arXiv:2610.08696v1 Announce Type: new Abstract: Integrated sensing and communication (ISAC) is a key technology for next generation wireless networks, requiring highly sensitive, compact receiver front ends with multiband coverage. Rydberg atomic receivers (RARs) provide a promising architecture that satisfies these requirements owing to their high sensitivity and continuous frequency tuning capability. Unlike in classical ISAC systems utilizing orthogonal resource allocation, executing concurrent multi band tasks within a single atomic ensemble relies on shared energy state transitions. Owing to this shared structure, the communication and sensing tradeoff in RAR-based ISAC introduces an atomic-response tradeoff beyond the classical subspace and deterministic-random tradeoffs. This paper studies a multi-branch RAR (MB-RAR) architecture for joint communication and radar sensing. By solving the five level Lindblad master equation at the local oscillator (LO) biased operating point and linearizing the communication and sensing radio frequency (RF) signals as small perturbations, we obtain the double-sideband dynamic signal response of the MB-RAR. The model reveals two intrinsic constraints. First, increasing the coupling laser strength broadens the response bandwidth but can weaken the atomic response. Second, strengthening one branch's LO can suppress the other branch's conversion gain through the shared Rydberg state, even when the latter's LO bias remains fixed, which is termed the inter band gain inhibition (IBGI). Based on these mechanisms, we formulate the achievable Cram\'er--Rao bound (CRB)-rate region and develop a rate-constrained joint search over coupling strength and LO power allocation. Numerical results validate the proposed response model and show that joint optimization provides a more complete characterization of the achievable CRB-rate region.