Tailoring optical Schrödinger cat states via orientation-dependent high-harmonic generation in rm{H}₂^+

We theoretically demonstrate that the molecular orientation angle θ provides a structurally intrinsic, continuously tunable control parameter for engineering optical Schrödinger cat states via high-harmonic generation (HHG) in H₂^+. Coupling time-dependent Schrödinger equation simulations to the fully quantized HHG framework, we evaluate the Wigner functions of the post-selected harmonic-mode states under two complementary conditioning strategies. Conditioning on resonance-enhanced low-order harmonics exploits the complementary dipole selection rules of the 1σ_g→1σ_u and 1σ_g→1π_u transitions, driving a kitten-cat crossover whose direction is opposite in the two channels as θ is varied. Conditioning on plateau harmonics instead exploits two-center destructive interference, producing a reentrant cat→kitten→cat transition controlled by the order-dependent interference angle θ^*(q). In both cases the crossover is decoupled from the laser intensity, focal geometry, and molecular density, offering a degree of control with no counterpart in atomic targets.