  Two-dimensional (2D) spectroscopy uses multiple electromagnetic pulses to
infer the properties of a complex system. A paradigmatic class of target
systems are molecular aggregates, for which one can obtain information on the
eigenstates, various types of static and dynamic disorder and on relaxation
processes. However, two-dimensional spectra can be difficult to interpret
without precise knowledge of how the signal components relate to microscopic
Hamiltonian parameters and system-bath interactions. Here we show that
two-dimensional spectroscopy can be mapped in the microwave domain to highly
controllable Rydberg quantum simulators. By porting 2D spectroscopy to Rydberg
atoms, we firstly open the possibility of its experimental quantum simulation,
in a case where parameters and interactions are very well known. Secondly, the
technique may provide additional handles for experimental access to coherences
between system states and the ability to discriminate different types of
decoherence mechanisms in Rydberg gases. We investigate the requirements for a
specific implementation utilizing multiple phase coherent microwave pulses and
a phase cycling technique to isolate signal components.
