Stability, Gain, and Robustness in Quantum Feedback Networks

This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and algebraic relationships determined by the network. Quantum feedback networks are shown to be stable if the loop gain is less than one-this is an extension of the famous small gain theorem of classical control theory. We illustrate the simplicity and power of the small gain approach with applications to important problems of robust stability and robust stabilization.Comment: 16 page

Early phase observations of extremely luminous Type Ia Supernova 2009dc

We present early phase observations in optical and near-infrared wavelengths for the extremely luminous Type Ia supernova (SN Ia) 2009dc. The decline rate of the light curve is $\Delta m_{15}(B)=0.65\pm 0.03$, which is one of the slowest among SNe Ia. The peak $V$-band absolute magnitude is $M_{V}=-19.90\pm 0.15$ mag even if the host extinction is $A_{V}=0$ mag. It reaches $M_{V}=-20.19\pm 0.19$ mag for the host extinction of $A_{V}=0.29$ mag as inferred from the observed Na {\sc i} D line absorption in the host. Our $JHK_{s}$-band photometry shows that the SN is one of the most luminous SNe Ia also in near-infrared wavelengths. These results indicate that SN 2009dc belongs to the most luminous class of SNe Ia, like SN 2003fg and SN 2006gz. We estimate the ejected $^{56}$Ni mass of $1.2\pm 0.3$ \Msun for no host extinction case (or 1.6$\pm$ 0.4 M$_{\odot}$ for the host extinction of $A_{V}=0.29$ mag). The C {\sc ii} $\lambda$6580 absorption line keeps visible until a week after maximum, which diminished in SN 2006gz before its maximum brightness. The line velocity of Si {\sc ii} $\lambda$6355 is about 8000 km s$^{-1}$ around the maximum, being considerably slower than that of SN 2006gz, while comparable to that of SN 2003fg. The velocity of the C {\sc ii} line is almost comparable to that of the Si {\sc ii}. The presence of the carbon line suggests that thick unburned C+O layers remain after the explosion. SN 2009dc is a plausible candidate of the super-Chandrasekhar mass SNe Ia

Ferromagnetism in multi--band Hubbard models: From weak to strong Coulomb repulsion

We propose a new mechanism which can lead to ferromagnetism in Hubbard models containing triangles with different on-site energies. It is based on an effective Hamiltonian that we derive in the strong coupling limit. Considering a one-dimensional realization of the model, we show that in the quarter-filled, insulating case the ground-state is actually ferromagnetic in a very large parameter range going from Tasaki's flat-band limit to the strong coupling limit of the effective Hamiltonian. This result has been obtained using a variety of analytical and numerical techniques. Finally, the same results are shown to apply away from quarter-filling, in the metallic case.Comment: 12 pages, revtex, 12 figures,needs epsf and multicol style file

Improving the Prospects for Detecting Extrasolar Planets in Gravitational Microlensing in 2002

Gravitational microlensing events of high magnification have been shown to be promising targets for detecting extrasolar planets. However, only a few events of high magnification have been found using conventional survey techniques. Here we demonstrate that high magnification events can be readily found in microlensing surveys using a strategy that combines high frequency sampling of target fields with online difference imaging analysis. We present 10 microlensing events with peak magnifications greater than 40 that were detected in real-time towards the Galactic Bulge during 2001 by MOA. We show that Earth mass planets can be detected in future events such as these through intensive follow-up observations around the event peaks. We report this result with urgency as a similar number of such events are expected in 2002.Comment: 11 pages, 3 embedded ps figures including 2 colour, revised version accepted by MNRA

Microlensing optical depth towards the Galactic bulge from MOA observations during 2000 with Difference Image Analysis

We analyze the data of the gravitational microlensing survey carried out by by the MOA group during 2000 towards the Galactic Bulge (GB). Our observations are designed to detect efficiently high magnification events with faint source stars and short timescale events, by increasing the the sampling rate up to 6 times per night and using Difference Image Analysis (DIA). We detect 28 microlensing candidates in 12 GB fields corresponding to 16 deg^2. We use Monte Carlo simulations to estimate our microlensing event detection efficiency, where we construct the I-band extinction map of our GB fields in order to find dereddened magnitudes. We find a systematic bias and large uncertainty in the measured value of the timescale $t_{\rm Eout}$ in our simulations. They are associated with blending and unresolved sources, and are allowed for in our measurements. We compute an optical depth tau = 2.59_{-0.64}^{+0.84} \times 10^{-6} towards the GB for events with timescales 0.3<t_E<200 days. We consider disk-disk lensing, and obtain an optical depth tau_{bulge} = 3.36_{-0.81}^{+1.11} \times 10^{-6}[0.77/(1-f_{disk})] for the bulge component assuming a 23% stellar contribution from disk stars. These observed optical depths are consistent with previous measurements by the MACHO and OGLE groups, and still higher than those predicted by existing Galactic models. We present the timescale distribution of the observed events, and find there are no significant short events of a few days, in spite of our high detection efficiency for short timescale events down to t_E = 0.3 days. We find that half of all our detected events have high magnification (>10). These events are useful for studies of extra-solar planets.Comment: 65 pages and 30 figures, accepted for publication in ApJ. A systematic bias and uncertainty in the optical depth measurement has been quantified by simulation

Probing the atmosphere of a solar-like star by galactic microlensing at high magnification

We report a measurement of limb darkening of a solar-like star in the very high magnification microlensing event MOA 2002-BLG-33. A 15 hour deviation from the light curve profile expected for a single lens was monitored intensively in V and I passbands by five telescopes spanning the globe. Our modelling of the light curve showed the lens to be a close binary system whose centre-of-mass passed almost directly in front of the source star. The source star was identified as an F8-G2 main sequence turn-off star. The measured stellar profiles agree with current stellar atmosphere theory to within ~4% in two passbands. The effective angular resolution of the measurements is <1 micro-arcsec. These are the first limb darkening measurements obtained by microlensing for a Solar-like star.Comment: Accepted for publication in A&A Letters. 5 pages, 2 embedded colour ps figures plus 1 jpg figure. Version with all figures embedded available from: http://www.roe.ac.uk/~iab/moa33paper