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Journal of Optics

Dispersion cancellation in a triple Laue interferometer

Hartmut Lemmel

Published Sep 4, 2014• 1 citation
Publisher

Abstract

The concept of dispersion cancellation has been established in light optics to improve the resolution of interferometric measurements on dispersive media. Odd order dispersion cancellation allows to measure phase shifts without defocusing the interferometer due to wave packet displacements, while even order dispersion cancellation allows to measure time lags without losing resolution due to wave packet spreading. We report that either type of dispersion cancellation can be realized very easily in a triple Laue interferometer. Such interferometers are Mach–Zehnder interferometers based on Bragg diffraction, and are commonly used for neutrons and x-rays. Although the first x-ray interferometer was built nearly five decades ago, the feature of dispersion cancellation hasnʼt been recognized so far because the concept was hardly known in the neutron and x-ray community. However, it explains right away the surprising decoupling of phase shift and spatial displacement that we have discovered recently in neutron interferometry (Lemmel and Wagh 2010 Phys. Rev. A 82 033626). Furthermore, this article might inspire the light optics community to consider whether a triple Laue interferometer for laser light would be useful and feasible. We explain how dispersion cancellation works in neutron interferometry, and we describe the setup rigorously by solving the Schrodinger equation and by calculating the path integral. We point out, that the latter has to be evaluated with special care since in our setup the beam trajectory moves with respect to the crystal lattice of the interferometer.

DOI
10.1088/2040-8978/16/10/105704

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The concept of dispersion cancellation has been established in light optics to improve the resolution of interferometric measurements on dispersive media. Odd order dispersion cancellation allows to measure phase shifts without defocusing the interferometer due to wave packet displacements, while even order dispersion cancellation allows to measure time lags without losing resolution due to wave packet spreading. We report that either type of dispersion cancellation can be realized very easily in a triple Laue interferometer. Such interferometers are Mach–Zehnder interferometers based on Bragg diffraction, and are commonly used for neutrons and x-rays. Although the first x-ray interferometer was built nearly five decades ago, the feature of dispersion cancellation hasnʼt been recognized so far because the concept was hardly known in the neutron and x-ray community. However, it explains right away the surprising decoupling of phase shift and spatial displacement that we have discovered recently in neutron interferometry (Lemmel and Wagh 2010 Phys. Rev. A 82 033626). Furthermore, this article might inspire the light optics community to consider whether a triple Laue interferometer for laser light would be useful and feasible. We explain how dispersion cancellation works in neutron interferometry, and we describe the setup rigorously by solving the Schrodinger equation and by calculating the path integral. We point out, that the latter has to be evaluated with special care since in our setup the beam trajectory moves with respect to the crystal lattice of the interferometer.
A phase shifter in neutron interferometry creates not only a phase shift but also a spatial displacement of the neutron wave packet, leading to a reduced interference contrast. This wave-packet displacement constitutes a major hindrance in measuring large phase shifts. Here we present a nondispersive configuration with two identical phase shifters placed on one path in successive gaps of a symmetric triple Laue (LLL) interferometer. As compared to a single phase shifter, the dual phase shifter generates double the phase shift, yet a net null displacement of the wave packet. The interferometer thus remains fully focused however large the phase shift or the incident wavelength spread, permitting a white incident neutron beam as in the case of a purely topological phase measurement. Misalignment angles of a monolithic nondispersive dual phase shifter are equal and opposite in the two gaps. Its phase therefore remains nondispersive over a much wider angular range and attains a minimum magnitude at the correct orientation, obviating the need to alternate the phase shifter between the two interferometer paths during its alignment. The setup is hence ideally suited for measuring neutron coherent scattering lengths to ultrahigh precision.
Abstract Among the various areas of neutron optical research, neutron interferometry has provided some of the most challenging and spectacular developments. In most cases, separated coherent beams are used which are produced either by wavefront division (Young’s type) or by amplitude division (Mach− Zehnder type). These beams are subsequently coherently superposed after passing through regions of space where the neutron wavefunction is modified in phase and amplitude by various interactions: nuclear, magnetic, electromagnetic, gravitational, or by geometry and topology (as in Aharonov−Bohm-type experiments). Various types of neutron interferometers that have been tested are shown in Fig. 2.1. The first neutron interferometer was based upon wavefront division and biprism deflection, but it had several constraints for interferometric applications mainly due to the small beam separation (100 μm) (Maier-Leibnitz and Springer 1962). Nevertheless, this method gained further interest for diffraction experiments from macroscopic objects and for the detection of weak interaction effects where the long flight paths (10 m) enhance the sensitivity for the measurements of these effects (Gähler et al. 1980; Klein et al. 1981a). The perfect-crystal interferometer (Rauch et al. 1974) provides widely separated coherent beams and has become a standard method for advanced neutron optical investigations. The development of diffraction and phase grating interferometers extended the Mach-Zehnder interferometer method to very slow neutrons (loffe et al. 1985; Gruber et al. 1989). The superposition of spin-up and spin-down states in the longitudinal direction provides the basis for Larmor and Ramsey interferometry, where no lateral beam splitting is necessary. The well-known spin-echo systems (Mezei 1972) and zero-field spin-echo systems (Gähler and Golub 1987; Dubbers et al. 1989) are examples of such interferometers, which also play an important role in atom interferometry (Bord é 1989; Kasevich and Chu 1991; Riehle et al. 1991).
Interference has long been used for precision measurement of path-length changes. Since the advent of the laser, interference has become one of the most versatile tools in metrology. Specifically, ultra-short laser pulses allow unprecedented resolution in absolute length measurements. While ultra-short laser pulses lead to high resolution, for example in white-light interferometry, they are very susceptible to dispersion. \n \nQuantum resources have been proposed to overcome some of the problems related to distortions in the interferometric signal. For example, the Hong-Ou-Mandel (HOM) interferometer relies on frequency-entangled photon pairs and features automatic even-order dispersion cancellation and high interference visibility resilient to unbalanced loss. Quantum-OCT is a technique based on HOM interferometry, that promises to overcome Optical Coherence Tomography (OCT) a classical imaging technique based on low coherence light. Furthermore, straightforward modifications of the HOM interferometer can display several different interferometric signals, including the HOM peak, quantum beating, and phase super-resolution. However, the quantum resources required are hard to produce and dim, leading to long integration times and single-photon counting. \n \nIn this thesis, we introduce the theory behind Chirped-Pulse Interferometry (CPI), a new technique that combines all the advantages of Q-OCT, including even-order dispersion cancellation, but without the need for any quantum resources. We then experimentally implement CPI and demonstrate all the important characteristics shared by the HOM interferometer, but at dramatically larger signal levels. We show how CPI can be used to measure dispersion cancelled axial profiles of an optical sample and show the improvement in resolution over white-light interferometry. Finally, we show that by modifying CPI in analogous ways to HOM, CPI can also be made to produce interferometric signal identical to the HOM peak, quantum beating, and phase super-resolution.
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.
We describe our theoretical and experimental results demonstrating two new techniques for manipulating dispersion in quantum interferometry using spectral and spatial properties of optical entanglement. First, we present a novel interferometer design allowing to demonstrate a new effect of simultaneous even- and odd-order spectral dispersion cancellation in a single experiment using entangled photons with frequency anti-correlated spectrum. Second, we for the first time demonstrate a spatial counterpart of the known quantum dispersion cancellation that leads to the removal of a detrimental effect of spatial aberrations. We discuss potential applications of novel technologies in high-resolution optical measurement and for designing aberration-free imaging schemes.