Continuous variable entanglement of phase locked light beams

We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in self-phase locked nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing high level phase coherence between two generated modes, unlike to the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing(that is 50% relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of self-phase locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, non-dissipative dynamics of the system under consideration is also cleared up

Quadrature entanglement and photon-number correlations accompanied by phase-locking

We investigate quantum properties of phase-locked light beams generated in a nondegenerate optical parametric oscillator (NOPO) with an intracavity waveplate. This investigation continuous our previous analysis presented in Phys.Rev.A 69, 05814 (2004), and involves problems of continuous-variable quadrature entanglement in the spectral domain, photon-number correlations as well as the signatures of phase-locking in the Wigner function. We study the role of phase-localizing processes on the quantum correlation effects. The peculiarities of phase-locked NOPO in the self-pulsing instability operational regime are also cleared up. The results are obtained in both the P-representation as a quantum-mechanical calculation in the framework of stochastic equations of motion, and also by using numerical simulation based on the method of quantum state diffusion.Comment: Subm. to PR

Semiparametric estimation for a class of time-inhomogenous diffusion processes

Copyright @ 2009 Institute of Statistical Science, Academia SinicaWe develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines

Using XMM-Newton to study the energy dependent variability of H 1743-322 during its 2014 outburst

Black hole transients during bright outbursts show distinct changes of their spectral and variability properties as they evolve during an outburst, that are interpreted as evidence for changes in the accretion flow and X-ray emitting regions. We obtained an anticipated XMM-Newton ToO observation of H 1743-322 during its outburst in September 2014. Based on data of eight outbursts observed in the last 10 years we expected to catch the start of the hard-to-soft state transition. The fact that neither the general shape of the observed power density spectrum nor the characteristic frequency show an energy dependence implies that the source still stays in the low-hard state at the time of our observation near outburst peak. The spectral properties agree with the source being in the low-hard state and a Swift/XRT monitoring of the outburst reveals that H 1743-322 stays in the low-hard state during the entire outburst (a. k. a. 'failed outburst'). We derive the averaged QPO waveform and obtain phase-resolved spectra. Comparing the phase-resolved spectra to the phase averaged energy spectrum reveals spectral pivoting. We compare variability on long and short time scales using covariance spectra and find that the covariance ratio does not show an increase towards lower energies as has been found in other black hole X-ray binaries. There are two possible explanations: either the absence of additional disc variability on longer time scales is related to the rather high inclination of H 1743-322 compared to other black hole X-ray binaries or it is the reason why we observe H 1743-322 during a failed outburst. More data on failed outbursts and on high-inclination sources will be needed to investigate these two possibilities further.Comment: 9 pages, 7 figures, accepted by MNRA

Detection of distinct power spectra in soft and hard X-ray bands in the hard state of GRS 1915+105

The well-known black hole X-ray binary GRS 1915+105 is a unique source in the sense that it cannot be classified within the standard picture of black hole binary states. In this work we study archival XMM-Newton observations taken between 2003 and 2004 of the \c{hi} variability class of GRS 1915+105, which corresponds to the hard state in the standard black hole X-ray binary state classification. The crucial point of our study is that by using XMM-Newton data we can access the variability below 3 keV, an energy range that is not covered with RXTE. We focus on the study of the power spectral shape in the soft and hard X-ray band, in light of our work done with Swift on MAXI J1659-152. In the hard band (above 2.5 keV) power density spectra consist of band-limited noise and quasi-periodic oscillations, corresponding to the power spectral shape seen in the hard or intermediate state, while in the soft band the averaged power density spectrum is consistent with a power-law noise, corresponding to the power spectral shape usually seen in the soft state. The coexisting of two different power spectral shapes in the soft and hard band, where the soft band power spectrum is dominated by a power-law noise, is consistent with MAXI J1659-152, and confirms the energy dependence of power spectral states. Our additional spectral analysis shows that the disc component does contribute to the soft band flux. These findings support that the observed black hole power spectral state depends on which spectral component we are looking at, which implies that power spectral analysis is probably a more sensitive method than spectral modeling to trace the emergence of the disc component in the hard or intermediate state.Comment: 9 pages, 5 figures, submitted to MNRA

Coherent State Control of Non-Interacting Quantum Entanglement

We exploit a novel approximation scheme to obtain a new and compact formula for the parameters underlying coherent-state control of the evolution of a pair of entangled two-level systems. It is appropriate for long times and for relatively strong external quantum control via coherent state irradiation. We take account of both discrete-state and continuous-variable degrees of freedom. The formula predicts the relative heights of entanglement revivals and their timing and duration.Comment: Published in PRA, 10 pages, 7 figure

Sudden Death of Entanglement of Two Jaynes-Cummings Atoms

We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.Comment: 3 pages, 3 figure