  Quantum dimer models are known to host topological quantum spin liquid
phases, and it has recently become possible to simulate such models with
Rydberg atoms trapped in arrays of optical tweezers. Here, we present
large-scale quantum Monte Carlo simulation results on an extension of the
triangular lattice quantum dimer model with terms in the Hamiltonian
annihilating and creating single dimers. We find distinct odd and even
$\mathbb{Z}_2$ spin liquids, along with several phases with no topological
order: a staggered crystal, a nematic phase, and a trivial symmetric phase with
no obvious broken symmetry. We also present dynamic spectra of the phases, and
note implications for experiments on Rydberg atoms.
