Abstract
Measuring small separations between two optical sources, either in space or in time, constitute an important metrological challenge as standard intensity-only measurements fail for vanishing separations. Contrarily, it has been established that appropriate coherent mode projections can appraise arbitrarily small separations with quantum-limited precision. However, the question of whether the optical coherence brings any metrological advantage to mode projections is still a point of debate. Here, we elucidate this problem by experimentally investigating the effect of varying coherence on estimating the temporal separation between two single-photon pulses. We show that, for an accurate interpretation, special attention must be paid to properly normalize the quantum Fisher information to account for the strength of the signal. Our experiment demonstrates that coherent mode projections are optimal for any degree of coherence.
Highlights
In numerous applications, including radar signal processing [1,2,3], radio acoustic sounding [4,5], ultrasonic testing [6], and medical imaging [7], one is faced with the challenge of determining the temporal delay between two closely spaced, overlapping, ultrashort pulses
The same pitfall appears in the spatial domain: The resolution of an imaging system is limited by the size of its point spread function (PSF), which specifies the intensity response to a point source [9]
Detecting the upconverted photons realizes projective measurements, in which the temporalmode projections are defined by the shapes of the gating pulse
Summary
In numerous applications, including radar signal processing [1,2,3], radio acoustic sounding [4,5], ultrasonic testing [6], and medical imaging [7], one is faced with the challenge of determining the temporal delay between two closely spaced, overlapping, ultrashort pulses. When the quantum FI (i.e., optimized over all measurements allowed by quantum mechanics) is calculated, it stays constant, evidencing that the Rayleigh limit is not essential These remarkable predictions have fuelled a number of experimental implementations, both in the spatial [19,20,21,22] and the time-frequency [23] domains. Of two time-delayed pulses can be decomposed in terms of in-phase and antiphase combinations of the two pulses These two channels are not equivalent concerning the strength of the signal: The antiphase mode does carry the information about the temporal separation, but the intensity in this mode vanishes as the time offset decreases. We confirm here these predictions with an experiment that benefits from classical and quantum resources, both contained in the quantum FI of the signal
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