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arXiv:1107.2322 · Physical Review Letters

Multiband Spectroscopy of Ultracold Fermions: Observation of Reduced Tunneling in Attractive Bose-Fermi Mixtures

Jannes Heinze, Sören Götze, J. S. Krauser, Bastian Hundt, Nick Fläschner, Dirk-Sören Lühmann, C. Becker, K. Sengstock

Published Sep 23, 2011• 68 citations
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Abstract

We perform a detailed experimental study of the band excitations and tunneling properties of ultracold fermions in optical lattices. Employing a novel multiband spectroscopy for fermionic atoms, we can measure the full band structure and tunneling energy with high accuracy. In an attractive Bose-Fermi mixture we observe a significant reduction of the fermionic tunneling energy, which depends on the relative atom numbers. We attribute this to an interaction-induced increase of the lattice depth due to the self-trapping of the atoms.

DOI
10.1103/physrevlett.107.135303

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We perform a detailed experimental study of the band excitations and tunneling properties of ultracold fermions in optical lattices. Employing a novel multiband spectroscopy for fermionic atoms, we can measure the full band structure and tunneling energy with high accuracy. In an attractive Bose-Fermi mixture we observe a significant reduction of the fermionic tunneling energy, which depends on the relative atom numbers. We attribute this to an interaction-induced increase of the lattice depth due to the self-trapping of the atoms.
Spectroscopic tools are fundamental for the understanding of complex quantum systems. Here we demonstrate high-precision multi-band spectroscopy in a graphene-like lattice using ultracold fermionic atoms. From the measured band structure, we characterize the underlying lattice potential with a relative error of 1.2 10^(-3). Such a precise characterization of complex lattice potentials is an important step towards precision measurements of quantum many-body systems. Furthermore, we explain the excitation strengths into the different bands with a model and experimentally study their dependency on the symmetry of the perturbation operator. This insight suggests the excitation strengths as a suitable observable for interaction effects on the eigenstates.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.