  Over the last couple of decades, quantum simulators have been probing quantum
many-body physics with unprecedented levels of control. So far, the main focus
has been on the access to novel observables and dynamical conditions related to
condensed-matter models. However, the potential of quantum simulators goes
beyond the traditional scope of condensed-matter physics: Being based on
driven-dissipative quantum optical platforms, quantum simulators allow for
processes that are typically not considered in condensed-matter physics. These
processes can enrich in unexplored ways the phase diagram of well-established
models. Taking the extended Bose-Hubbard model as the guiding example, in this
work we examine the impact of coherent pair injection, a process readily
available in, for example, superconducting circuit arrays. The interest behind
this process is that, in contrast to the standard injection of single
excitations, it can be configured to preserve the U(1) symmetry underlying the
model. We prove that this process favors both superfluid and density-wave
order, as opposed to insulation or homogeneous states, thereby providing a
novel route towards the access of lattice supersolidity.
