纹;ⅱ)由于各向异性的速度分布,涡旋的反射率也呈各向异性,因此反射回来的部分与入射部分形成的干涉条纹宽度以及疏密程度与入射速度以及速度各向异性的程度有关;ⅲ)由于玻色凝聚体中原子间相互作用的存在,反射过程中凝聚体会产生激发,破坏涡旋的结构,使得反射后的涡旋不再是中心对称。我们还根据反射后涡旋的稳定性给出了相应的稳定相图,并利用膨胀比作为稳定与非稳定区域的边界,为实验上观察这一现象提供了指导。
3.研究了玻色-爱因斯坦凝聚体与蓝失谐激光形成的势垒之间的相互作用,在凝聚体速度一定的情况下通过改变蓝失谐激光的强度(即势垒的高度)得到了相应的反射率。根据反射率的大小,我们提出了:ⅰ)无限深方势阱中观察物质波包的运动及碰撞的实验方案;ⅱ)调节激光强度,得到可控的相干分束器(尤其是半反半透分束器),对物质波包实现分裂及囚禁等操作。
Bose-Einstein condensates (BECs) is a relatively newly discovered form of matter that was observed in dilute atomic gases for the first time in 1995, and is now a subject of intensive theoretical and experimental study. Because of its unique properties, the investigation of BECs has unanticipated impact for people to understand and exploit the important and fundamental issue in quantum mechanics. The past decade has seen a dramatic progress in the research of BECs both theoretically and experimentally. In this dissertation, we focus our investigation on the quantized vortex and the quantum reflection in BECs. The main contents are as follows:
1. We have proposed the concept of vortex-antivortex coherently superposed state (VAVCSS) in BECs and verified that the VAVCSS can be stable in a harmonic potential. And we also have investigated the fundamental properties of VAVCSS. The density distribution of the VAVCSS has a petal structure which is determined by the quantum circulations and proportion of the vortex and antivortex. Furthermore, we have proposed a feasible scheme to generate a single quantized coherently superposed vortex and antivortex state with arbitrary proportion by compressing and rehabilitating the harmonic trap with specific time order, which is proven by numerical simulations.
2. We have investigated the two-dimensional quantum reflection with vortices in Bose-Einstein condensates incident on a solid surface of silicon. This is a unique quantum reflection process considering the fundamental properties of quantized vortex. Our investigation has shown that:ⅰ) there was an interference effect between the incident and reflected matter waves as all the atoms in BECs were coherent;ⅱ) considering the rotation of a vortex, the nonuniform velocity distribution along the surface would play an important role in the quantum reflection process. For example, they would change the characteristics of the interference fringes between the incident and reflected matter waves;ⅲ) the reflected vortex became unstable for sufficiently low incident velocity or strong interaction. This sort of instability physically originated from dynamics excitations induced by the atomic interaction in the quantum reflection process. The stability diagram was given and we have found that a simple expansion ratio described the boundary between the stable and unstable regions.
3. We have investigated the interaction between BECs and the potential barrier formed by the far-off resonant blue-detuned laser. According to the interaction between BECs and the potential, we have proposed:ⅰ) an experimental scheme to observe the collision between two wave packets in in an infinitely deep well formed by two far-off resonance laser beams (which are used to avoid exciting of the atom) of sufficiently high intensity.ⅱ) an experimental scheme to achieve a controllable coherent beam-splitter (especially the beam-splitter with 50/50 splitting ratio) by tuning the intensity of the laser beams and then trapping the wave packets after being split with far-off resonance laser beams of sufficiently high intensity.
1.提出了玻色-爱因斯坦凝聚中涡旋-反涡旋相干叠加态的概念,并证明了涡旋-反涡旋相干叠加态能稳定存在于系统中。同时也研究了涡旋-反涡旋相干叠加态的相关性质及其产生方法,比如在轴对称的谐振子束缚势下涡旋-反涡旋相干叠加态呈现规则的花瓣结构,通过按照一定的时序压缩以及恢复单个涡旋的束缚势,可以产生稳定的单量子化涡旋-反涡旋相干叠加态。
2.研究了玻色-爱因斯坦凝聚中单量子化涡旋与硅固体表面之间的量子反射过程。由于涡旋的特殊性质,其量子反射有更丰富的量子特性。我们的研究表明:ⅰ)由于相干性质的存在,在涡旋与固体表面相互作用的过程中,被固体表面反射回去的部分与正在入射的部分在空间叠加后一定会产生清晰的干涉条纹;ⅱ)由于各向异性的速度分布,涡旋的反射率也呈各向异性,因此反射回来的部分与入射部分形成的干涉条纹宽度以及疏密程度与入射速度以及速度各向异性的程度有关;ⅲ)由于玻色凝聚体中原子间相互作用的存在,反射过程中凝聚体会产生激发,破坏涡旋的结构,使得反射后的涡旋不再是中心对称。我们还根据反射后涡旋的稳定性给出了相应的稳定相图,并利用膨胀比作为稳定与非稳定区域的边界,为实验上观察这一现象提供了指导。
3.研究了玻色-爱因斯坦凝聚体与蓝失谐激光形成的势垒之间的相互作用,在凝聚体速度一定的情况下通过改变蓝失谐激光的强度(即势垒的高度)得到了相应的反射率。根据反射率的大小,我们提出了:ⅰ)无限深方势阱中观察物质波包的运动及碰撞的实验方案;ⅱ)调节激光强度,得到可控的相干分束器(尤其是半反半透分束器),对物质波包实现分裂及囚禁等操作。
Bose-Einstein condensates (BECs) is a relatively newly discovered form of matter that was observed in dilute atomic gases for the first time in 1995, and is now a subject of intensive theoretical and experimental study. Because of its unique properties, the investigation of BECs has unanticipated impact for people to understand and exploit the important and fundamental issue in quantum mechanics. The past decade has seen a dramatic progress in the research of BECs both theoretically and experimentally. In this dissertation, we focus our investigation on the quantized vortex and the quantum reflection in BECs. The main contents are as follows:
1. We have proposed the concept of vortex-antivortex coherently superposed state (VAVCSS) in BECs and verified that the VAVCSS can be stable in a harmonic potential. And we also have investigated the fundamental properties of VAVCSS. The density distribution of the VAVCSS has a petal structure which is determined by the quantum circulations and proportion of the vortex and antivortex. Furthermore, we have proposed a feasible scheme to generate a single quantized coherently superposed vortex and antivortex state with arbitrary proportion by compressing and rehabilitating the harmonic trap with specific time order, which is proven by numerical simulations.
2. We have investigated the two-dimensional quantum reflection with vortices in Bose-Einstein condensates incident on a solid surface of silicon. This is a unique quantum reflection process considering the fundamental properties of quantized vortex. Our investigation has shown that:ⅰ) there was an interference effect between the incident and reflected matter waves as all the atoms in BECs were coherent;ⅱ) considering the rotation of a vortex, the nonuniform velocity distribution along the surface would play an important role in the quantum reflection process. For example, they would change the characteristics of the interference fringes between the incident and reflected matter waves;ⅲ) the reflected vortex became unstable for sufficiently low incident velocity or strong interaction. This sort of instability physically originated from dynamics excitations induced by the atomic interaction in the quantum reflection process. The stability diagram was given and we have found that a simple expansion ratio described the boundary between the stable and unstable regions.
3. We have investigated the interaction between BECs and the potential barrier formed by the far-off resonant blue-detuned laser. According to the interaction between BECs and the potential, we have proposed:ⅰ) an experimental scheme to observe the collision between two wave packets in in an infinitely deep well formed by two far-off resonance laser beams (which are used to avoid exciting of the atom) of sufficiently high intensity.ⅱ) an experimental scheme to achieve a controllable coherent beam-splitter (especially the beam-splitter with 50/50 splitting ratio) by tuning the intensity of the laser beams and then trapping the wave packets after being split with far-off resonance laser beams of sufficiently high intensity.
引文
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