Quantum sensing represents one of the possible fields where quantum mechanics permits to obtain increased performances with respect to classical strategies. The estimation of an optical phase through interferometric experiments is an ubiquitous technique, which can find several applications in optical interferometry as well as in the measurement of the optical properties of a system. In this scenario, the typical strategy to measure an optical phase consists in sending an optical probe on the system and in measuring the probe state after the interaction. The aim of these protocols is to obtain the maximum resolution with minimal disturbance upon the system to be measured. However, while quantum strategies turn out to be useful in increasing the achievable performances, quantum benefits are typically extremely fragile under the action of losses.
Within the context of phase estimation, recently a strong research effort has been devoted to the development of the optimal strategies in presence of lossy experimental conditions. One possible approach consisted in the determination of the optimal probe states in a lossy scenario. Thetheoretical and experimental investigations of quantum states of light has attracted much attention, leading to the best possible precision in optical two-mode interferometry, even in presence of experimental imperfections.
We investigate a different approach based on protecting the information encoded in a few photons probe state from the action of losses, meing minimally invasive on the sample. The proposed scheme employs a simple, conventional interferometric phase sensing stage with microscopic probes, which are amplified with an optical parametric amplifier (OPA) after the interaction with the sample, but before the lossy detectors. No post-selection is employed to filter the output signal. The OPA (an optimal phase-covariant quantum cloning machine) transfers the properties of the injected state into a field with a larger number of particles, robust under losses and decoherence. Our approach is suitable for the analysis of fragile samples (weak regime of the interaction), since the amplification acts after the interaction of the probe state with the sample.
Such scheme has been investigated with two classes of probe states, namely single photons [1], and coherent states [2], leading to a significant enhancement in the performances of lossy phase estimation protocols.