  Applying time-periodic modulations is routinely used to control and design
synthetic matter in quantum-engineered settings. In lattice systems, this
approach is explored to engineer band structures with non-trivial topological
properties, but also to generate exotic interaction processes. A prime example
is density-assisted tunneling, by which the hopping amplitude of a particle
between neighboring sites explicitly depends on their respective occupations.
Here, we show how density-assisted tunneling can be tailored in view of
simulating the effects of strain in synthetic graphene-type systems.
Specifically, we consider a mixture of two atomic species on a honeycomb
optical lattice: one species forms a Bose-Einstein condensate in an anisotropic
harmonic trap, whose inhomogeneous density profile induces an effective
uniaxial strain for the second species through density-assisted tunneling
processes. In direct analogy with strained graphene, the second species
experiences a pseudo magnetic field, hence exhibiting relativistic Landau
levels and the valley Hall effect. Our proposed scheme introduces a unique
platform for the investigation of strain-induced gauge fields and their
possible interplay with quantum fluctuations and collective excitations.
