Prethermalization and Many-body localization (MBL) in trapped ion spins.

We present experimental investigations of quantum thermalization and equilibration dynamics in a precisely controlled, interacting, 171Yb+ spin chain, with up to 25 ions. We quench the trapped ion spins in a quantum many-body Hamiltonian with single-atom addressing techniques and measure the long-term dynamics with single-site resolution. With a long-range XY model spin Hamiltonian, we observe emergence of an exotic prethermal phase in the quench dynamics. This non-trivial prethermal phase arise from an inhomogeneous effective potential landscape, due to a combination of the long-range interactions and the open boundary condition. We also observe the absence of spin transport due to many-body localization (MBL) in the transverse-field Ising model with programmable disorder[1]. We measure the Hamming distance and verify the growth of entanglement through the Quantum Fisher Information (QFI) entanglement witness, consistent with expectations for the MBL state. [1] J. Smith et, al. arXiv: 1512.06172(2015).