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We demonstrate a spectrally correlated photon-pair source at telecom wavelengths (spanning across the S-, C-, and L-bands), based on type-0 spontaneous parametric downconversion (SPDC) in a fiber-coupled Zn-indiffused MgO doped periodically poled lithium niobate (PPLN) ridge waveguide. Modal analysis of the waveguide performed through numerical finite element method (FEM) simulation indicates that device temperature can be used to dramatically vary and control the emission spectrum. Efficient photon-pair generation is measured over a broad wavelength range from ∼1520 − 1580 nm [full width at half maximum (FWHM) > 45 nm] with a coincidence-to-accidental ratio (CAR) as high as ∼668 and spectral brightness ∼2.5 × 107 pairs/s/mW/nm. Such sources can be employed in wavelength division multiplexed (WDM) quantum key distribution (QKD) over existing fiber-optic networks.

We study the effects of pump beam focusing and polarization inhomogeneity on second-harmonic generation (SHG) in a 3 cm long type-II ppKTP crystal. Focusing leads to an asymmetry in the SHG output power around the phase-matching temperature (PMT), along with a shift of the PMT to a lower temperature. Theoretical predictions are experimentally verified for different focusing parameters at various pump wavelengths, showing maximum SHG of 0.24 % W−1 (close to optimal focusing). Further, an inhomogeneous polarization across the pump beam cross-section is theoretically predicted to break up the SHG transverse (intensity) profile into several lobes, resulting in an overall decrease in the total output power. We experimentally show that a radially/azimuthally polarized pump beam (generated via a Q-plate) results in a four-lobed SHG similar to the Hermite–Gaussian HG 11 mode with an optimal focusing parameter that is four times higher than that for the homogeneously polarized pump.

We present optimal designs for nanowaveguides on standard 220-nm SOI platform yielding ultra-broadband phase-matching over bandwidths >500-nm spanning the entire telecommunication spectrum (O-, E-, S-, C-, L-, U- bands, ~1250-1750 nm) for degenerate-pump four-wave mixing (FWM). A complete study of FWM bandwidth as a function of waveguide dimensional parameters like width, etching depth and sidewall slant-angle is presented. Extensive numerical mode simulations show that the proposed device designs exhibit promising tolerances towards fabrication inaccuracies. These designs can be used for WDM (wavelength division multiplexing) systems in classical optical communication and/or broadband photon-pair sources for multi-channel quantum communication.

We have theoretically investigated Zeeman Electromagnetically Induced Transparency (EIT) using the density-matrix formulation in thermal 87Rb vapor and obtained narrow EIT widths ~ 54 KHz with high peak transmissions >85% at room temperature (300 K).

We propose simplified reduced 5-level and 7-level rate equation models to calculate saturated absorption spectra of the Rb D2 line, and experimentally verify for transitions from upper and lower hyperfine ground state of 87Rb, respectively.

We present a 5-level rate model for the Doppler-broadened Rb D2-line absorption spectrum and experimentally verify that it correctly predicts upto 10 × lower saturation intensity as compared to the simple 2-level system, induced by hyperfine pumping.

We theoretically demonstrate the generation of spectrally pure (purity ~ 95%) heralded single photons, and also broadband (~60-nm around 1550-nm) polarization-entangled photon pairs (concurrence>0.96), at telecom wavelengths via extensive dispersion engineering in silicon nano-waveguides.

A compact, fiber-pigtailed, periodically-poled, type II phase-matched, MgO-doped congruent lithium niobate (MgO:ppLN) ridge waveguide module is characterised by 1560nm to 780nm conversion through frequency-doubling at an overall conversion efficiency of 1.408%/W.

Here we theoretically study the spatio-temporal properties of the photons emitted from a narrowband (~ 0.18 nm) type-II spontaneous parametric down-conversion source for a collinear configuration with no/negligible walk-off in a periodically-poled potassium titanyl phosphate (ppKTP) crystal.

We report an efficient source of correlated photons spanning the C- & L-bands of the telecom spectrum with a coincidence-to-accidental ratio (CAR) > 1300 and spectral brightness 2.5x107 pairs/s/mW/nm using a fiber-pigtailed Zn-indiffused MgO:PPLN ridgewaveguide.

We demonstrate the transition of photon-pair generation from the degenerate+collinear to non-degenerate+non-collinear regime by selective tuning of pumpwavelength and crystal temperature in a 3-cm long type-II ppKTP crystal.

We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error < 5 % ) with the experimental data for a wide range of probe intensities (from ∼ 0.001 I s a t 0 all the way up to ∼ 10 I s a t 0 , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width ∼ 1 − 6 mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to ∼ 10 × lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.

We present optimized air-clad silicon waveguides for broadband wavelength conversion spanning nearly the entire telecom band (1260–1625 nm) via degenerate-pump four-wave mixing (FWM). The waveguides with optimized design parameters are fabricated in silicon-on-insulator (SOI) platform with a device layer thickness of 220 nm for experimental demonstration. Wavelength conversion efficiency ∼−20 dB is measured for pump power

We present SOI waveguide designs capable of generating filter-free single photons with high spectral purity (> 98%) at telecom wavelengths via discrete-band phase- matched SFWM. The proposed designs could prove useful for large-scale integrated LOQC networks and long-distance fiber-based QKD.

We study the temporal properties and Schmidt decomposition of the biphotons generated through spontaneous parametric down-conversion in a type-II lithium niobate ridge waveguide, deriving an explicit expression of the mode function for a waveguide.

In this paper, we study the possible parametric down-conversion processes in a type II phase-matched, Lithium Niobate ridge waveguide, designed to generate photon pairs in the telecommunication range. A quantum analysis of spontaneous parametric down-conversion (SPDC), first, with a pulsed Gaussian pump beam and second, with a pulsed, spatially anti-symmetric Hermite-Gaussian HG (1,0) pump beam predict the possible down conversion processes in each case. In case of the former, degenerate photon pairs are emitted at 1550 nm with the highest efficiency in the fundamental waveguide mode. While, in case of the latter, non-degenerate photon pairs in different higher-order spatial modes are generated. The joint spectral amplitude (JSA) analysis of these processes, prove that the generated photons pairs having orthogonal polarizations are negatively correlated. With multiple degrees of freedom, like polarization and spatial modes, such photons can be further harnessed towards modal-entangled and hyper-entangled photons for quantum information applications. This study involving the JSA is one of the first kinds, especially, to show the possibility of photon pairs generated in different spatial modes and polarization, after being incident with a spatially anti-symmetric pump beam in a ridge waveguide scenario.

In this paper, we propose the generation of hyperentangled photon pairs using type-II spontaneous parametric down-conversion in a biperiod, 5% MgO-doped lithium-niobate ridge waveguide. The photon pairs are entangled in spatial mode and polarization degrees of freedom. A pulsed laser source at 687 nm, having an antisymmetric Hermite-Gaussian HG (1,0) spatial mode, is considered as the pump. Down-converted photon pairs, with the signal being at the telecommunication wavelength of 1550 nm, are characterized through a joint spectral amplitude analysis of their biphoton state.

In this paper, we propose a single integrated waveguide device to generate two different polarization-entangled Bell states involving nondegenerate photon pairs (with the signal photons being emitted in the telecom $C$ band) by utilizing type-0, type-I, and type-II quasi-phase-matching (QPM). In this context, we have studied ppKTP (periodically-poled potassium titanyl phosphate) in detail. To obtain polarization entanglement of the emitted photons, we have used two different situations, two cascaded QPM gratings (of the same length) to obtain $|{\ensuremath{\psi}}^{+}\ensuremath{\rangle}$, and two separate QPM gratings (of different lengths) to obtain $|{\ensuremath{\phi}}^{+}\ensuremath{\rangle}$. In such a scenario, maximal entanglement can be quantified in terms of overlap bandwidths of the two phase-matched processes.

We studied the joint spectral intensity (JSI) of modal-entangled photons pairs generated through spontaneous parametric down conversion (SPDC) using a spatial Hermite-Gaussian HG(1,0) pulsed pump beam in a periodically-poled lithium niobate (ppLN) ridge waveguide.

In this paper, we propose the generation of all four polarization-entangled Bell states in a potassium titanyl phosphate waveguide device. This is achieved through non-degenerate spontaneous parametric downconversion and quasi-phase-matching with special non-uniform poling in different lengths. These biphoton states consist of the signal being emitted in a telecommunication wavelength. Through their joint spectral amplitude, we study the frequency correlation properties of the photon pairs. Polarization-entangled photon pairs are used as a resource of entanglement in various quantum optics experiments and there is a demand for generating all four photonic Bell states in a single waveguide-based device in quantum information applications.

North Atlantic tropical cyclones (TCs) and hurricanes are responsible for a large number of fatalities and economic damage. Skillful seasonal predictions of the North Atlantic TC activity can provide basic information critical to our improved preparedness. This study focuses on the development of statistical–dynamical seasonal forecasting systems for different quantities related to the frequency and intensity of North Atlantic TCs. These models use only tropical Atlantic and tropical mean sea surface temperatures (SSTs) to describe the variability exhibited by the observational records because they reflect the importance of both local and non-local effects on the genesis and development of TCs in the North Atlantic basin. A set of retrospective forecasts of SSTs by six experimental seasonal-to-interannual prediction systems from the North American Multi-Model Ensemble are used as covariates. The retrospective forecasts are performed over the period 1982–2015. The skill of these statistical–dynamical models is quantified for different quantities (basin-wide number of tropical storms and hurricanes, power dissipation index and accumulated cyclone energy) for forecasts initialized as early as November of the year prior to the season to forecast. The results of this work show that it is possible to obtain skillful retrospective forecasts of North Atlantic TC activity with a long lead time. Moreover, probabilistic forecasts of North Atlantic TC activity for the 2016 season are provided.

In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy distributions as default priors for the regression coefficients in logistic regression, even in the case of separation, and reported posterior modes in their analyses. As the mean does not exist for the Cauchy prior, a natural question is whether the posterior means of the regression coefficients exist under separation. We prove theorems that provide necessary and sufficient conditions for the existence of posterior means under independent Cauchy priors for the logit link and a general family of link functions, including the probit link. We also study the existence of posterior means under multivariate Cauchy priors. For full Bayesian inference, we develop a Gibbs sampler based on Pólya-Gamma data augmentation to sample from the posterior distribution under independent Student- $t$ priors including Cauchy priors, and provide a companion R package $\mathtt{tglm}$ , available at CRAN. We demonstrate empirically that even when the posterior means of the regression coefficients exist under separation, the magnitude of the posterior samples for Cauchy priors may be unusually large, and the corresponding Gibbs sampler shows extremely slow mixing. While alternative algorithms such as the No-U-Turn Sampler (NUTS) in Stan can greatly improve mixing, in order to resolve the issue of extremely heavy tailed posteriors for Cauchy priors under separation, one would need to consider lighter tailed priors such as normal priors or Student- $t$ priors with degrees of freedom larger than one.

In this article, we highlight some interesting facts about Bayesian variable selection methods for linear regression models in settings where the design matrix exhibits strong collinearity. We first demonstrate via real data analysis and simulation studies that summaries of the posterior distribution based on marginal and joint distributions may give conflicting results for assessing the importance of strongly correlated covariates. The natural question is which one should be used in practice. The simulation studies suggest that posterior inclusion probabilities and Bayes factors that evaluate the importance of correlated covariates jointly are more appropriate, and some priors may be more adversely affected in such a setting. To obtain a better understanding behind the phenomenon, we study some toy examples with Zellner’s g-prior. The results show that strong collinearity may lead to a multimodal posterior distribution over models, in which joint summaries are more appropriate than marginal summaries. Th...

Our improved capability to adapt to the future changes in discharge is linked to our capability to predict the magnitude or at least the direction of these changes. For the agricultural United States Midwest, too much or too little water has severe socioeconomic impacts. Here, we focus on the Raccoon River at Van Meter, Iowa, and use a statistical approach to examine projected changes in discharge. We build on statistical models using rainfall and harvested corn and soybean acreage to explain the observed discharge variability. We then use projections of these two predictors to examine the projected discharge response. Results are based on seven global climate models part of the Coupled Model Intercomparison Project Phase 5 and two representative concentration pathways (RCPs 4.5 and 8.5). There is not a strong signal of change in the discharge projections under the RCP 4.5. However, the results for the RCP 8.5 point to a stronger changing signal related to larger projected increases in rainfall, resulting in increased trends, in particular, in the upper part of the discharge distribution (i.e., 60th percentile and above). Examination of two hypothetical agricultural scenarios indicates that these increasing trends could be alleviated by decreasing the extent of the agricultural production. We also discuss how the methodology presented in this study represents a viable approach to move forward with the concept of return period for engineering design and management in a nonstationary world.

In the Bayesian approach to model selection, models and model specific parameters are treated as unknown quantities and uncertainty about them are expressed through prior distributions. Given the observed data, updating of the prior distribution to the posterior distribution occurs via Bayes' theorem. The posterior probability of a given model may be interpreted as the support it gets based on the observed data. The highest probability model (HPM) that receives the maximum support from the data is a possible choice for model selection. For large model spaces, Markov chain Monte Carlo (MCMC) algorithms are commonly used to estimate the posterior distribution over models. However, estimates of posterior probabilities of individual models based on MCMC output are not reliable because the number of MCMC samples is typically far smaller than the size of the model space. Thus, the HPM is difficult to estimate and for large model spaces it often has a very small posterior probability. An alternative to the HPM is the median probability model (MPM) of Barbieri and Berger, which has been shown to be the optimal model for prediction using a squared error loss function, under certain conditions. In this article we review some of the conditions for which the MPM is optimal, and provide real data examples to evaluate the performance of the MPM under small and large model spaces. We also discuss the behavior of the MPM under collinearity. WIREs Comput Stat 2015, 7:185–193. doi: 10.1002/wics.1352 For further resources related to this article, please visit the WIREs website. Conflict of interest: The author has declared no conflicts of interest for this article.

When multiple data owners possess records on different subjects with the same set of attributes--known as horizontally partitioned data--the data owners can improve analyses by concatenating their databases. However, concatenation of data may be infeasible because of confidentiality concerns. In such settings, the data owners can use secure computation techniques to obtain the results of certain analyses on the integrated database without sharing individual records. We present secure computation protocols for Bayesian model averaging and model selection for both linear regression and probit regression. Using simulations based on genuine data, we illustrate the approach for probit regression, and show that it can provide reasonable model selection outputs.

Monte Carlo algorithms are commonly used to identify a set of models for Bayesian model selection or model averaging. Because empirical frequencies of models are often zero or one in high-dimensional problems, posterior probabilities calculated from the observed marginal likelihoods, renormalized over the sampled models, are often employed. Such estimates are the only recourse in several newer stochastic search algorithms. In this paper, we prove that renormalization of posterior probabilities over the set of sampled models generally leads to bias that may dominate mean squared error. Viewing the model space as a finite population, we propose a new estimator based on a ratio of Horvitz--Thompson estimators that incorporates observed marginal likelihoods, but is approximately unbiased. This is shown to lead to a reduction in mean squared error compared to the empirical or renormalized estimators, with little increase in computational cost. Copyright 2012, Oxford University Press.

A three-level atom in a Λ configuration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. This system allows for efficient storage of cavity photons into long-lived atomic excitations, and their retrieval with high fidelity, in an adiabatic transfer process through the ‘dark state’ by a slow variation of the control laser intensity. We study the full quantum mechanics of this transfer process with a view to examine the non-adiabatic effects arising from inevitable excitations of the system to states involving the upper level of Λ, which is radiative. We find that the fidelity of storage is better, the stronger the control field and the slower the rate of its switching off. On the contrary, unlike the adiabatic notion, retrieval is better with faster rates of switching on of an optimal control field. Also, for retrieval, the behaviour with dissipation is non-monotonic. These results lend themselves to experimental tests. Our exact computations, when applied to slow variations of the control intensity for strong atom–photon couplings, are in very good agreement with Berry’s superadiabatic transfer results without dissipation.

Choosing the subset of covariates to use in regression or generalized linear models is a ubiquitous problem. The Bayesian paradigm addresses the problem of model uncertainty by considering models corresponding to all possible subsets of the covariates, where the posterior distribution over models is used to select models or combine them via Bayesian model averaging (BMA). Although conceptually straightforward, BMA is often difficult to implement in practice, since either the number of covariates is too large for enumeration of all subsets, calculations cannot be done analytically, or both. For orthogonal designs with the appropriate choice of prior, the posterior probability of any model can be calculated without having to enumerate the entire model space and scales linearly with the number of predictors, p. In this article we extend this idea to a much broader class of nonorthogonal design matrices. We propose a novel method which augments the observed nonorthogonal design by at most p new rows to obtain...

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.

We study modal characteristics of a customized ridge waveguide in lithium niobate designed to generate twin photons at telecom wavelength. A quantum analysis of SPDC predicts the possible down conversion processes and optimizes the input beam parameters for fundamental mode emission. Further, a joint spectral amplitude analysis ensures that the parameters are ambient for generating frequency-correlated photons throughout the phase-matching spectrum. Moreover, negatively correlated degenerate signal/idler photon pairs in the fundamental mode emission occurs at 1550 nm. A key result of our paper is an explicit expression and plot for comparing the generated signal power in case of waveguides as compared to bulk crystals. Our calculations clearly show a dependence of for a waveguide of length compared to a linear dependence in case of a bulk crystal.

Electromagnetically-induced transparency (EIT) in three-level Λ-systems is based on quantum interference effects involving coherence between the two lower levels, which allow propagation of a resonant probe light beam in the presence of a strong coupling field. We have observed transparency in ultra-narrow (

4He∗ at room temperature is a particularly interesting system as velocity changing collisions (VCCs) are necessary to observe ultra-narrow (less than 10 kHz) EIT windows for purely electronic spins in the presence of Doppler broadening. Such narrow resonances are known to be linked to a dramatic reduction of the group velocity of a probe pulse, although the medium is transparent. The evolution of the delay is recorded with respect to the coupling beam intensity and to small Raman detunings. We also demonstrate that it is possible to use optically detuned resonances (Fano-like profiles) to see a transition from slow light to negative group velocity. All these measurements are found to be in good agreement with a simple model based on an effective homogeneous linewidth. To cite this article: F. Goldfarb et al., C. R. Physique 10 (2009).

Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal prior distributions for factor loadings and inverse gamma prior distributions for residual variances are a popular choice because of their conditionally conjugate form. However, such prior distributions require elicitation of many hyperparameters and tend to result in poorly behaved Gibbs samplers. In addition, one must choose an informative specification, as high variance prior distributions face problems due to impropriety of the posterior distribution. This article proposes a default, heavy-tailed prior distribution specification, which is induced through parameter expansion while facilitating efficient posterior computation. We also develop an approach to allow uncertainty in the number of factors. The methods are illustrated through simulated examples and epidemiology and toxicology applications. Data sets and computer code used in this article are available online.

When several data owners possess data on different records but the same variables, known as horizontally partitioned data, the owners can improve statistical inferences by sharing their data with each other. Often, however, the owners are unwilling or unable to share because the data are confidential or proprietary. Secure computation protocols enable the owners to compute parameter estimates for some statistical models, including linear regressions, without sharing individual records' data. A drawback to these techniques is that the model must be specified in advance of initiating the protocol, and the usual exploratory strategies for determining good-fitting models have limited usefulness since the individual records are not shared. In this paper, we present a protocol for secure adaptive regression splines that allows for flexible, semi-automatic regression modeling. This reduces the risk of model mis-specification inherent in secure computation settings. We illustrate the protocol with air pollution data.

In this work we present a simple method to reconstruct the complex spectral wavefunction of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, is applicable to biphoton states produced with a monochromatic pump when a shift of the pump frequency produces a shift in the relative frequencies contributing to the biphoton. We demonstrate an example of such a situation in type-II parametric down-conversion (SPDC) allowing arbitrary paraxial spatial pump and detection modes. Moreover, our test cases demonstrate the possibility to shape the spectral wavefunction. This is achieved by choosing the spatial mode of the pump and of the detection modes, and takes advantage of spatiotemporal correlations., Supplementary information also available. Comments and feedback appreciated. Compared to the previous version, here we have made the following changes: -corrected a typo in the text between Eq. (11) and (12) -corrected a typo in the references -added references

We propose a method to study and characterize the spatial and temporal properties of degenerate photon pairs emitted in SPDC, using a filtering system combined with temperature variation of the nonlinear crystal. The photons can be distinguished. We relate these to the measured Hong-Ou-Mandel interference dip of the photons, measured in a parallel experiment. The theoretical plots match very well with the experimental results.