We consider a condensate of ultracold boson atoms in a linear optical cavity illuminated by a two-pump configuration with each pump making a different angle to the direction of the cavity axis. We show that such a configuration enables a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by cavity-atom interactions. Using the Holstein-Primakov transform, we find atomic density profiles of such self-assembled ground states in superradiative phases as a function of the angular orientation of the pump in such dynamical quantum optical lattices, and also provide an analysis. of their structure in coordinate and momentum space. Later in the paper, we show how the corresponding results can be qualitatively understood in terms of the extended Bose-Hubbard model in such a quantum optical lattice potential.
