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arXiv:2008.06611 · Optics Express

Dispersion cancellation in a quantum interferometer with independent single photons

Dong-Gil Im, Yosep Kim, Yoon-Ho Kim

Published Jan 3, 2021• 13 citations
arXivHTMLPDF

Abstract

A key technique to perform proper quantum information processing is to get a high visibility quantum interference between independent single photons. One of the crucial elements that affects the quantum interference is a group velocity dispersion that occurs when single photons pass through a dispersive medium. We theoretically and experimentally demonstrate that an effect of group velocity dispersion on the two-photon interference can be cancelled if two independent single photons experience the same amount of pulse broadening. This dispersion cancellation effect can be applied to a multi-path linear interferometer with multiple independent single photons. As multi-path quantum interferometers are at the heart of quantum communication, photonic quantum computing, and boson sampling applications, our work should find wide applicability in quantum information science.

DOI
10.1364/oe.415610

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A key technique to perform proper quantum information processing is to get a high visibility quantum interference between independent single photons. One of the crucial elements that affects the quantum interference is a group velocity dispersion that occurs when single photons pass through a dispersive medium. We theoretically and experimentally demonstrate that an effect of group velocity dispersion on the two-photon interference can be cancelled if two independent single photons experience the same amount of pulse broadening. This dispersion cancellation effect can be applied to a multi-path linear interferometer with multiple independent single photons. As multi-path quantum interferometers are at the heart of quantum communication, photonic quantum computing, and boson sampling applications, our work should find wide applicability in quantum information science.
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.
We have demonstrated for the first time that single photons in glass travel at the group velocity, and have observed a novel, nonlocal dispersion-cancellation effect. We used a two-photon interferometer in which a conjugate pair of photons produced in parametric fluorescence travel separate paths and are detected in coincidence after being recombined at a beam splitter. A piece of glass was placed in the path of one of the photons, and a variable delay was adjusted to precisely compensate for it. The single-photon propagation time was thus measured to within approximately 4 fsec.
It is a well-known and remarkable fact that in certain coincidence photon-counting experiments with cw-pumped parametric down-converters, the effects of group-velocity dispersion arising from media interposed between source and detectors are completely canceled, even if the media physically affect only one of the photons of the pair. Recently Perina et al. [Phys. Rev. A 59, 2359 (1999)] showed that this phenomenon does not occur when certain classical timing information is available about the arrival of individual photons at the detectors, as is the case when the photon pairs are produced via spontaneous parametric down-conversion using an ultrashort pump pulse. In this paper we show that the nonlocal cancellation of dispersion for such a source of entangled photons can be restored in principle by proper engineering of the source properties. In particular, we describe techniques for recovering interference in coincidence-counting experiments by suppressing distinguishing information without the post selection of photons. Moreover, a precise classical timing signal coincident with the photon pair is still available.
In the process of spontaneous parametric down-conversion, conjugate pairs of broadband photons are emitted simultaneously from a nonlinear crystal. We use coincidence detection in a fourth-order interferometer to measure the propagation delay of one photon with respect to that of its conjugate. One photon of every pair enters each arm of the interferometer, and when the path-length difference is adjusted such that the two photons meet essentially simultaneously at the output beam splitter, a dip is observed in the coincidence rate between photon counters placed at the two output ports. In our experiment, the rms width of this dip is 15 fs. By placing various dielectric media in the path of one of the photons and then adjusting the free-space path lengths until the coincidence dip reappears, we have measured the propagation time of single photons and found it to agree with predictions based on the group velocity.1 Because of a surprising quantum-mechanical effect, group-velocity dispersion cancels out, such that the expected wave packet broadening has essentially no effect on the high time resolution of this technique.2
We report on an experiment to determine both the group and phase delays experienced by orthogonally polarized photon pairs traveling through a birefringent medium. Both types of delay are determined from the same set of coincidence-counting data. The experiment is based on an interference technique using two-photon multipath indistinguishability to produce an interference feature. Earlier work has shown that this interference feature can be used to measure the group velocity of single-photon wave packets in dielectric media. In the current work, the two-photon interferometer has been modified to produce an additional interference feature that is sensitive to the phase velocity of the light. We have used this technique to simultaneously measure the group delay in crystal quartz with a precision of 0.1 fs and the phase delay with a precision of 8 attoseconds. Our analysis clarifies the effects of group and phase delays and shows the unexpected result that dispersive temporal broadening, which is well known to be canceled for the original interferometer setup, is not canceled for this type of ``postponed compensation'' interferometer.
Temporal filtering is widely recognized as an effective strategy for improving the visibility of the Hong-Ou-Mandel interferometer, an important tool for observing the phenomenon of two-photon quantum interference. However, such manipulation may lead to additional effects on the measurement. In addition to demonstrating the degradation of photon-detection efficiency, this paper demonstrates that temporal filtering can significantly broaden the interference width, especially in scenarios where photons experience substantial dispersion. This broadening effect is also presented in the nonlocal Franson interferometer. The good agreement between experimental results and theoretical simulations not only reveals the mechanism behind dispersion-induced broadening in two-photon quantum interference but also provides an alternative and convenient method for measuring dispersion without the need for extra equipment.