Quantum Rabi interferometry of motion and radiation

Kimin Park1,2, Petr Marek1, Ulrik L. Andersen2, and Radim Filip1

1Department of Optics, Palacky University, 77146 Olomouc, Czech Republic
2Center for Macroscopic Quantum States (bigQ), Department of Physics, Technical University of Denmark, Building 307, Fysikvej, 2800 Kgs. Lyngby, Denmark

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The precise determination of a displacement of a mechanical oscillator or a microwave field in a predetermined direction in phase space can be carried out with trapped ions or superconducting circuits, respectively, by coupling the oscillator with ancilla qubits.

Through that coupling, the displacement information is transferred to the qubits which are then subsequently read out. However, unambiguous estimation of displacement in an unknown direction in the phase space has not been attempted in such oscillator-qubit systems. Here, we propose a hybrid oscillator-qubit interferometric setup for the unambiguous estimation of phase space displacements in an arbitrary direction, based on feasible Rabi interactions beyond the rotating-wave approximation. Using such a hybrid Rabi interferometer for quantum sensing, we show that the performance is superior to the ones attained by single-mode estimation schemes and a conventional interferometer based on Jaynes-Cummings interactions. Moreover, we find that the sensitivity of the Rabi interferometer is independent of the thermal occupation of the oscillator mode, and thus cooling it to the ground state before sensing is not required. We also perform a thorough investigation of the effect of qubit dephasing and oscillator thermalization. We find the interferometer to be fairly robust, outperforming different benchmark estimation schemes even for large dephasing and thermalization.

We have developed a new hybrid oscillator-qubit interferometric setup that enables the unambiguous estimation of phase space displacements in any direction, improving upon previous methods that were limited to predetermined directions. This innovative approach, called the Rabi interferometer, offers superior performance compared to single-mode estimation schemes and conventional interferometers. Notably, it does not require cooling the oscillator to the ground state, and it remains robust even in the presence of qubit dephasing and oscillator thermalization. This advancement in quantum sensing could have significant implications for a range of applications.

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