  We experimentally emulate, in a controlled fashion, the non-Markovian
dynamics of a pure dephasing spin-boson model at zero temperature.
Specifically, we use a randomized set of external radio-frequency fields to
engineer a desired noise power-spectrum to effectively realize a non-Markovian
environment for a single NMR qubit. The information backflow, characteristic to
the non-Markovianity, is captured in the nonmonotonicity of the decoherence
function and von Neumann entropy of the system. Using such emulated
non-Markovian environments, we experimentally study the efficiency of the
Carr-Purcell-Meiboom-Gill dynamical decoupling (DD) sequence to inhibit the
loss of coherence. Using the filter function formalism, we design optimized DD
sequences that maximize coherence protection for non-Markovian environments and
study their efficiencies experimentally. Finally, we discuss DD-assisted tuning
of the effective non-Markovianity.
