玻色-爱因斯坦凝聚体Rosen-Zener跃迁中的多体量子涨落效应

Many-body quantum fluctuation effects of Rosen-Zener transition in Bose-Einstein condensates

研究了处于对称双势阱中玻色-爱因斯坦凝聚体Rosen-Zener跃迁过程的多体量子涨落效应,分析了末态平均布居数差与扫描周期的关系.线性情况下,得到了末态平均布居数差关于扫描周期的解析表达式,该结果与平均场下的结果完全一致,并利用数值方法进行了验证.非线性情况下,通过数值计算发现,快速扫描时末态平均布居数差与平均场情况下的结果符合比较好;然而绝热扫描时与平均场情况却有着很大的不同:末态平均布居数差随扫描周期的变化不再是平均场情况下的方波形式而是类似于正弦型的振荡,而且振荡周期会随着粒子数N以及非线性参数c的增加而增大.

We investigate many-body quantum fluctuation effects of Rosen-Zener transition of Bose-Einstein condensate （BEC） in a sym- metric double-well potential through the relation between the average population imbalance of the final state （APIFS） and scanning period. In the linear case, we deduce the analytical expression of the APIFS which has the same behavior as in the mean-field level. We also employ numerical calculation to demonstrate it. In the nonlinear case, numerical results show that the APIFS in the sudden limit also accords with that in the mean-field level whereas in the adiabatic limit the many-body result is quite different from that of the mean-field case： the behavior of APIFS with respect to scanning period is similar to sinusoidal rather than rect^ngular oscillation, besides the oscillation period increases with both the total number N and the nonlinear parameter c increasing.