两能级Tonks-Girardeau气体的Ramsey干涉
Ramsey interferometry with a two-level Tonks-Girardeau gas
摘要：
我们提出了一个推广的Tonks-Girardeau模型，它描述了一个相干气体的冷两级玻色子与两个外部领域的拉姆齐干涉仪。它们之间也通过接触碰撞相互作用，交换动量和内部状态。我们研究了相应的拉姆齐条纹和量子投影噪声，基本上不受相互作用的影响，仍然是理想玻色子。这种气体的对偶系统是一种理想气体，由二能级费米子通过与分离场的相互作用耦合而成，它产生同样的条纹和噪声涨落。研究了时间分离场和空间分离场的情形。对于空间分离的场，增加粒子数可以使条纹稍宽一些，但这只适用于粒子数很大的情况，而粒子数与目前用Tonks-Girardeau气体进行的实验相差甚远。在确定原子跃迁频率的不确定性减少，基本上与粒子数的倒数根。
英文摘要：
We propose a generalization of the Tonks-Girardeau model that describes a coherent gas of cold two-level Bosons which interact with two external fields in a Ramsey interferometer. They also interact among themselves by contact collisions with interchange of momentum and internal state. We study the corresponding Ramsey fringes and the quantum projection noise which, essentially unaffected by the interactions, remains that for ideal Bosons. The dual system of this gas, an ideal gas of two-level Fermions coupled by the interaction with the separated fields, produces the same fringes and noise fluctuations. The cases of time-separated and spatially-separated fields are studied. For spatially separated fields the fringes may be broadened slightly by increasing the number of particles, but only for large particle numbers far from present experiments with Tonks-Girardeau gases. The uncertainty in the determination of the atomic transition frequency diminishes, essentially with the inverse root of the particle number.
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