BEC混合物量子玻色约瑟夫森结
Quantum Bose Josephson Junction with binary mixtures of BECs
摘要：
从双模玻色-哈伯德哈密顿量出发，研究了双势阱中玻色-爱因斯坦凝聚体（BEC）的量子行为。我们专注于小隧穿振幅制度和微扰理论应用到二阶。得到了能量本征值和本征态的解析表达式。然后在完全局域态和相干自旋态两种不同的初始条件下，研究了两个势阱中玻色子数差的量子演化。在第一种情况下的短期和长期的动力学研究和丰富的行为被发现，从小振幅振荡和崩溃和复苏相干隧穿。在第二种情况下，确定了数差的短时间尺度演化，并证明了更不规则的动力学。最后，薛定谔猫态的形成被认为是影响动量分布。
英文摘要：
We study the quantum behaviour of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. We focus on the small tunneling amplitude regime and apply perturbation theory up to second order. Analytical expressions for the energy eigenvalues and eigenstates are obtained. Then the quantum evolution of the number difference of bosons between the two potential wells is fully investigated for two different initial conditions: completely localized states and coherent spin states. In the first case both the short and the long time dynamics is studied and a rich behaviour is found, ranging from small amplitude oscillations and collapses and revivals to coherent tunneling. In the second case the short-time scale evolution of number difference is determined and a more irregular dynamics is evidenced. Finally, the formation of Schroedinger cat states is considered and shown to affect the momentum distribution.
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