Quantum-enhanced sensing of bosonic modes with cat states

Quantum coherence is critical resource for applications in quantum technology, among which quantumenhanced 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 infinitedimension 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.