Detector Readout of a Transverse Field Ising model

Reliable detection of the many-body correlations in quantum simulators is a key element in analog quantum simulation. However, in finite systems, the detector backaction can affect the detector readout of the simulators significantly. Here we examine the backaction of a cavity detector on two simulators: a single qubit and a transverse field Ising model. We find that the successful extraction of the correlators of the quantum simulators relies on the validity of the Wick's theorem for the coupling operators. We also analyze the conditions for the Wick’s theorem to be approximately valid for the transverse field Ising model. [1] L. Tian, I. Schwenk, and M. Marthaler, arXiv:1612.07419. [2] I. Schwenk, J.-M. Reiner, S. Zanker, L. Tian, J. Leppaekangas, M. Marthaler, arXiv:1701.02683.