玻色子约瑟夫森结中的电子尺寸效应
Finite-size effects in a bosonic Josephson junction
摘要：
采用两格点玻色-哈伯德模型，研究了$N$玻色粒子在两格点间隧穿时的有限尺寸量子效应。利用含时原子相干态（ACS），我们推广了基于含时Glauber相干态的玻色约瑟夫森结的标准平均场方程。通过这种方式，我们发现$1/N$修正熟悉的平均场（MF）的结果：两个网站之间的宏观振荡的频率，动态宏观量子自陷（MQST）的临界参数，和有吸引力的临界相互作用强度的基态的自发对称性破缺（SSB）。为了验证我们的分析结果，我们进行量子动力学的数值模拟。在平衡组态周围的约瑟夫森振荡的情况下，我们发现，也对少数原子的数值结果与含时ACS变分方法的预测，提供的时间演化不是太长。与MF方法相比，ACS方法能更好地再现SSB的数值结果。相反，只有在大的$N$状态下，ACS理论才能正确地再现MQST的发生，对于这种现象，MF公式的$1/N$校正是不可靠的。
英文摘要：
We investigate finite-size quantum effects in the dynamics of $N$ bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACS) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find $1/N$ corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we find that also for a few atoms the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also the numerical results of SSB are better reproduced by the ACS approach with respect to the MF one. Instead the onset of MQST is correctly reproduced by ACS theory only in the large $N$ regime and, for this phenomenon, the $1/N$ correction to the MF formula is not reliable.
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