Exploring Novel Quantum Phases of Bose-Fermi Mixtures Trapped in an Optical Lattice


Kensuke Inaba and Makoto Yamashita
Optical Science Laboratory

 Recently, atomic gases trapped in a vacuum chamber can be cooled down to several nano-Kelvins regime, where the quantum effects govern physical properties of the system. The high controllability of atoms provides us with sophisticated tools for measuring the quantum phenomena. Thus, this system can be regarded as a quantum simulator [1], which attracts much interest of many researchers in various fields, such as condensed matter physics, elementary particle physics, quantum chemistry, and so on. In particular, the atoms trapped in an optical lattice, which is the artificially created periodic potential by laser interference, are expected to make great progress in condensed matter physics, because such fermionic atoms mimic electrons in a metallic crystal [2]. We can explore the pure quantum many-body effects by using this system without any lattice distortions and impurities. Interestingly, this controllable system allows us to expand the current knowledge in the electron systems.
 Collaborating with the group at Kyoto University, we investigated the Bose-Fermi mixtures trapped in an optical lattice both theoretically and experimentally, and clarified appearance of novel quantum phases not observed in condensed matters [3]. Here, we introduce a part of our results on the attractively interacting Bose-Fermi mixtures. Kyoto University group measured the pair occupancies with photo-association spectroscopy by changing the number of fermionic atoms. We developed the numerical method for analyzing this system and applied it to the experiments. We show our results in Fig. 1(a) and (b), and briefly explain the proceeding of the measurements in Fig. 1(c). Our calculations show good quantitative agreements with experiments. We further analyzed the quantities that are difficult to be directly measured by the current experimental techniques. Based on these results, we clarified that the nonmonotonic behavior of Bose-Bose pair occupancy seen in Fig. 1(b) results from the crossover among novel quantum phases. We also investigated the repulsively interacting system and found a different type of crossover.

[1] I. Bloch, Nature Phys. 1 (2005) 23.
[2] M. Greiner and S. Fölling, Nature 453 (2008) 736.
[3] S. Sugawa, K. Inaba et al., Nature Phys. 7 (2011) 642.

Fig. 1. (a) Bose-Fermi pair and (b) Bose-Bose pair occupancies observed by photo-association spectroscopy.
The number of bosons is fixed at 5000. Numerical calculations consider the experimental ambiguity
of estimated temperatures. (c) Schematic diagrams of the Bose-Fermi pair occupancy measurements.
Irradiated laser induces photo-associated transition from a pair of atoms to a molecular state at each site,
and the molecule immediately moves outside of the optical lattice. By counting the lost atoms, we can
thus determine the Bose-Fermi pair occupancies. Another excitation laser is used for the Bose-Bose pair

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