Extended Wiener-Khinchin theorem for quantum spectral analysis

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.Comment: 13 pages, 5 figure

Effects on brain structural and functional in deaf children after aerobic exercise training: a pilot cluster randomized controlled study

Purpose: To examine effects of aerobic exercise interventions on brain via the structural Magnetic Resonance Imaging (MRI), as well as functional change during working memory (WM) task using fMRI in deaf children.Method: The study applied a cluster randomized controlled design. Twelve deaf children in the intervention group were required to complete an eleven-week aerobic exercise intervention, while other twelve age and gender matched deaf children in the control group were required to keep their normal daily life. Task fMRI images of each participant were acquired in the baseline and post intervention period. The surface-based morphometry (SBM) analysis and functional activation analysis were employed to probe the effects of 11-week aerobic exercise on cerebral structural and functional in deaf children, respectively.Results: The 11-week aerobic exercise intervention did not change brain structure in deaf children. However, behavior performance (reaction time and mean accuracy rate) presented significant improvements after the 11-week aerobic exercise intervention. Compared to the control group, the intervention group showed decreased reaction time in the 2-back (p p p = 0.034). Furthermore, enhanced brain activations in the left supplementary motor cortex (p p Conclusion: 11-week aerobic exercise intervention may not be able to modulate brain structure in deaf children, but may have significantly positive effects on behavior performance and brain functional activation during WM task.</p