Generalised Hong-Ou-Mandel Experiments with Bosons and Fermions

The Hong-Ou-Mandel (HOM) dip plays an important role in recent linear optics experiments. It is crucial for quantum computing with photons and can be used to characterise the quality of single photon sources and linear optics setups. In this paper, we consider generalised HOM experiments with $N$ bosons or fermions passing simultaneously through a symmetric Bell multiport beam splitter. It is shown that for even numbers of bosons, the HOM dip occurs naturally in the coincidence detection in the output ports. In contrast, fermions always leave the setup separately exhibiting perfect coincidence detection. Our results can be used to verify or employ the quantum statistics of particles experimentally.Comment: 11 pages, 2 figures, more references adde

De Broglie Wavelength of a Nonlocal Four-Photon

Superposition is one of the most distinct features of quantum theory and has been demonstrated in numerous realizations of Young's classical double-slit interference experiment and its analogues. However, quantum entanglement - a significant coherent superposition in multiparticle systems - yields phenomena that are much richer and more interesting than anything that can be seen in a one-particle system. Among them, one important type of multi-particle experiments uses path-entangled number-states, which exhibit pure higher-order interference and allow novel applications in metrology and imaging such as quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit or quantum lithography beyond the classical diffraction limit. Up to now, in optical implementations of such schemes lower-order interference effects would always decrease the overall performance at higher particle numbers. They have thus been limited to two photons. We overcome this limitation and demonstrate a linear-optics-based four-photon interferometer. Observation of a four-particle mode-entangled state is confirmed by interference fringes with a periodicity of one quarter of the single-photon wavelength. This scheme can readily be extended to arbitrary photon numbers and thus represents an important step towards realizable applications with entanglement-enhanced performance.Comment: 19 pages, 4 figures, submitted on November 18, 200

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Second harmonic generation : the solution for an amplitude-modulated initial pulse

Original article can be found at: http://www.sciencedirect.com/science/journal/00304018 Copyright Elsevier B.V. [Full text of this article is not available in the UHRA]We address the initial value problem for one-dimensional second harmonic generation starting from a purely amplitude-modulated fundamental wave. A general method to solve the problem in terms of a Schrödinger equation is presented, in which the initial pulse-shape is taken as a potential. Several examples with the complete solution given in analytical form are discussed. A much broader class of solutions can be found with the help of a single numerical integration. In particular, solutions with incident pulses approximating a sech2 -shape have been obtained.Peer reviewe