  We show that in laser-driven coupled optomechanical systems, photon
antibunching can occur under weak optomechanical coupling, contrarily to common
expectation. This unconventional photon blockade originates from destructive
quantum interference between different excitation pathways bringing from the
ground to two-photon states. Using a quantum open-system approach, we study the
antibunching as a function of driving field amplitude, temperature, and pure
dephasing rate, and derive optimal values of the system parameters for its
occurrence. These values are remarkably close to those characterizing
optomechanical systems in some current experimental studies.
