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We show that almost all $\pi_1$-injective proper maps between two non-compact surfaces, where surfaces are possibly of infinite type, can be properly homotoped to finite-sheeted covering maps., Comment: 19 Pages, 1 figure. Comments welcome!

We show that a homotopy equivalence between two non-compact orientable surfaces is homotopic to a homeomorphism if and only if it preserves the Goldman bracket, provided our surfaces are neither the plane nor the punctured plane., Comment: to appear in Algebraic and Geometric Topology

We show that finite-type surfaces are characterized by a topological analog of the Hopf property. Namely, an oriented surface $\Sigma$ is of finite-type if and only if every proper map $f\colon\Sigma\to \Sigma$ of degree one is homotopic to a homeomorphism., Comment: 8 pages, 4 figures. v2: incorporates the referee's comments, accepted in the Comptes Rendus Math\'ematique

We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided surfaces are neither the plane nor the punctured plane. Thus all non-compact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense., Comment: 42 pages, 9 figures. v3: incorporates the referee's comments, accepted in the Algebraic & Geometric Topology

We investigate the possibility of realizing a loophole-free violation of Bell's inequality using deterministic single-photon sources. We provide a detailed analysis of a scheme to achieve such violations over long distances with immediate extensions to device-independent quantum key distribution. We investigate the effect of key experimental imperfections that are unavoidable in real-world single-photon sources including the finite degree of photon indistinguishability, single-photon purity, and the overall source efficiency. We benchmark the performance requirements to state-of-the-art deterministic single-photon sources based on quantum dots in photonic nanostructures and find that experimental realizations appear to be within reach. We also evaluate the requirements for a post-selected version of the protocol, which relaxes the demanding requirements with respect to the source efficiency., Comment: 17 pages, 8 figures

The authors [3] proved that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and described its monolith. Here we prove that the endomorphism semiring of a commutative inverse semigroup with at least two idempotents is always subdirectly irreducible and describe its monolith.

We develop a formalism based on a time-dependent wave-function ansatz to study correlations of photons emitted from a collection of two-level quantum emitters. We show how to simulate the system dynamics and evaluate the intensity of the scattered photons and the second-order correlation function $g^{(2)}$ in terms of the amplitudes of the different components of the wave function. Our approach is efficient for considering systems that contain up to two excitations. To demonstrate this we first consider the example of spectral filtering of photons emitted from a single quantum emitter. We show how our formalism can be used to study spectral filtering of the two-photon component of the emitted light from a single quantum emitter for various kinds of filters. Furthermore, as a general application of our formalism, we show how it can be used to study photon-photon correlations in an optically dense ensemble of two-level quantum emitters. In particular we lay out the details of simulating correlated photon transport in such ensembles reported recently by S. Mahmoodian {\it et.al.} [Phys. Rev. Lett. {\bf 121}, 143601 (2018)]. Compared to other existing techniques, the advantage of our formalism is that it is applicable to any generic spectral filter and quantum many-body systems involving a large number of quantum emitters while requiring only a modest computational resource., Comment: 20 pages, 8 figures

Due to its ability to bond with living tissues upon dissolution, 45S5 bioglass and related compositions are promising materials for the replacement, regeneration, and repair of hard tissues in the human body. However, the details of their atomic structure remain unclear. This is partially due to the non-equilibrium nature of glasses, as their non-crystalline structure is highly dependent on their thermal history, namely, the cooling rate used during quenching. Herein, using molecular dynamics (MD) simulations and magic angle spinning nuclear magnetic resonance (MAS-NMR) spectroscopy experiments, we investigate the structure of the nominal 45S5 bioglass composition prepared using cooling rates ranging over several orders of magnitude. We show that the simulations results are in very good agreement with experimental data, provided that they are extrapolated toward lower cooling rates achieved in experiments. These results highlight that previously reported inconsistencies between simulations and experiments stem from the difference in cooling rate, thereby addressing one of the longstanding questions on the structure of bioglass. Based on these results, we demonstrate the existence of a Si--P avoidance behavior, which may be key in controlling the bioactivity of 45S5 bioglass., Comment: 22 pages, 13 figures

Many studies have recently explored the information from the satellite-remotely sensed data (SRSD) for estimating the crop production statistics. The value of this information depends on the aerial and spatial resolutions of SRSD. The SRSD with fine spatial resolution is costly and the aerial coverage is less. Use of multiple frames of SRSD in the estimation process of crop production can increase the precision. We propose an estimator for the average yield of wheat for the state of Haryana, India. This estimator uses the information from the Wide Field Sensor (WiFS) and the Linear Imaging Self Scanner (LISS-III) data from the Indian Remote Sensing satellite (IRS-1D) and the crop cutting experiment data collected by probability sampling design from a list frame of villages. We find that the relative efficiencies of the multiple-frame estimators are high in comparison to the single frame estimators.

This paper presents algorithms of decision making agents for an integrated air defense (IAD) system. The advantage of using agent based over conventional decision making system is its ability to automatically detect and track targets and if required allocate weapons to neutralize threat in an integrated mode. Such approach is particularly useful for futuristic network centric warfare. Two agents are presented here that perform the basic decisions making tasks of command and control (C2) like detection and action against jamming, threat assessment and weapons allocation, etc. The belief-desire-intension (BDI) architectures stay behind the building blocks of these agents. These agents decide their actions by meta level plan reasoning process. The proposed agent based IAD system runs without any manual inputs, and represents a state of art model for C2 autonomy., Comment: 8 pages,9 figure,2 tables

Accurate predictions of electro-optical imager performance are important for defence decision-making. The predictions serve as a guide for system development and are used in war game, simulations that directly influence engagement tactics. In the present study, mathematical models have been developed which involves detection of different military targets using their opto-electronics properties in different environmental conditions. The method first calculates the signal-to-noise ratio received by the observing sensors reflected from the target by quantifying the light energy in terms of photons, which is used for evaluating the detection probability., Comment: 9 pages,4 tables, 5 figures

Hard and soft classification techniques are the conventional ways of image classification on satellite data. These classifiers have number of drawbacks. Firstly, these approaches are inappropriate for mixed pixels. Secondly, these approaches do not consider spatial variability. Kriging based soft classifier (KBSC) is a non-parametric geostatistical method. It exploits the spatial variability of the classes within the image. This letter compares the performance of KBSC with other conventional hard/soft classification techniques. The satellite data used in this study is the Wide Field Sensor (WiFS) from the Indian Remote Sensing Satellite -1D (IRS-1D). The ground hyperspectral signatures acquired from the agricultural fields by a hand held spectroradiometer are used to detect subpixel targets from the satellite images. Two measures of closeness have been used for accuracy assessment of the KBSC to that of the conventional classifications. The results prove that the KBSC is statistically more accurate than the other conventional techniques., Comment: 5 pages,3 figures 3 tables

The paper is a half-way between the agent technology and the mathematical reasoning to model tactical decision making tasks. These models are applied to air defense (AD) domain for command and control (C2). It also addresses the issues related to evaluation of agents. The agents are designed and implemented using the agent-programming paradigm. The agents are deployed in an air combat simulated environment for performing the tasks of C2 like electronic counter counter measures, threat assessment, and weapon allocation. The simulated AD system runs without any human intervention, and represents state-of-the-art model for C2 autonomy. The use of agents as autonomous decision making entities is particularly useful in view of futuristic network centric warfare.

The battle of Kursk between Soviet and German is known to be the biggest tank battle in the history. The present paper uses the tank and artillery data from the Kursk database for fitting both forms of homogeneous and heterogeneous Lanchester model. Under homogeneous form the Soviet (or German) tank casualty is attributed to only the German(or Soviet) tank engagement. For heterogeneous form the tank casualty is attributed to both tank and artillery engagements. A set of differential equations using both forms have been developed, and the commonly used least square estimation is compared with maximum likelihood estimation for attrition rates and exponent coefficients. For validating the models, different goodness-of-fit measures like R2, sum-of-square-residuals (SSR), root-mean-square error (RMSE), Kolmogorov-Smirnov (KS) and chi-square statistics are used for comparison. Numerical results suggest the model is statistically more accurate when each day of the battle is considered as a mini-battle. The distribution patterns of the SSR and likelihood values with varying parameters are represented using contour plots and 3D surfaces.

This paper presents fracture response of alkali-activated slag (AAS) mortars with up to 30% (by volume) of slag being replaced by waste iron powder which contains a significant fraction of elongated particles. The elongated iron particles act as micro-reinforcement and improve the crack resistance of AAS mortars by increasing the area of fracture process zone (FPZ). Increased area of FPZ signifies increased energy-dissipation which is reflected in the form of significant increase in the crack growth resistance as determined from R-curves. Fracture response of notched AAS mortar beams under three-point bending is simulated using extended finite element method (XFEM) to develop a tool for direct determination of fracture characteristics such as crack extension and fracture toughness in particulate-reinforced AAS mortars. Fracture response simulated using the XFEM based framework correlates well with experimental observations. The comprehensive fracture studies reported here provide an economical and sustainable means towards improving the ductility of AAS systems which are generally more brittle than their conventional ordinary portland cement counterparts., Comment: This article has been accepted for publication in ASCE's Journal of Materials in Civil Engineering

Efficient transduction of electromagnetic signals between different frequency scales is an essential ingredient for modern communication technologies as well as for the emergent field of quantum information processing. Recent advances in waveguide photonics have enabled a breakthrough in light-matter coupling, where individual two-level emitters are strongly coupled to individual photons. Here we propose a scheme which exploits this coupling to boost the performance of transducers between low-frequency signals and optical fields operating at the level of individual photons. Specifically, we demonstrate how to engineer the interaction between quantum dots in waveguides to enable efficient transduction of electric fields coupled to quantum dots. Owing to the scalability and integrability of the solid-state platform, our transducer can potentially become a key building block of a quantum internet node. To demonstrate this, we show how it can be used as a coherent quantum interface between optical photons and a two-level system like a superconducting qubit., Comment: The maintext has 6 pages, two column and 4 figures

We show that strongly correlated photon transport can be observed in waveguides containing optically dense ensembles of emitters. Remarkably, this occurs even for weak coupling efficiencies. Specifically, we compute the photon transport properties through a chirally coupled system of $N$ two-level systems driven by a weak coherent field, where each emitter can also scatter photons out of the waveguide. The photon correlations arise due to an interplay of nonlinearity and coupling to a loss reservoir, which creates a strong effective interaction between transmitted photons. The highly correlated photon states are less susceptible to losses than uncorrelated photons and have a power-law decay with $N$. This is described using a simple universal asymptotic solution governed by a single scaling parameter which describes photon bunching and power transmission. We show numerically that, for randomly placed emitters, these results hold even in systems without chirality. The effect can be observed in existing tapered fiber setups with trapped atoms., Comment: 6 pages + 10 page supplement

In a preceding paper we introduced a formalism to study the scattering of low intensity fields from a system of multi-level emitters embedded in a $3$D dielectric medium. Here we show how this photon-scattering relation can be used to analyze the scattering of single photons and weak coherent states from any generic multi-level quantum emitter coupled to a $1$D waveguide. The reduction of the photon-scattering relation to $1$D waveguides provides for the first time a direct solution of the scattering problem involving low intensity fields in the waveguide QED regime. To show how our formalism works, we consider examples of multi-level emitters and evaluate the transmitted and reflected field amplitude. Furthermore, we extend our study to include the dynamical response of the emitters for scattering of a weak coherent photon pulse. As our photon-scattering relation is based on the Heisenberg picture, it is quite useful for problems involving photo-detection in the waveguide architecture. We show this by considering a specific problem of state generation by photo-detection in a multi-level emitter, where our formalism exhibits its full potential. Since the considered emitters are generic, the $1$D results apply to a plethora of physical systems like atoms, ions, quantum dots, superconducting qubits, and nitrogen-vacancy centers coupled to a $1$D waveguide or transmission line., Comment: This is part-II of the series of papers "Photon Scattering from a System of Multi-Level Quantum Emitters.". It has 22 pages, two column and 15 figures

We introduce a formalism to solve the problem of photon scattering from a system of multi-level quantum emitters. Our approach provides a direct solution of the scattering dynamics. As such the formalism gives the scattered fields amplitudes in the limit of a weak incident intensity. Our formalism is equipped to treat both multi-emitter and multi-level emitter systems, and is applicable to a plethora of photon scattering problems including conditional state preparation by photo-detection. In this paper, we develop the general formalism for an arbitrary geometry. In the following paper (part II), we reduce the general photon scattering formalism to a form that is applicable to $1$-dimensional waveguides, and show its applicability by considering explicit examples with various emitter configurations., Comment: This is first part of a two part series of papers. It has 11 pages, double column, and one figure

We show that spin squeezing criteria commonly used for entanglement detection can be erroneous, if the probe is not symmetric. We then derive a lower bound on squeezing for separable states in spin systems probed asymmetrically. Using this we further develop a procedure that allows us to verify the degree of entanglement of a quantum state in the spin system. Finally, we apply our method for entanglement verification to existing experimental data, and use it to prove the existence of tri-partite entanglement in a spin squeezed atomic ensemble., Comment: 7 pages, 2 figures (Include Supplemental material)

We propose an efficient light-matter interface at optical frequencies between a single photon and a superconducting qubit. The desired interface is based on a hybrid architecture composed of an organic molecule embedded inside an optical waveguide and electrically coupled to a superconducting qubit placed near the outside surface of the waveguide. We show that high fidelity, photon-mediated, entanglement between distant superconducting qubits can be achieved with incident pulses at the single photon level. Such a low light level is highly desirable for achieving a coherent optical interface with superconducting qubit, since it minimizes decoherence arising from the absorption of light., Comment: 5 pages of main text and 13 pages of supplementary material

We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The resulting gate can be implemented with cavities of moderate finesse which allows for highly efficient processing of quantum information encoded in photons. As a particular example of this, we show how the gate can be employed to increase the communication rate of quantum repeaters based on atomic ensembles., Comment: main manuscript 5 pages with 11 pages of supplementary information

As a unique feature, the $^{229}$Th nucleus has an isomeric transition in the vacuum ultraviolet that can be accessed by optical lasers. The interference effects occurring in the interaction between coherent optical light and an ensemble of $^{229}$Th nuclei are investigated theoretically. We consider the scenario of nuclei doped in vacuum ultraviolet-vacuum ultraviolet transparent crystals and take into account the effect of different doping sites and therefore different lattice fields that broaden the nuclear transition width. This effect is shown to come in interplay with interference effects due to the hyperfine splitting of the ground and isomeric nuclear states. We investigate possible experimentally available situations involving two-, three- and four-level schemes of quadrupole sublevels of the ground and isomeric nuclear states coupling to one or two coherent fields. Specific configurations which offer clear signatures of the isomer excitation advantageous for the more precise experimental determination of the transition energy are identified. Furthermore, it is shown that population trapping into the isomeric state can be achieved. This paves the way for further nuclear quantum optics applications with $^{229}$Th such as nuclear coherent control., Comment: 14 papes, 13 figures

The possibility of steady-state population inversion in a small sample of strongly driven two-level emitters like quantum dots (QDs) in micro-cavities, and its utilization towards amplification of light and acoustic waves is investigated theoretically. We find that inversion and absorption spectrum of photons, and phonons crucially depend on the interplay between the intrinsic vacuum and phonon environments. The absorption profiles of photons and phonons show marked novel features like gain instead of transparency and absorption reversed to gain, respectively. Furthermore, we report collectivity induced substantial enhancement of inversion and pronounced gain in the photon, and phonon absorption spectrum for a wavelength size QD ensemble., Comment: 5 pages, 3 figures

The impact of coherent light propagation on the excitation and fluorescence of thorium nuclei in a crystal lattice environment is investigated theoretically. We find that in the forward direction the fluorescence signal exhibits characteristic intensity modulations dominated by an orders of magnitude faster, sped-up initial decay signal. This feature can be exploited for the optical determination of the isomeric transition energy. In order to obtain a unmistakable signature of the isomeric nuclear fluorescence, we put forward a novel scheme for the direct measurement of the transition energy via electromagnetically modified nuclear forward scattering involving two fields that couple three nuclear states., Comment: 11 pages, 2 figures; v2 updated to the published version (minor changed in text)

We propose an efficient scheme for the generation and the manipulation of Raman fields in an homogeneously broadened atomic vapor in a closed three levels $\Lambda$-configuration. The key concept in generating the Raman and sub-Raman fields efficiently at lower optical densities involve the microwave induced atomic coherence of the lower levels. We show explicitly that, generation efficiency of the Raman fields can be controlled by manipulating the coherences via phase and amplitude of the microwave field., Comment: 6 pages, 5 figures

We consider a semiconductor quantum well in a microcavity driven by coherent light and coupled to a squeezed vacuum reservoir. By systematically solving the pertinent quantum Langevin equations in the strong coupling and low excitation regimes, we study the effect of exciton-photon detuning, external coherent light, and the squeezed vacuum reservoir on vacuum Rabi splitting and on quantum statistical properties of the light emitted by the quantum well. We show that the exciton-photon detuning leads to a shift in polariton resonance frequencies and a decrease in fluorescence intensity. We also show that the fluorescent light exhibits quadrature squeezing which predominately depends on the exciton-photon detuning and the degree of the squeezing of the input field., Comment: 8 pages, 10 figures

We analyze the effect of position dependent excitation phase on the properties of entanglement between two qubits formed in atomic systems. We show that the excitation phase induces a vacuum mediated quantum interference in the system that affects the dynamical behavior of entanglement between the qubits. It is also found that the quantum interference leads to a coherent population transfer between the symmetric and antisymmetric states which can considerably modify the dynamics of two-qubit entanglement and can even prevent finite time disentanglement (sudden death) under certain conditions., Comment: 9 pages, 8 figures

We study the polarization dependent second order correlation of a pair of photons emitted in a four level radiative cascade driven by an external field. It is found that the quantum correlations of the emitted photons, degraded by the energy splitting of the intermediate levels in the radiative cascade can be efficiently revived by a far detuned external field. The physics of this revival is linked to an induced stark shift and the formation of dressed states in the system by the non-resonant external field. Further, we investigated the competition between the effect of the coherent external field and incoherent dephasing of the intermediate levels. We found that the degradation of quantum correlations due to the incoherent dephasing can be content for small dephasing with the external field. We also studied the non-locality of the correlations by evaluating the Bell's inequality in the linear polarization basis for the radiative cascade. We find that the Bell parameter decreases rapidly with increase in the intermediate level energy splitting or incoherent dephasing rate to the extent that there is no violation. However, the presence of an external field leads to control over the degrading mechanisms and preservation of nonlocal correlation among the photons. This in turn can induce, violation of Bell's inequality in the radiative cascade for arbitrary intermediate level splitting and small incoherent dephasing.

We show that coherence between two excited ro-vibrational states belonging to the same molecular electronic configuration arises quite naturally due to their interaction with electromagnetic vacuum. For initial preparation of a molecule in the desired ro-vibrational states, we propose to employ the method of ultracold photoassociation. Spontaneous decay of the excited molecule then gives rise to vacuum induced coherence between the excited ro-vibrational states. We demonstrate theoretically an interesting interplay of effects due to vacuum induced coherence and photoassociation. We apply our theory to photoassociation of bosonic Ytterbium (^{174}Yb) atoms which appear to be a promising system for exploring such interplay. The effects discussed here can be important for controlling decoherence and dissipation in molecular systems., Comment: 5 pages, 4 figures

In this work we report a quantum interference mediated control of the resonance profiles in a generic three-level system and investigate its effect on key quantum interference (QI) phenomena. Namely in a three level configuration with doublets in the ground or excited states, we show control over enhancement and suppression of the emission (absorption) profiles. This is achieved by manipulation of the strength of QI and the energy spacing of the doublets. We analyze the application of such QI induced control of the resonance profile in the framework of two limiting cases of lasing without inversion and photo-detection., Comment: 8 pages, 5 figures

We show that vacuum induced coherence in three level atomic systems can lead to preservation of bi-partite entanglement, when two such atoms are prepared as two initially entangled qubits each independently interacting with their respective vacuum reservoirs. We explicitly calculate the time evolution of concurrence for two different Bell states and show that a large amount of entanglement can survive in the long time limit. The amount of entanglement left among the two qubits depends strongly on the ratio of the non- orthogonal transitions in each qubit and can be more than 50%, Comment: 4 pages, 3 figures

We investigate the viability of coupled waveguides as basic units of quantum circuits. In particular, we study the dynamics of entanglement for the single photon state, and single mode squeezed vacuum state. We further consider the case of entangled inputs in terms of the two mode mode squeezed vacuum states and the two photon NOON state. We present explicit analytical results for the measure of entanglement in terms of the logarithmic negativity. We also address the effect of loss on entanglement dynamics of waveguide modes. Our results indicate that the waveguide structures are reasonably robust against the effect of loss and thus quite appropriate for quantum architectures as well as for the study of coherent phenomena like random walks. Our analysis is based on realistic structures used currently., Comment: 9 pages, 10 figures

We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems like ion traps, semicondutor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for wide variety of models of the environment. We present analytical results for the time dependence of concurrence for all the models. The periodic disentanglement and entanglement behavior is seen to be precursor to the sudden death of entanglement (ESD) and can happen, for environments which do not show ESD for noninteracting qubits. Further we also find that this phenomenon can even lead to delayed death of entanglement for correlated environments., Comment: New published version, new figures

Interaction among the qubits are basis to many quantum logic operations. We report how such inter-qubit interactions can lead to new features, in the form of bright and dark periods in the entanglement dynamics of two qubits subject to environmental perturbations. These features are seen to be precursors to the well known phenomenon of sudden death of entanglement [Yu $&$ Eberly, Phys. Rev. Lett. {\bf 93}, 140404 (2004)] for noninteracting qubits. Further we find that the generation of bright and dark periods are generic and occur for wide varieties of the models of environment. We present explicit results for two popular models., Comment: New published version, corrected figures

We develop a theoretical model to study the Intensity-Intensity correlation of polarization entangled photons emitted in a biexciton-exciton cascade. We calculate the degree of correlation and show how polarization correlation are affected by the presence of dephasing and energy level splitting of the excitonic states. Our theoretical calculations are in agreement with the recent observation of polarization dependent Intensity-Intensity correlations from a single semiconductor quantum dot [R. M. Stevenson et. al., Nature 439, 179 (2006)] . Our model can be extended to study polarization entangled photon emission in coupled quantum dot systems.

We report generation of a new quantum interference effect in spontaneous emission from a resonantly driven system of two identical two-level atoms due to the spatial variation of the laser phase at the positions of the atoms. This interference affects significantly the spectral features of the emitted radiation and the quantum entanglement in the system. The interference leads to dynamic coupling of the populations and coherences in a basis, determined by the laser phase and represents a kind of vacuum mediated super-exchange between the symmetric and antisymmetric states.

We report a fundamental effect of the electromagnetic field induced modification of the branching ratios for emission into several final states. The modifications are especially significant if the vacuum into which the atom is radiating has a finite spectral width comparable with the separation of the final states. This is easily realizable in cavity QED. Further our results are quite generic and are applicable to any system interacting with a structured reservoir., Comment: 7 pages, 6 figures, Submitted to New Journal of Physics

We present new experimental implications of the effects of vacuum induced coherence on the photon -photon correlation in the pi-polarized fluorescence in j = 1/2 to j = 1/2 transition. These effects should be thus observable in measurements of photon statistics in for example Hg and Ba ion traps., Comment: 7 pages, 6 figures, submitted to Physical Review A