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arXiv:1712.01898 · International Journal of Quantum Information

Which role does multiphoton interference play in small phase estimation in quantum Fourier transform interferometers?

Olaf Zimmermann, Vincenzo Tamma

Published Dec 1, 2017• 3 citations
arXivHTMLPDF

Abstract

Recently, quantum Fourier transform interferometers have been demonstrated to allow a quantum metrological enhancement in phase sensitivity for a small number [Formula: see text] of identical input single photons [J. P. Olson, K. R. Motes, P. M. Birchall, N. M. Studer, M. LaBorde, T. Moulder, P. P. Rohde and J. P. Dowling, Phys. Rev. A 96 (2017) 013810; K. R. Motes, J. P. Olson, E. J. Rabeaux, J. P. Dowling, S. J. Olson and P. P. Rohde, Phys. Rev. Lett. 114 (2015) 170802; O. Zimmermann, Bachelor Thesis (Ulm University, 2015) arXiv: 1710.03805.]. However, multiphoton distinguishability at the detectors can play an important role from an experimental point of view [V. Tamma and S. Laibacher, Phys. Rev. Lett. 114 (2015) 243601.]. This raises a fundamental question: How is the phase sensitivity affected when the photons are completely distinguishable at the detectors and therefore do not interfere? In other words, which role does multiphoton interference play in these schemes? Here, we show that for small phase values, the phase sensitivity achievable in the proposed schemes with indistinguishable photons is enhanced only by a constant factor with respect to the case of completely distinguishable photons at the detectors. Interestingly, this enhancement arises from the interference of only a polynomial number (in [Formula: see text]) of the total [Formula: see text] multiphoton path amplitudes in the [Formula: see text]-port interferometer. These results are independent of the number [Formula: see text] of single photons and of the phase weight factors employed at each interferometer channel.

DOI
10.1142/s0219749917400202

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Recently, Motes et al. proposed in Phys. Rev. Lett. 114, 170802 (2015) a linear optics interferometer with N identical single photon input states as a tool for sub-shot-noise phase estimation which does not require NOON states sources. This thesis investigates how the degree of distinguishability between the input photonic spectra affects the interferometric phase sensitivity, by employing the results obtained by Tamma and Laibacher in Phys. Rev. Lett. 114, 243601 (2015). Remarkably, the obtained results show, that for small phases, the phase sensitivity in the case of completely distinguishable photons is identical to the one in the case of identical photons considered by Motes et al. apart from a constant factor that is independent of the number N of input photons. Consequently, multiphoton interference does not provide in the scheme proposed by Motes et al. any sub-shot-noise sensitivity for a large number N of photons.
Quantum Fourier transforms (QFTs) have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology. Here, we present and demonstrate a general technique that simplifies the construction of QFT interferometers using both path and polarization modes. On that basis, we first observe the generalized Hong-Ou-Mandel effect with up to four photons. Furthermore, we directly exploit number-path entanglement generated in these QFT interferometers and demonstrate optical phase supersensitivities deterministically.
Multiphoton interference results in modulations of output probabilities with phase shift periods that are much shorter than $2\ensuremath{\pi}$. Here, we investigate the physics behind these statistical patterns in the case of well-defined photon numbers in the input and output modes of a two-path interferometer. We show that the periodicity of the multiphoton interference is related to the weak value of the unobserved intensity difference between the two arms of the interferometer. This means that the operator relations between the photon number differences in input, path, and output can be used to determine the periodicity of the experimentally observed quantum interference, establishing an important link between the classical causality of random phase interference and quantum effects that depend on the superposition of classically distinct possibilities.
We report a theoretical and experimental study on the role of indistinguishability in the estimation of an interferometric phase. In particular, we show that the quantum Fisher information, which limits the maximum precision achievable in the parameter estimation, increases linearly with respect to the degree of indistinguishability between the input photons in a two-port interferometer, in the ideal case of a pure probe state. We experimentally address the role played by the indistinguishability for the case of two photons entering a polarization-based interferometer, where the degree of indistinguishability is characterized by the overlap between two spatial modes. The experimental results support the fact that, even in the presence of white noise, a quantum enhancement in the interferometric phase estimation can be obtained from a minimum degree of indistinguishability.
Abstract Quantum interference is known to become extinct with distinguishing information, as illustrated by the ubiquitous double-slit experiment or the two-photon Hong–Ou–Mandel effect. In the former case single particle interference is destroyed with which-path information while in the latter bunching interference tails-off as photons become distinguishable. It has been observed that when more than two particles are involved, these interference patterns are in general a non-monotonic function of the distinguishability. Here we perform a comprehensive characterization, both theoretically and experimentally, of four-photon interference by analyzing the corresponding correlation functions, contemplating several degrees of distinguishability across different parameters. This study provides all the necessary tools to quantify the impact of multi-photon interference on precision measurements of parameters such as phase, frequency, and time difference. We apply these insights to quantify the precision in the estimation of an interferometric phase in a two-port interferometer using a four-photon state. Our results reveal that, for certain phase values, partially distinguishable multi-photon states can achieve higher Fisher information values compared to the two-photon experiment. These findings highlight the potential of distinguishable multi-photon states for enhanced precision in quantum metrology and related applications.