This paper investigates an uplink rate-splitting multiple access (RSMA) network empowered by a Rydberg atomic quantum receiver (RAQR) to maximize energy efficiency (EE). To overcome the amplitude-only measurement limitation of the considered direct readout RAQR, we devise a phase alignment mechanism that linearizes the received signal while retaining full channel energy, thereby enabling tractable optimization. The resulting non-convex fractional EE problem is transformed via Dinkelbach's method. For IoT scenarios with symmetric rate requirements, we derive exact closed-form power allocation from the Karush-Kuhn-Tucker (KKT) conditions, which yields a globally optimal bisection search with negligible computational latency. For asymmetric rate requirements, we develop a generalized block coordinate descent-based power allocation (BCD-PA) framework that eliminates reliance on expensive interior-point solvers. We further propose a low-complexity paired allocation (LC-Paired) that exploits user pairing and closed-form bandwidth solutions via the Lambert-W function. Simulation results confirm that the KKT-based scheme attains the highest EE, while the BCD-PA offers a flexible complexity-performance trade-off. The LC-Paired scheme drastically reduces computational cost with only moderate EE degradation.

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