A rotating black hole can be clouded by light bosons via superradiance, resulting in an atom-like structure. The presence of a binary companion affects black hole superradiance at orbital frequencies away from the resonance bands of gravitational-collider-physics (GCP). When accompanied by a pulsar, transitions between energy levels of the gravitational atom can be triggered and detected through pulsar timing. We found that fine and hyperfine structure transitions are more likely to be probed in pulsar-black hole systems compared to the Bohr transition. These transitions offer better analytic control, making them ideal probes in the search for GCP signals. We also investigated the off-resonance effect. The companion leads to the coupling between a superradiant state and a strongly absorptive state, induced by the tidal perturbation of the companion, leads to a suppressed superradiance rate. Below a critical binary separation, the superradiance rate becomes negative, resulting in the absorption of the boson cloud by the black hole. This critical binary separation imposes constraints on GCP, particularly for companions with mass ratios q > 10( − 3). Fine structure transitions are invalidated in such cases, along with most Bohr transitions except for those from the |211⟩ state. The termination of cloud growth due to superradiance can potentially alleviate current bounds on the mass of ultralight bosons from null detections. Furthermore, the backreaction on the companion manifests as a torque on the binary system, significantly modulating the binary evolution, especially for Extreme Mass Ratio Inspiral (EMRI) systems. The backreaction drives the system towards large circular equatorial orbits with a reduced termination rate, even outside the resonance bands. This analysis paves the way for future investigations into probing ultralight bosons through statistical analysis of EMRI binary parameters.