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

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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.