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Quantum interferometric spectroscopy

Rui‐Bo Jin, Ryōsuke Shimizu

Published Jan 1, 2018• 0 citations
Publisher

Abstract

The difference- and sum-frequency distribution of the biphoton wavefunctions were extracted by applying a Fourier transform on the time-domain Hong-Ou-Mandel interference (HOMI) and the NOON state interference (NOONI) patterns.
DOI
10.1364/cleopr.2018.th3h.4

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The classical Wiener-Khinchin theorem (WKT), which can extract spectral information by classical interferometers through Fourier transform, is a fundamental theorem used in many disciplines. However, there is still need for a quantum version of WKT, which could connect correlated biphoton spectral information by quantum interferometers. Here, we extend the classical WKT to its quantum counterpart, i.e., extended WKT (e-WKT), which is based on two-photon quantum interferometry. According to the e-WKT, the difference-frequency distribution of the biphoton wavefunctions can be extracted by applying a Fourier transform on the time-domain Hong-Ou-Mandel interference (HOMI) patterns, while the sum-frequency distribution can be extracted by applying a Fourier transform on the time-domain NOON state interference (NOONI) patterns. We also experimentally verified the WKT and e-WKT in a Mach-Zehnder interference (MZI), a HOMI and a NOONI. This theorem can be directly applied to quantum spectroscopy, where the spectral correlation information of biphotons can be obtained from time-domain quantum interferences by Fourier transform. This may open a new pathway for the study of light-matter interaction at the single photon level.
We propose theoretically a quantum interferometer in which the NOON state interferometer is combined with the Hong-Ou-Mandel interferometer. With this interferometer, the temporal interference patterns associated with biphoton frequency sum and difference can be shown in different parts of a single interferogram. It is thus possible to simultaneously obtain the spectral correlation information of biphotons in both frequency sum and difference by taking the Fourier transform from such an interferogram. This provides a method for complete spectral characterization of an arbitrary two-photon state with exchange symmetry and might be useful in quantum Fourier-transform spectroscopy where direct spectral measurement is difficult. Furthermore, as it can realize the measurement of time intervals on three scales at the same time, we expect that it can provide a method in quantum metrology. Finally, we discuss another potential application of such an interferometer in the generation and characterization of high-dimensional and phase-controlled frequency entanglement.
Hong-Ou-Mandel (HOM) interference of multi-mode frequency entangled states plays a crucial role in quantum metrology. However, as the number of modes increases, the HOM interference pattern becomes increasingly complex, making it challenging to comprehend intuitively. To overcome this problem, we present the theory and simulation of multi-mode-HOM interference (MM-HOMI) and compare it to multi-slit interference (MSI). We find that these two interferences have a strong mapping relationship and are determined by two factors: the envelope factor and the details factor. The envelope factor is contributed by the single-mode HOM interference (single-slit diffraction) for MM-HOMI (MSI). The details factor is given by sin ( Nx )/sin ( x ) ([sin ( Nv )/sin ( v )] 2 ) for MM-HOMI (MSI), where N is the mode (slit) number and x ( v ) is the phase spacing of two adjacent spectral modes (slits). As a potential application, we demonstrate that the square root of the maximal Fisher information in MM-HOMI increases linearly with the number of modes, indicating that MM-HOMI is a powerful tool for enhancing precision in time estimation. We also discuss multi-mode Mach-Zehnder interference, multi-mode NOON-state interference, and the extended Wiener-Khinchin theorem. This work may provide an intuitive understanding of MM-HOMI patterns and promote the application of MM-HOMI in quantum metrology.