Realisation of density-dependent Peierls phases to couple dynamical gauge fields to matter.
arXiv: Quantum Gases(2018)
摘要
The coupling between gauge and matter fields plays an important role in many models of high-energy and condensed matter physics [1-3]. In these models, the gauge fields are dynamical quantum degrees of freedom in the sense that they are influenced by the spatial configuration and motion of the matter field. Since the resulting dynamics is hard to compute, it was proposed to implement this fundamental coupling mechanism in quantum simulation platforms with the ultimate goal to emulate lattice gauge theories [4-7]. So far, synthetic magnetic fields for atoms in optical lattices were intrinsically classical, as these did not feature back-action from the atoms [8,9]. Here, we realize the fundamental ingredient for a density-dependent gauge field by engineering non-trivial Peierls phases that depend on the site occupation of fermions in a Hubbard dimer. Our method relies on breaking time-reversal symmetry (TRS) by driving the optical lattice simultaneously at two frequencies. This creates interfering pathways for density-induced tunnelling, each in resonance with the on-site interaction of two fermionic atoms, and controllable in amplitude and phase. We demonstrate a technique to quantify the amplitude of the resulting density-assisted tunnelling matrix element and to directly measure its Peierls phase with respect to the single-particle hopping. The tunnel coupling features two distinct regimes as a function of the two modulation amplitudes, which can be characterised by a Z2-invariant. Moreover, we provide a full tomography of the winding structure of the Peierls phase around a Dirac point that appears in the driving parameter space. For future experiments, this structure provides unique tuneability of the associated density-dependent gauge field by using modulation parameters with temporal or spatial dependencies.
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