Quantum coherence is critical resource for applications in quantum technology, among which quantum-enhanced sensing represents a typical example. Compared with quantum metrology with entangled states of multiple qubits, bosonic interferometers have the advantage of being hardware efficient, enabled by the infinite-dimension Hilbert space of bosonic modes. Phase estimations with precisions approaching the Heisenberg limit have been demonstrated with superpositions of Fock states of single bosonic modes. We here present a scheme for realizing quantum metrology based on a fundamentally distinct kind of superposition states, Schrödinger cat states, defined as quantum superpositions of two quasiclassial states of a bosonic mode. The interferometer aims to estimate the frequency shift of a photonic mode with respect to a reference frequency, which produces a phase-space rotation. We find that such a phase-space rotation can be extracted with a qubit, without mapping the state of the photonic mode to the qubit. This phase-space rotation is directly related to the qubit's population through the combination of a phase-space displacement, a dispersive qubit-photon interaction, and two qubit rotations. The signal-to-noise ratio exhibits a scaling approaching the Heisenberg limit, like interferometers based on Fock state superpositions, but without requiring a step-by-step procedure to prepare the resource state.

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• Quantum communication, protocols & technology
• Quantum metrology