How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this work, we observe and analyse 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. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles and observe the experimental evidence for the theoretically predicted regime of many-body dephasing. We experiment 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 find that the measured fluctuations are exponentially suppressed with increasing system size, consistent with theoretical predictions.

1 aKaplan, Harvey, B.1 aGuo, Lingzhen1 aTan, Wen, Lin1 aDe, Arinjoy1 aMarquardt, Florian1 aPagano, Guido1 aMonroe, Christopher uhttps://arxiv.org/abs/2001.02477