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Oxford University Press eBooks

Experiments in linear optics

J. C. Garrison, R. Y. Chiao

Published Jun 5, 2008• 0 citations
Publisher

Abstract

This chapter presents experiments employing the optical devices described in Chapter 8 and the detection schemes discussed in Chapter 9. Single-photon interference — described by a first-order correlation function — is destroyed by measurements yielding “which-path” information. The Hanbury Brown-Twiss effect is described by a second-order (intensity-intensity) correlation function. Two-photon interference is observed with the Hong-Ou-Mandel (HOM) interferometer, in which a pair of photons interfere at a single beam splitter. In the Franson interferometer, the interference occurs between photons at spatially separated beam splitters. The HOM effect is used to measure the propagation speed of a single photon in a dielectric medium and the tunneling speed across an optical barrier. Similar techniques show that the mere possibility of observing which-path information destroys single-photon interference, even if no measurements are actually made.

DOI
10.1093/acprof:oso/9780198508861.003.0011

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This chapter presents experiments employing the optical devices described in Chapter 8 and the detection schemes discussed in Chapter 9. Single-photon interference — described by a first-order correlation function — is destroyed by measurements yielding “which-path” information. The Hanbury Brown-Twiss effect is described by a second-order (intensity-intensity) correlation function. Two-photon interference is observed with the Hong-Ou-Mandel (HOM) interferometer, in which a pair of photons interfere at a single beam splitter. In the Franson interferometer, the interference occurs between photons at spatially separated beam splitters. The HOM effect is used to measure the propagation speed of a single photon in a dielectric medium and the tunneling speed across an optical barrier. Similar techniques show that the mere possibility of observing which-path information destroys single-photon interference, even if no measurements are actually made.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
Controlling light at the level of individual photons has led to advances in fields ranging from quantum information and precision sensing to fundamental tests of quantum mechanics. A central development that followed the advent of single-photon sources was the observation of the Hong–Ou–Mandel (HOM) effect, a novel two-photon path interference phenomenon experienced by indistinguishable photons. The effect is now a central technique in the field of quantum optics, harnessed for a variety of applications such as diagnosing single-photon sources and creating probabilistic entanglement in linear quantum computing. Recently, several distinct experiments using atomic sources have realized the requisite control to observe and exploit Hong–Ou–Mandel interference of atoms. This chapter provides a summary of this phenomenon and discusses some of its implications for atomic systems. Transitioning from the domain of photons to atoms opens new perspectives on fundamental concepts, such as the classification of entanglement of identical particles. It aids in the design of novel probes of quantities such as entanglement entropy by combining well-established tools of AMO physics—unity single-atom detection, tunable interactions, and scalability—with the Hong–Ou–Mandel interference. Furthermore, it is now possible for established protocols in the photon community, such as measurement-induced entanglement, to be employed in atomic experiments that possess deterministic single-particle production and detection. Hence, the realization of the HOM effect with atoms represents a productive union of central ideas in quantum control of atoms and photons.
Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.
The emergence of Quantum Optics, in the second half of the 20th century, was closely related to landmark experiments, which were permitted by the development of single photon detection and correlation measurements. Photon correlation techniques allowed experimentalists to demonstrate effects closely linked to two-photon amplitudes interference with entangled states, a phenomenon emblematic of the second quantum revolution. In the Atom Optics group at Institut d'Optique, we revisit these experiments with photons replaced by metastable Helium atoms, which can be detected individually. After the Hanbury Brown Twiss and the Hong Ou Mandel experiments, we aim at realizing a test of Bell's inequalities with atoms entangled in momentum, i.e., in external degrees of freedom sensitive to mass.