This document briefly reviews recent short-range gravity experiments that were performed at below laboratory scales to test the Newtonian inverse square law of gravity. To compare sensitivities of these measurements, estimates using the conventional Yukawa parametrization are introduced. Since these experiments were triggered by the prediction of the large extra-dimension model, experiments performed at different length scales are compared with this prediction. In this paper, a direct comparison between laboratory-scale experiments and the LHC results is presented for the first time. A laboratory experiment is shown to determine the best limit at M D > 4.6 TeV and λ < 23 µm. In addition, new analysis results are described for atomic systems used as gravitational microlaboratories.

It is known that weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment, implies the possibility to estimate a very small parameter using the weak measurement technique. But does the weak measurement really bring about the increase of ginformationh for parameter estimation? This paper clarifies that, in a general situation, the answer is NO; more precisely, the weak measurement cannot further decrease the lower bound of the estimation error, i.e. the so-called CramLer-Rao bound, which is proportional to the inverse of the quantum Fisher information.

We analyze the amplification by the Aharonov-Albert-Vaidman weak quantum measurement on a Sagnac interferometer [P. B. Dixon et al., Phys. Rev. Lett. 102, 173601 (2009)] up to all orders of the coupling strength between the measured system and the measuring device. The amplifier transforms a small tilt of a mirror into a large transverse displacement of the laser beam. The conventional analysis has shown that the measured value is proportional to the weak value, so that the amplification can be made arbitrarily large in the cost of decreasing output laser intensity. It is shown that the measured displacement and the amplification factor are in fact not proportional to the weak value and rather vanish in the limit of infinitesimal output intensity. We derive the optimal overlap of the pre-and post-selected states with which the amplification become maximum. We also show that the nonlinear effects begin to arise in the performed experiments so that any improvements in the experiment, typically with an amplification greater than 100, should require the nonlinear theory in translating the observed value to the original displacement.Introduction.-The standard theory of measurement in quantum mechanics deals with the situation that one performes a measurement on a quantum state to obtain a measured value and the resulting state according to certain probabilitic laws. It was established by von Neumann [1] in the case of projective measurements and generalized later to non-projective measurements [2][3][4]. In experiments as well as in theory, weak measurements, where the system is weakly coupled with, hence weakly disturbed by, the measuring device, have been widely considered and have proved to be useful.Aharonov, Albert, and Vaidman (AAV) [5] proposed a particular type of weak measurement which is characterized by the pre-and post-selection (PPS) of the system. One prepares the initial state |i of the system and that |Φ i of the device, and after a certain interaction between the system and the meter, one post-selects a state |f of the system and reads the meter value. If one measures an observable A of the system, one obtains the weak value

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A systematic investigation of the polymerization of representative diphenylacetylenes with TaCl 5 and cocatalysts suggested that low-valent Ta species, which are formed by in situ reduction of TaCl 5 by the cocatalysts, are involved in the polymerization and that the polymerization reaction proceeds by an insertion ring expansion mechanism via the formation of tantalacyclopentadiene intermediates, rather than the previously considered metathesis mechanism. This polymerization mechanism indicates the production of unprecedented cis-stereoregular cyclic poly(diphenylacetylene)s. Indeed, the possibilities of a cyclic structure and high cis-stereoregularity of the resulting polymers were reasonably supported by the results of their detailed atomic force microscopy (AFM) and NMR analyses, respectively.