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Physical Review A

Nonlocal cancellation of dispersive broadening in Mach-Zehnder interferometers

Todd S. Larchuk, Malvin Carl Teich, Bahaa E. A. Saleh

Published Nov 1, 1995• 40 citations
Publisher

Abstract

We present theoretical and experimental second- and fourth-order interference patterns for entangled photons of different colors entering single and dual Mach-Zehnder interferometers in which dispersive elements have been deliberately placed. Although photon wave packets are generally broadened, as well as delayed, by passage through dispersive optical elements, coincidence measurements made with entangled photon pairs can be free of such broadening. This occurs for materials with particular dispersive behavior, as well as when the dispersion is balanced in both arms. This nonlocal behavior arises from the entanglement in the frequencies of the down-converted pair photons. We also show that nonlocal pump-frequency oscillations are present in the coincidence rate patterns for long path-length-difference times, confirming the robustness of this phenomenon in the presence of dispersion. However, the magnitude of these oscillations is reduced when an arbitrary dispersive material is used in an unbalanced configuration. Difference-frequency oscillations are also robust in the presence of dispersion, although they decay for large path-length-difference times.

DOI
10.1103/physreva.52.4145

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We present theoretical and experimental second- and fourth-order interference patterns for entangled photons of different colors entering single and dual Mach-Zehnder interferometers in which dispersive elements have been deliberately placed. Although photon wave packets are generally broadened, as well as delayed, by passage through dispersive optical elements, coincidence measurements made with entangled photon pairs can be free of such broadening. This occurs for materials with particular dispersive behavior, as well as when the dispersion is balanced in both arms. This nonlocal behavior arises from the entanglement in the frequencies of the down-converted pair photons. We also show that nonlocal pump-frequency oscillations are present in the coincidence rate patterns for long path-length-difference times, confirming the robustness of this phenomenon in the presence of dispersion. However, the magnitude of these oscillations is reduced when an arbitrary dispersive material is used in an unbalanced configuration. Difference-frequency oscillations are also robust in the presence of dispersion, although they decay for large path-length-difference times.
In a Franson interferometer two-photon interference fringes occur despite the photons never encountering each other [1]. This phenomenon is a fundamental demonstration of the nonlocal nature of quantum mechanics. It serves also as a direct proof of frequency-time-entanglement. Furthermore, it can benefit not only from local, but also nonlocal dispersion cancellation techniques [2], which is a very useful property when working with spectrally broad photon pairs. More specifically, one has to distinguish between dispersion occuring before the individual Mach-Zehnder interferometers (MZIs), which constitute the Franson interferometer, and within them. Analysis of influences up to second order has shown that no loss of contrast can be expected from dispersion before the Franson interferometer. Differential second-order dispersion inside the interferometer, however, can cause a reduction of contrast in the interferogram [3].
A pair of light quanta with different colors (155.9-nm difference in center wavelength) generated from parametric down-conversion was injected collinearly into one input port of a Mach-Zehnder interferometer. Coincidence interference behavior was studied over a wide range of optical path differences of the interferometer. A measurement of 75% interference visibility with oscillation of the pump frequency for a large optical path difference of the interferometer (43 cm) is the signature of a quantum two-photon entangled state, which reflects both particle and wave nature of the light quanta in one experiment.
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
Pairs of 826.8-nm correlated photons, generated by parametrically down-converting 413.4-nm krypton-ion laser light, are directed into a single Mach-Zehnder interferometer such that each photon of the pair enters a different input port. The rate of coincidence at the two output ports displays oscillations (as the path-length difference is swept) with a spatial period equal to the 413-nm wavelength of the pump photons, and with a visibility of 62% when the path-length difference exceeds the coherence length of the individual photon beams. This unequivocally demonstrates the nonclassical and entangled nature of the two-photon state.
Fourth-order interference patterns of biphotons generated by type-I spontaneous parametric downconversion are examined for beams with partial angular and spectral entanglement, both for degenerate and nondegenerate constituent photons. Two-beam configurations using a single beam-splitter interferometer and a Mach-Zehnder interferometer are explicitly studied, as are four-beam configurations using pairs of beam splitters and Mach-Zehnder interferometers. The interference pattern generally comprises a number of harmonic functions of the path-length difference with frequencies and visibilities that usually depend on direction, and may have a finite or infinite duration (fourth-order coherence length). The relation between the visibility and the spectral indistinguishability of the two beams is established. Certain components of the interference pattern are independent of direction so that they are not washed out by the use of apertures of finite size.