Nano-displacement measurements using spatially multimode squeezed light

We demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below the quantum noise limit.Comment: 21 pages, 9 figures, submitted to "Special Issue on Fluctuations & Noise in Photonics & Quantum Optics" of J. Opt.

DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction

We discuss the perturbative approach a` la Dyson to a quantum field theory with nonlocal self-interaction :phi*...*phi:, according to Doplicher, Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction of non locally time--ordered products of Wick monomials can be performed as usual, and we discuss a very simple Dyson diagram.Comment: 15 pages, pdf has active hyperlinks. To appear in the proceedings of the conference on "Rigorous quantum Field Theory", held at Saclay on July 19-21, 2004, on the occasion of Jacques Bros' 70th birthda

Optimum Small Optical Beam Displacement Measurement

We derive the quantum noise limit for the optical beam displacement of a TEM00 mode. Using a multimodal analysis, we show that the conventional split detection scheme for measuring beam displacement is non-optimal with 80% efficiency. We propose a new displacement measurement scheme that is optimal for small beam displacement. This scheme utilises a homodyne detection setup that has a TEM10 mode local oscillator. We show that although the quantum noise limit to displacement measurement can be surpassed using squeezed light in appropriate spatial modes for both schemes, the TEM10 homodyning scheme out-performs split detection for all values of squeezing.Comment: 13 pages, 7 figure

Characterization of Turing diffusion-driven instability on evolving domains

In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains. The main result is that Turing diffusion-driven instability for reaction-diffusion systems on evolving domains is characterised by Lyapunov exponents of the evolution family associated with the linearised system (obtained by linearising the original system along a spatially independent solution). This framework allows for the inclusion of the analysis of the long-time behavior of the solutions of reaction-diffusion systems. Applications to two special types of evolving domains are considered: (i) time-dependent domains which evolve to a final limiting fixed domain and (ii) time-dependent domains which are eventually time periodic. Reaction-diffusion systems have been widely proposed as plausible mechanisms for pattern formation in morphogenesis

Synthesis optimization of carbon-supported ZrO2 nanoparticles from different organometallic precursors

Abstract We report here the synthesis of carbon-supported ZrO2 nanoparticles from zirconium oxyphthalocyanine (ZrOPc) and acetylacetonate [Zr(acac)4]. Using thermogravimetric analysis (TGA) coupled with mass spectrometry (MS), we could investigate the thermal decomposition behavior of the chosen precursors. According to those results, we chose the heat treatment temperatures (T HT) using partial oxidizing (PO) and reducing (RED) atmosphere. By X-ray diffraction we detected structure and size of the nanoparticles; the size was further confirmed by transmission electron microscopy. ZrO2 formation happens at lower temperature with Zr(acac)4 than with ZrOPc, due to the lower thermal stability and a higher oxygen amount in Zr(acac)4. Using ZrOPc at T HT ≥900 °C, PO conditions facilitate the crystallite growth and formation of distinct tetragonal ZrO2, while with Zr(acac)4 a distinct tetragonal ZrO2 phase is observed already at T HT ≥750 °C in both RED and PO conditions. Tuning of ZrO2 nanocrystallite size from 5 to 9 nm by varying the precursor loading is also demonstrated. The chemical state of zirconium was analyzed by X-ray photoelectron spectroscopy, which confirms ZrO2 formation from different synthesis routes

Perturbation theory of the space-time non-commutative real scalar field theories

The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian formalism of the second quantized operators, with the emphasis of the so-called minimal realization of the time-ordering step function and of the importance of the $\star$-time ordering. The Feynman rule is established and is presented using $\phi^4$ scalar field theory. It is shown that the divergence structure of space-time non-commutative theory is the same as the one of space-space non-commutative theory, while there is no UV-IR mixing problem in this space-time non-commutative theory.Comment: Latex 26 pages, notations modified, add reference