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Physical Review Letters

Dispersion cancellation in a measurement of the single-photon propagation velocity in glass

Aephraim M. Steinberg, Paul G. Kwiat, R. Y. Chiao

Published Apr 20, 1992• 274 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.68.2421

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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.
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
Group-velocity dispersion (GVD) places a fundamental limitation on the resolution possible when measuring the propagation time of short optical pulses through dielectric media. We show that due to a nonlocal, quantum-mechanical effect, a surprising cancellation can occur in fourth-order interference, allowing the time interval between photons emitted in spontaneous parametric down-conversion to be measured without significant degradation of the resolution due to the spreading of the individual photon wave packets. This may also prove useful for measuring the higher-order contributions to GVD.
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.
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.
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.
Classically, two coincident light pulses propagating through two dispersive media will become broadened and their degree of coincidence will be reduced. When entangled photon pairs from parametric down-conversion are considered instead, it is found that the dispersion experienced by one photon can exactly cancel the dispersion experienced by the other in such a way that their coincidence is maintained. The dispersion cancellation is independent of the separation between the two photons and provides a further example of the nonlocal nature of the quantum theory.