Many-Body Dephasing in a Trapped-Ion Quantum Simulator*

We observe and analyze the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator [1]. By measuring temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles encoded in an array of 171Yb+ atomic ions, we observe experimental evidence for many-body dephasing [2]. The properties of the system are closely related to that of an integrable Hamiltonian with a uniform spin-spin coupling, which enables approximate analytical predictions even for the long-time non-integrable dynamics. We find that the measured fluctuations are exponentially suppressed with increasing system size, consistent with theoretical predictions. [1] H. B. Kaplan, et al., arXiv: 2001.02477 (2020). [2] T.Kiendl, F.Marquardt, Phys. Rev. Lett. 118, 130601 (2017)