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arXiv:1805.02491 · Physical Review Letters

Quantum-Limited Time-Frequency Estimation through Mode-Selective Photon Measurement

John M. Donohue, Vahid Ansari, Jaroslav Řeháček, Z. Hradil, B. Stoklasa, Martin Paùr, Luis Lorenzo Sánchez-Soto, Christine Silberhorn

Published Aug 27, 2018• 97 citations
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Abstract

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a tenfold improvement in precision over the intensity-only Cramér-Rao bound.

DOI
10.1103/physrevlett.121.090501

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Accurate time-delay measurement is at the core of many modern technologies.We present a temporalmode demultiplexing scheme that achieves the ultimate quantum precision for the simultaneous estimation of the temporal centroid, the time offset, and the relative intensities of an incoherent mixture of ultrashort pulses at the single-photon level.We experimentally resolve temporal separations 10 times smaller than the pulse duration, as well as imbalanced intensities differing by a factor of 10 2 .This represents an improvement of more than an order of magnitude over the best standard methods based on intensity detection.
In optics, when attempting to find the distance separations s between two incoherent emitters, it is standard practice to take a full image and extract the single parameter s from it. In such scenarios, the smallest precisely measurable separation is limited by the point-spread function on the image plane, with a vanishingly small amount of information available for smaller and smaller separations especially when photon shot noise is the dominant noise source (as in, for example, astronomical observations). This limit can be formalised by the Fisher information, which quantifies the amount of information accessible per photon detection and is directly associated with Cramér-Rao lower bound. For direct intensity imaging, the Fisher information drops to zero for object separations smaller than the spread of the optical field, sometimes referred to as the Rayleigh's curse, which limits the usefulness of photon counting for metrology.
Abstract Direct measurements on the temporal envelope of quantum light are a challenging task and not many examples are known because most classical pulse characterisation methods do not work on the single-photon level. Knowledge of both spectrum and timing can, however, give insights on properties that cannot be determined by the spectral intensity alone. While temporal measurements on single photons on timescales of tens of picoseconds are possible with superconducting photon detectors, and picosecond measurements have been performed using streak cameras, there are no commercial single-photon sensitive devices with femtosecond resolution available. While time-domain sampling using sum-frequency generation has already been exploited for such a measurement, inefficient conversion has necessitated long integration times to build the temporal profile. We demonstrate a highly efficient waveguided sum-frequency generation process in Lithium Niobate to measure the temporal envelope of single photons with femtosecond resolution with short enough acquisition time to provide a live-view of the measurement. We demonstrate the measurement technique and combine it with spectral measurements using a dispersive-fibre time-of-flight spectrometer to determine upper and lower bounds for the spectral purity of heralded single photons. The approach complements the joint spectral intensity measurements as a measure on the purity can be given without knowledge of the spectral phase.
Measuring small separations between two optical sources, either in space or in time, constitutes 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.
Measuring small separations between two optical sources, either in space or in time, constitutes 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.