New intensity and visibility aspects of a double loop neutron interferometer

Various phase shifters and absorbers can be put into the arms of a double loop neutron interferometer. The mean intensity levels of the forward and diffracted beams behind an empty four plate interferometer of this type have been calculated. It is shown that the intensities in the forward and diffracted direction can be made equal using certain absorbers. In this case the interferometer can be regarded as a 50/50 beam splitter. Furthermore the visibilities of single and double loop interferometers are compared to each other by varying the transmission in the first loop using different absorbers. It can be shown that the visibility becomes exactly 1 using a phase shifter in the second loop. In this case the phase shifter in the second loop must be strongly correlated to the transmission coefficient of the absorber in the first loop. Using such a device homodyne-like measurements of very weak signals should become possible.Comment: 12 pages, 9 figures, accepted for publication in the Journal of Optics B - Quantum and Semiclassical Optic

Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere.Comment: 4 pages, revtex

Phase Dynamics of Two Entangled Qubits

We make a geometric study of the phases acquired by a general pure bipartite two level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\pi$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n \pi$ global phase. They can be identified as dynamical, geometrical and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory and the results obtained are shown to be in connection to those on mixed states phases.Comment: 9 figures, slightly different version from the accepted on

Flow Equations for Uplifting Half-Flat to Spin(7) Manifolds

In this short supplement to [1], we discuss the uplift of half-flat six-folds to Spin(7) eight-folds by fibration of the former over a product of two intervals. We show that the same can be done in two ways - one, such that the required Spin(7) eight-fold is a double G_2 seven-fold fibration over an interval, the G_2 seven-fold itself being the half-flat six-fold fibered over the other interval, and second, by simply considering the fibration of the half-flat six-fold over a product of two intervals. The flow equations one gets are an obvious generalization of the Hitchin's flow equations (to obtain seven-folds of G_2 holonomy from half-flat six-folds [2]). We explicitly show the uplift of the Iwasawa using both methods, thereby proposing the form of the new Spin(7) metrics. We give a plausibility argument ruling out the uplift of the Iwasawa manifold to a Spin(7) eight fold at the "edge", using the second method. For $Spin(7)$ eight-folds of the type $X_7\times S^1$, $X_7$ being a seven-fold of SU(3) structure, we motivate the possibility of including elliptic functions into the "shape deformation" functions of seven-folds of SU(3) structure of [1] via some connections between elliptic functions, the Heisenberg group, theta functions, the already known $D7$-brane metric [3] and hyper-K\"{a}hler metrics obtained in twistor spaces by deformations of Atiyah-Hitchin manifolds by a Legendre transform in [4].Comment: 12 pages, LaTeX; v3: (JMP) journal version which includes clarifying remarks related to connection between Spin(7)-folds and SU(3)structur

Adaptive Filtering for Large Space Structures: A Closed-Form Solution

In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system

Minimal Uncertainty in Momentum: The Effects of IR Gravity on Quantum Mechanics

The effects of the IR aspects of gravity on quantum mechanics is investigated. At large distances where due to gravity the space-time is curved, there appears nonzero minimal uncertainty $\Delta p_{0}$ in the momentum of a quantum mechanical particle. We apply the minimal uncertainty momentum to some quantum mechanical interferometry examples and show that the phase shift depends on the area surrounded by the path of the test particle . We also put some limits on the related parameters. This prediction may be tested through future experiments. The assumption of minimal uncertainty in momentum can also explain the anomalous excess of the mass of the Cooper pair in a rotating thin superconductor ring.Comment: 8 pages, revised version accepted by PR

Neutron optical beam splitter from holographically structured nanoparticle-polymer composites

We report a breakthrough in the search for versatile diffractive elements for cold neutrons. Nanoparticles are spatially arranged by holographical means in a photopolymer. These grating structures show remarkably efficient diffraction of cold neutrons up to about 50% for effective thicknesses of only 200 micron. They open up a profound perspective for next generation neutron-optical devices with the capability to tune or modulate the neutron diffraction efficiency.Comment: 4 pages, 2 figure

Neutron wave packet tomography

A tomographic technique is introduced in order to determine the quantum state of the center of mass motion of neutrons. An experiment is proposed and numerically analyzed.Comment: 4 pages, 3 figure

Temperature and Kinematics of CIV Absorption Systems

We use Keck HIRES spectra of three intermediate redshift QSOs to study the physical state and kinematics of the individual components of CIV selected heavy element absorption systems. Fewer than 8 % of all CIV lines with column densities greater than 10^{12.5} cm^{-2} have Doppler parameters b < 6 km/s. A formal decomposition into thermal and non-thermal motion using the simultaneous presence of SiIV gives a mean thermal Doppler parameter b_{therm}(CIV) = 7.2 km/s, corresponding to a temperature of 38,000 K although temperatures possibly in excess of 300,000 K occur occasionally. We also find tentative evidence for a mild increase of temperature with HI column density. Non-thermal motions within components are typically small (< 10 km/s) for most systems, indicative of a quiescent environment. The two-point correlation function (TPCF) of CIV systems on scales up to 500 km/s suggests that there is more than one source of velocity dispersion. The shape of the TPCF can be understood if the CIV systems are caused by ensembles of objects with the kinematics of dwarf galaxies on a small scale, while following the Hubble flow on a larger scale. Individual high redshift CIV components may be the building blocks of future normal galaxies in a hierarchical structure formation scenario.Comment: submitted to the ApJ Letters, March 16, 1996 (in press); (13 Latex pages, 4 Postscript figures, and psfig.sty included