Quantum Limits of Electromagnetic Axion and Hidden-Photon Dark Matter Searches

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We present fundamental limits of axion and hidden-photon dark matter searches probing the electromagnetic coupling. These limits are informed by constraints on noise in phase-insensitive amplifiers, as well as constraints on impedance matching. We motivate the use of quantum-limited amplifiers for dark matter searches, in particular at low masses/frequencies, where they provide a substantial enhancement due to sensitivity outside of the detector bandwidth. We discuss the role of priors, e.g. direct detection and astrophysical constraints, in optimizing scan strategies and comparing receiver architectures. We show that the figure of merit for wideband dark matter searches is the integrated sensitivity of the receiver circuit, and that the integrated sensitivity is constrained by the Bode-Fano criterion. The optimized single-pole resonator read out by a quantum-limited amplifier is close to the Bode-Fano limit, establishing such a search technique as a fundamentally near-ideal setup for dark matter measurement. We discuss the implications of these broad optimization statements for DM Radio, a lumped-element search for axion and hidden-photon dark matter operating in the 100 Hz (~0.5 peV)- 300 MHz (~1 ueV) range. Our results strongly motivate the use of quantum measurement techniques (e.g. squeezing, entanglement, photon counting, backaction evasion), which evade the limits, in future dark matter searches.