  Problems in the field of open quantum systems often involve an environment
that greatly impacts excitation dynamics. Here we show that there can be
coherent coupling between different system states of a form that only occurs in
a non-Markovian treatment of the bath. Because this involves entangled
system-bath states, we demonstrate that there are distinct signatures of this
physics in simple absorption spectra and two-dimensional electronic
spectroscopy. To do this we introduce a numerical method to simulate optical
spectra of non-Markovian open quantum systems. The method employs a process
tensor framework to efficiently compute multi-time correlation in a numerically
exact way.
