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arXiv:2111.04074 · Optics Express

Propagation of temporal mode multiplexed optical fields in fibers: influence of dispersion

Wen Zhao, Nan Huo, Liang Cui, Xiaoying Li, Z. Y. Ou

Published Dec 16, 2021• 5 citations
arXivHTMLPDF

Abstract

Exploiting two interfering fields which are initially in the same temporal mode but with the spectra altered by propagating through different fibers, we characterize how the spectral profiles of temporal modes change with the fiber induced dispersion by measuring the fourth-order interference when the order number and bandwidth of temporal modes are varied. The experiment is done by launching a pulsed field in different temporal modes into an unbalanced Mach-Zehnder interferometer, in which the fiber lengths in two arms are different. The results show that the mode mismatch of two interfering fields, reflected by the visibility and pattern of interference, is not only dependent upon the amount of unbalanced dispersion but also related to the order number of temporal mode. In particular, the two interfering fields may become orthogonal under a modest amount of unbalanced dispersion when the mode number of the fields is k ≥ 2. Moreover, we discuss how to recover the spectrally distorted temporal mode by measuring and compensating the transmission induced dispersion. Our investigation paves the way for further investigating the distribution of temporally multiplexed quantum states in fiber network.

DOI
10.1364/oe.448013

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Exploiting two interfering fields which are initially in the same temporal mode but with the spectra altered by propagating through different fibers, we characterize how the spectral profiles of temporal modes change with the fiber induced dispersion by measuring the fourth-order interference when the order number and bandwidth of temporal modes are varied. The experiment is done by launching a pulsed field in different temporal modes into an unbalanced Mach-Zehnder interferometer, in which the fiber lengths in two arms are different. The results show that the mode mismatch of two interfering fields, reflected by the visibility and pattern of interference, is not only dependent upon the amount of unbalanced dispersion but also related to the order number of temporal mode. In particular, the two interfering fields may become orthogonal under a modest amount of unbalanced dispersion when the mode number of the fields is k ≥ 2. Moreover, we discuss how to recover the spectrally distorted temporal mode by measuring and compensating the transmission induced dispersion. Our investigation paves the way for further investigating the distribution of temporally multiplexed quantum states in fiber network.
The field-orthogonal temporal modes (TM) of electromagnetic fields form a new framework for quantum information. A lot of efforts have been made to develop the tools for photonic quantum information processing in TM framework. However, the distribution of temporally multiplexed quantum states over long distance optical fibers has not been realized yet. As a first step toward long distance distribution of TMs, we study fourth-order interference and show how the dispersion influence the field spectrum by launching a pulsed field in different temporal modes into a M-Z interferometer with unbalanced dispersion induced by transmission fibers in two arms. The investigation is useful for further investigating the distribution of temporally multiplexed quantum states in fiber network.
With propagating through a dispersive medium, the temporal–spectral profile of optical pulses should be inevitably modified. Although such dispersion effect has been well studied in classical optics, its effect on a single-photon wave-packet has not yet been entirely revealed. In this paper, we investigate the effect of dispersion on indistinguishability between single-photon wave-packets through the Hong–Ou–Mandel (HOM) interference. By dispersively manipulating two weak coherent single-photon wave-packets which are prepared by attenuating mode-locked laser pulses before interfering with each other, we observe that the difference of the second-order dispersion between two optical paths of the HOM interferometer can be mapped to the interference curve, indicating that (i) with the same amount of dispersion effect in both paths, the HOM interference curve must be only determined by the intrinsic indistinguishability between the wave-packets, i.e., dispersion cancellation due to the indistinguishability between Feynman paths; and (ii) unbalanced dispersion effect in two paths cannot be canceled and will broaden the interference curve thus providing a way to measure the second-order dispersion coefficient. Our results suggest a more comprehensive understanding of the single-photon wave-packet and pave ways to explore further applications of the HOM interference.
Temporal coherence of individual signal or idler beam, determined by the spectral correlation property of photon pairs, is important for realizing quantum interference among independent sources. Based on spontaneous four-wave mixing in optical fibers, we study the effect of chirp on the temporal coherence property by introducing a different amount of chirp into either the pulsed pump or individual signal (idler) beam. The investigation shows that the pump chirp induces additional frequency correlation into photon pairs; the mutual spectral correlation of photon pairs and the coherence of individual beam can be characterized by measuring the intensity correlation function g(2){g}^{(2)}g(2) of the individual beam. To improve the coherence degree, the pump chirp should be minimized. Moreover, a Hong-Ou-Mandel--type two-photon interference experiment with the signal beams generated in two different fibers illustrates that the chirp of the individual signal (idler) beam does not change the temporal coherence degree, but affects the temporal mode matching. To achieve high visibility among multiple sources, apart from improving the coherence degree, mode matching should be optimized by managing the chirps of individual beams.
We theoretically and experimentally demonstrate the influence of dispersion on the temporal mode properties of the spontaneous Raman scattering pumped by picosecond pulses in single mode optical fiber. We model the process of the ultrafast spontaneous Raman scattering, calculate and measure the intensity correlation function of the Raman photons with different dispersion by varying the detuning between pump and Raman photons or changing the optical length. The intensity correlation function decreases with the increase of dispersion induced temporal walk-off both by increasing the detuning and by increasing the fiber length. We evaluate the dispersion parameter of the single mode fiber by fitting the measured data with the theoretical equation we deduced. The estimated value is close to the labelled one. Our study provides a new way to evaluate dispersion parameters of the media in which Raman scattering can occur and is beneficial for efficient distillation of entanglement in optical fibers.
By investigating the intensity correlation function, we study the temporal mode properties of spontaneous Raman photons generated in single mode fibers pumped by short pulses. We find that the intensity correlation function of the Raman photons is related to the dispersion induced temporal mismatch among the Raman photons generated in different subparts of the fiber. When no temporal mismatch exists, the intensity correlation function only depends on the ratio between the pulse width of the pump and the coherence time of the Raman photons. With the ratio decreasing, the intensity correlation function increase. Our study is helpful for easily creating high-quality true thermal light which will be a useful resource for second-order coherence based remote sensing.
Spatial double-slit experiments have been central to understanding wave-particle duality, demonstrating how single photons interfere in transverse momentum when given two spatially separated alternatives. Analogue demonstrations have shown the corresponding relationship in the time-frequency domain with classical electric fields. Extending this to quantum states of light reveals how different photon states acquire different phases through the same temporal separation, producing distinct spectral interference signatures. In this work, we investigate temporal interference with three different quantum states of light — a single-photon state, a separable two-photon state, and a two-photon NOON state — all on the same physical platform and with the same temporal delay. Experimentally, we prepare ultrafast pulses of photon states in polarization and use the birefringent delay of beta-barium borate (BBO) crystals to introduce a femtosecond temporal separation between the orthogonal polarization components. A polarization projection in a superposition basis then removes the which-time information and produces spectral interference, providing an analogue of the temporal double slit. The photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a Sagnac interferometer, tuned to produce all three quantum states by adjusting the pump polarization, with the NOON state reaching a measured visibility of (88.99 ± 0.21)%. The spectra are recorded through dispersive Fourier transform using a long single-mode fiber and single photon detectors. The measured spectra show that single-photon and separable two-photon states both oscillate at the same rate, consistent with a phase given by the photon frequency multiplied by the temporal delay, with the two-photon spectral pattern being the product of the individual single-photon spectra. The NOON state, in contrast, oscillates twice as fast, governed by the collective phase of the two photons, which depends on the sum of their frequencies rather than on the individual photon spectral modulations, and which reduces to twice the single-photon phase along the equal-frequency diagonal. This doubled phase accumulation makes NOON-state temporal interference directly relevant to quantum-enhanced sensing and metrology. Different polarization projections further allow tuning of the interference patterns across all three states.