Quantum Rabi interferometry of motion and radiation

Abstract

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. I. INTRODUCTIONQuantum sensing is about estimating unknown processes of interest using a finite ensemble of probes and detectors with a sensitivity that goes beyond the reach of classical sensing [1-5]. Historically, optical probes have been at the center of this field due to the experimental accessibility of lasers and non-classical light resources, high-efficiency detectors, and the strong robustness of light to external noise sources [6][7][8][9]. Quantum optical interferometers exploit the interference between a probe and a reference beam to detect weak signals [10], a prominent example being the detection of gravitational waves from black hole mergers [11,12]. A similar approach can be adopted for microwave traveling waves [13], microwave cavity fields [14], matter waves [15,16], between light and atomic ensembles [17,18], and optomechanics [19][20][21].Numerous sensing proposals use quantum non-Gaussian states as probes for improved estimation of phase and displacement [22][23][24]. For example, quantum displacement sensing has been performed with Fock states and non-Gaussian superpositions of Fock states of the phononic modes of trapped ions [25,26]. Similarly, for superconducting circuits, the preparation of microwave Fock states and their superpositions has been recently mastered [27][28][29][30] as well as the preparation of non-Gaussian acoustic modes of a quartz crystal [31], which can be also used for measuring displacements. Superconducting transmon has been recently used for sensing magnons [32][33][34], search for dark matter [35], microwave radiometry [36][37][38] including sensing...