Error correction assisted determination of the non-local membrane order parameter

Non-local order parameters are expected to distinguish exotic phases of the quantum system. The membrane order parameter, which can determine the phases of the Bose-Hubbard model in two dimensions, is an example of such non-local order parameter. However, the membrane order parameter in the optical lattice system is difficult to measure because of the parity projected measurement and incoherent holes. In this presentation, we will introduce the method to detour the errors from the incoherent holes by introducing the error correction scheme. This error correction method is applied to analyze the superfluid to Mott Insulator system in an optical lattice. We prepared 1200 atoms in the optical lattice and took snapshots of the atoms with different values of J/U with quantum gas microscope imaging. Our system has incoherent holes with probability p = 0.02 from the thermal fluctuation and the losses during the imaging process [1]. Using the error correction assisted membrane order parameter, we could identify the phase boundary between the superfluid and Mott Insulator phases. Furthermore, the scaling depending on the system size consists of the theoretically expected result. Our error correction scheme can be generalized to any system where errors from incoherent sources are unavoidable.

[1] K. Kwon, K. Kim, J. Hur, S. Huh, and J.-y. Choi, Site-resolved imaging of a bosonic Mott insulator of 7Li atoms, Phys. Rev. A 105, 033323 (2022).