Many-Body Dephasing after Quantum Quench with a Trapped Ion Quantum Simulator

We investigate many-body dephasing in the 1D transvese-filed Ising chain with long-range power-law interactions. We work in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions even for the long-time non-integrable dynamics. We study the dependence of temporal fluctuations of the average magnetization as a function of the system size. Using the eigenstate thermalization hyperthesis (ETH), we are able to give an analytical expresssion for the temopral fluctuations. We also show the first experimental observation of persistent temporal fluctuations after a quantum quench. The measured fluctuations are exponentially suppressed with increasing system size, which is consistent with our theoretical predictions.