Quantum noise in optical interferometers

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum is injected into the usually unused input port. It is investigated under which conditions the gravitational wave signal may be amplified without increasing counting noise concurrently. Such a possibility was suggested as a consequence of the entanglement of the two output ports of a beam splitter. We find that amplification without concurrent increase of noise is not possible for reasonable squeezing parameters. Photon distributions for various beam splitter angles and squeezing parameters are calculated.Comment: 15 pages, 7 figure

Cohomology of Conformal Algebras

Conformal algebra is an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality property. The main examples of such Lie algebras are those ``based'' on the punctured complex plane, like the Virasoro algebra and loop algebras. In the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module. It possesses standard properties of cohomology theories; for example, it describes extensions and deformations. We offer explicit computations for most of the important examples.Comment: 46 pp., AMSLaTeX, uses epsfig, amssymb, amsc

Reduction of quantum noise in optical interferometers using squeezed light

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so called `dark port case', when the beam splitter is oriented close to 90{\deg} to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (`dark port'). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R.Barak and Y.Ben-Aryeh, J.Opt.Soc.Am.B25(361)2008]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.Comment: 8 pages, 1 figur

Q-phonon description of low lying 1^- two-phonon states in spherical nuclei

The properties of 1^-_1 two-phonon states and the characteristics of E1 transition probabilities between low-lying collective states in spherical nuclei are analysed within the Q-phonon approach to the description of collective states. Several relations between observables are obtained. Microscopic calculations of the E1 0^+_1 -> 1^-_1 transition matrix elements are performed on the basis of the RPA. A satisfactory description of the experimental data is obtained.Comment: 16 pages, 2 figures, 9 table

On Weyl Quantization from geometric Quantization

A. Weinstein has conjectured a nice looking formula for a deformed product of functions on a hermitian symmetric space of non-compact type. We derive such a formula for symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional symplectic manifolds: the euclidean plane, the sphere and the hyperbolic plane. For the euclidean plane we obtain the well known Moyal-Weyl product. The other cases show that Weinstein's original idea should be interpreted with care. We conclude with comments on the status of our result.Comment: 11 pages. (v2: corrected a couple of typos

Quantum correlations of twophoton polarization states in the parametric down-conversion process

We consider correlation properties of twophoton polarization states in the parametric down-conversion process. In our description of polarization states we take into account the simultaneous presence of colored and white noise in the density matrix. Within the considered model we study the dependence of the von Neumann entropy on the noise amount in the system and derive the separability condition for the density matrix of twophoton polarization state, using Perec-Horodecki criterion and majorization criterion. Then the dependence of the Bell operator (in CHSH form) on noise is studied. As a result, we give a condition for determining the presence of quantum correlation states in experimental measurements of the Bell operator. Finally, we compare our calculations with experimental data [doi:10.1103/PhysRevA.73.062110] and give a noise amount estimation in the photon polarization state considered there.Comment: 10 pages, 7 figures; corrected typo

Higher Derivative Quantum Gravity with Gauss-Bonnet Term

Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4-\epsilon$ renormalization group for this theory, an approach which proved fruitful in $2-\epsilon$ models. A consistent formulation in dimension $n=4-\epsilon$ requires taking quantum effects of the topological term into account, hence we perform calculation which is more general than the ones done before. In the special $n=4$ case we confirm a known result by Fradkin-Tseytlin and Avramidi-Barvinsky, while contributions from topological term do cancel. In the more general case of $4-\epsilon$ renormalization group equations there is an extensive ambiguity related to gauge-fixing dependence. As a result, physical interpretation of these equations is not universal unlike we treat $\epsilon$ as a small parameter. In the sector of essential couplings one can find a number of new fixed points, some of them have no analogs in the $n=4$ case.Comment: LaTeX file, 30 pages, 5 figures. Several misprints in the intermediate expressions correcte

How to turn a brand's friends (and detractors) into evangelists: The case of Canadian wine

With conversion rituals, cool-climate wineries in Ontario managed to overcome a reputation for low quality, write Felipe G. Massa, Wesley Helms, Maxim Voronov and Liang Wan

Digital twins in logistics

The logistics industry has undergone significant transformation over the years, thanks to advancements in technology. One of the most promising technologies disrupting the industry is digital twins. In this article, we explore the concept of digital twins in logistics, their benefits, and their potential impact on the industry