Correlations in a Tonks-Girardeau Gas and Hanbury Brown-Twiss Noise Correlation Interferometry

近9年来，释放的超冷量子气体的吸收成像一直是揭示捕获势中原子宏观量子态信息的标准检测方法。然而，对于光学晶格中的强关联量子态，人们通常观察到的动量分布中的平均信号，例如物质的莫特绝缘态，是一个无特征的高斯波包。从这个高斯波包中，除了相位相干性已经丧失的事实之外，人们不能推出任何关于晶格势中强关联量子态的东西。然而，最近，在光学晶格中的强关联量子气体的广泛兴趣，导致了迷人的新的量子相位的超冷原子的预测，例如与反铁磁结构，自旋波或电荷密度波。到目前为止，人们还不清楚如何检测这些状态。最近，Altman等人的一个理论提议[1]表明，噪声相关干涉术可能是直接可视化这种量子态的强大工具。基于我们在美因茨小组的首次成功实验，我们确实观察到了这种噪声相关性，我们计划探索这种强大的方法在光学晶格中超冷原子的全部潜力。在87 Rb的自旋混合物中，我们计划设计反铁磁相和自旋波，这些相位和自旋波将用这种方法直接检测到。最近，我们的团队也已经能够实现费米子化玻色子的Tonks-Girardeau气体。使用光缔合的原子，我们计划测量显着的变化，在现场的密度-密度相关函数的一个交叉从弱相互作用玻色气体到制度的Tonks-Girardeau气体。

For now almost 9 years, absorption imaging of released ultracold quantum gases has been a standard detection method for revealing information on the macroscopic quantum state of the atoms in the trapping potential. For strongly correlated quantum states in optical lattices, however, the average signal in the momentum distribution that one usually observes, e.g. for a Mott insulating state of matter, is a featureless Gaussian wave packet. From this Gaussian wave packet one cannot deduce anything about the strongly correlated quantum states in the lattice potential apart from the fact that phase coherence has been lost. Recently, however, the widespread interest in strongly correlated quantum gases in optical lattices, has lead to the prediction of fascinating new quantum phases for ultracold atoms, e.g. with anti-ferromagnetic structure, spin waves or charge density waves. So far it has not been clear how one could detect those states. Recently a theoretical proposal by Altman et al. [1] has shown that noise correlation interferometry could be a powerful tool to directly visualize such quantum states. Based on first successful experiments in our group in Mainz, where we have indeed observed such noise correlations, we are planning to explore the full potential of this powerful method for ultracold atoms in optical lattices. In spin-mixtures of 87Rb, we plan to engineer antiferromagnetic phases and spin waves that will be directly detected with this method. Very recently, our group has also been able to realize a Tonks- Girardeau gas of fermionized bosons. Using photoassociation of atoms, we plan to measure the striking change in the on-site density-density correlation function as one crosses over from a weakly interacting Bose gas into the regime of the Tonks-Girardeau gas.