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Owing to their strong dipole moment and long coherence times, superconductingqubits have demonstrated remarkable success in hybrid quantum circuits.However, most qubit architectures are limited to the GHz frequency range,severely constraining the class of systems they can interact with. Thefluxonium qubit, on the other hand, can be biased to very low frequency whilebeing manipulated and read out with standard microwave techniques. Here, wedesign and operate a heavy fluxonium with an unprecedentedly low transitionfrequency of $1.8~\mathrm{MHz}$. We demonstrate resolved sideband cooling ofthe ``hot'' qubit transition with a final ground state population of $97.7~\%$,corresponding to an effective temperature of $23~\mu\mathrm{K}$. We furtherdemonstrate coherent manipulation with coherence times $T_1=34~\mu\mathrm{s}$,$T_2^*=39~\mu\mathrm{s}$, and single-shot readout of the qubit state.Importantly, by directly addressing the qubit transition with a capacitivelycoupled waveguide, we showcase its high sensitivity to a radio-frequency field.Through cyclic qubit preparation and interrogation, we transform thislow-frequency fluxonium qubit into a frequency-resolved charge sensor. Thismethod results in a charge sensitivity of$33~\mu\mathrm{e}/\sqrt{\mathrm{Hz}}$, or an energy sensitivity (in joules perhertz) of $2.8~\hbar$. This method rivals state-of-the-art transport-baseddevices, while maintaining inherent insensitivity to DC charge noise. The highcharge sensitivity combined with large capacitive shunt unlocks new avenues forexploring quantum phenomena in the $1-10~\mathrm{MHz}$ range, such as thestrong-coupling regime with a resonant macroscopic mechanical resonator.

High-sensitivity AC-charge detection with a MHz-frequency fluxonium qubit