Delayed-choice quantum eraser for the undergraduate laboratory

In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical path length of the photons carrying which-way information. In the second setup, we use fiber-optic cables to elongate the path of these photons after their passage through the polarization analyzer but prior to their arrival at the detector. We compare our results to data obtained in the absence of a delay and find excellent agreement. This shows that the timing of the erasure is irrelevant, as also predicted by quantum mechanics. The experiment can serve as a valuable pedagogical tool for conveying the fundamentals of quantum mechanics.Comment: 13 pages, 5 figures, identical to published versio

A note on the uniqueness of the Neumann matrices in the plane-wave background

In this note, we prove the uniqueness of the Neumann matrices of the open-closed vertex in plane-wave light-cone string-field theory, first derived for all values of the mass parameter mu in hep-th/0311231. We also prove the existence and uniqueness of the inverse of an infinite dimensional matrix necessary for the cubic vertex Neumann matrices, and give an explicit expression for it in terms of mu-deformed Gamma functions. Methods of complex analysis are used together with the analytic properties of the mu-deformed Gamma functions. One of the implications of these results is that the geometrical continuity conditions suffice to determine the bosonic part of the vertices as in flat space.Comment: 10 pages, Latex, 2 references adde

Observation of the quantum paradox of separation of a single photon from one of its properties

We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.Comment: 9 pages, 4 figures, identical to published versio

Topological Complexity is a Fibrewise L-S Category

Topological complexity \TC{B} of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version \TCM{B} of topological complexity with an additional condition: in a robot motion planning, a motion must be stasis if the initial and the terminal states are the same. Our main goal is to show the equalities \TC{B} = \catBb{\double{B}}+1 and \TCM{B} = \catBB{\double{B}}+1, where \double{B}=B{\times}B is a fibrewise pointed space over $B$ whose projection and section are given by p_{\double{B}}=\proj_{2} : B{\times}B \to B the canonical projection to the second factor and s_{\double{B}}=\Delta_{B} : B \to B{\times}B the diagonal. In addition, our method in studying fibrewise L-S category is able to treat a fibrewise space with singular fibres. Recently, we found a problem with the proof of Theorem 1.13 which states that for a fibrewise well-pointed space X$over$B$, we have$\catBB{X} = \catBb{X} and that for a locally finite simplicial complex $B$, we have \TC{B} = \TCM{B}. While we still conjecture that Theorem 1.13 is true, this problem means that, at present, no proof is given to exist. Alternatively, we show the difference between two invariants \catBb{X} and \catBB{X} is at most 1 and the conjecture is true for some cases. We give further corrections mainly in the proof of Theorem 1.12.Comment: 12pages original + 5pages errat

He 2-104: A link between symbiotic stars and planetary nebulae

Ultraviolet, optical and infrared observations of He 2-104 are presented, and estimates for some of the physical properties of the nebular shell are made. It is argued that He 2-104 is in transition between the D-type symbiotic star and bipolar planetary nebula phases and, as such, represents a link between subclasses of these two types of objects. The model includes a binary system with a Mira variable and a hot, evolved star. Previous mass loss has resulted in the formation of a disk of gas and dust around the whole system, while the hot star has an accretion disk which produces the observed highly ionized emission line spectrum. Emission lines from cooler, lower density gas is also observed to come from the nebula. In addition, matter is flowing out of the system in a direction perpendicular to the disk with a high velocity and is impacting upon the previously-ejected red giant wind and/or the ambient interstellar medium

S-Duality at the Black Hole Threshold in Gravitational Collapse

We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.Comment: 8 pages of LaTeX, uses style "revtex"; 1 figure, available in archive, or at ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-15.ep

BAT - The Bayesian Analysis Toolkit

We describe the development of a new toolkit for data analysis. The analysis package is based on Bayes' Theorem, and is realized with the use of Markov Chain Monte Carlo. This gives access to the full posterior probability distribution. Parameter estimation, limit setting and uncertainty propagation are implemented in a straightforward manner. A goodness-of-fit criterion is presented which is intuitive and of great practical use.Comment: 31 pages, 10 figure

Chaotic Coupling Constants

We examine some novel physical consequences of the general structure of moduli spaces of string vacua. These include (1) finiteness of the volume of the moduli space and (2) chaotic motion of the moduli in the early universe. To fix ideas we examine in detail the example of the (conjectural) dilaton-axion ``$S$-duality'' of four-dimensional string compactifications. The facts (1) and (2) together might help to solve some problems with the standard scenarios for supersymmetry breaking and vacuum selection in string theory.Comment: 18 pages (4 figs), YCTP-P2-94, RU-94-2