Aspects of coherent states of nonlinear algebras

Various aspects of coherent states of nonlinear su(2) and su(1,1) algebras are studied. It is shown that the nonlinear su(1,1) Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived. (C) 2010 American Institute of Physics. doi:10.1063/1.3514118]

Coherent phonons in pyrochlore titanates A(2)Ti(2)O(7) (A = Dy, Gd, Tb): A phase transition in Dy2Ti2O7 at 110 K

We study the generation of coherent optical phonons in spin-frustrated pyrochlore single crystals Dy2Ti2O7, Gd2Ti2O7, and Tb2Ti2O7 using femtosecond laser pulses (65 fs, 1.57 eV) in degenerate time-resolved transmission experiments as a function of temperature from 4 to 296 K. At 4 K, two coherent phonons are observed at similar to 5.3 THz (5.0 THz) and similar to 9.3 THz (9.4 THz) for Dy2Ti2O7 (Gd2Ti2O7), whereas three coherent phonons are generated at similar to 5.0, 8.6, and 9.7 THz for Tb2Ti2O7. In the case of spin-ice Dy2Ti2O7, a clear discontinuity is observed in the linewidths of both the coherent phonons as well as in the phase of lower-energy coherent phonon mode, indicating a subtle structural change at 110 K. Another important observation is a phase difference of pi between the modes in all the samples, thus suggesting that the driving forces behind the generation of these modes could be different in nature, unlike a purely impulsive or displacive mechanism.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

Influence of two photon absorption induced free carriers on coherent polariton and phonon generation in ZnTe crystals

Combination of femtosecond Kerr, two photon absorption, and impulsive stimulated Raman scattering (ISRS) experiments have been carried out to investigate the effect of pulse energy and crystal temperature on the generation of coherent polaritons and phonons in 〈110〉 cut ZnTe single crystals of three different resistivities. We demonstrate that the effect of two photon induced free carriers on the creation of both the polaritons and phonons is largest at 4 K where the free carrier lifetime is enhanced. The temperature dependant ISRS on high and low purity ZnTe crystals allows us to unambiguously assign the phonon mode at 3.5 THz to the longitudinal acoustic mode at X-point in the Brillouin zone, LA(X).

Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.

Ultrasound modulation of coherent light in a multiple-scattering medium: experimental verification of nonzero average phase carried by light

We demonstrate the phase fluctuation introduced by oscillation of scattering centers in the focal volume of an ultrasound transducer in an optical tomography experiment has a nonzero mean. The conditions to be met for the above are: (i) the frequency of the ultrasound should be in the vicinity of the most dominant natural frequency of vibration of the ultrasound focal volume, (ii) the corresponding acoustic wavelength should be much larger than l(n)*, a modified transport mean-free-path applicable for phase decorrelation and (iii) the focal volume of the ultrasound transducer should not be larger than 4 - 5 times (l(n)*)(3). We demonstrate through simulations that as the ratio of the ultrasound focal volume to (l(n)*)(3) increases, the average of the phase fluctuation decreases and becomes zero when the focal volume becomes greater than around 4(l(n)*)(3); and through simulations and experiments that as the acoustic frequency increases from 100 Hz to 1 MHz, the average phase decreases to zero. Through experiments done in chicken breast we show that the average phase increases from around 110 degrees to 130 degrees when the background medium is changed from water to glycerol, indicating that the average of the phase fluctuation can be used to sense changes in refractive index deep within tissue.

Compressive sensing for music signals: comparison of transforms with coherent dictionaries

Compressive Sensing (CS) is a new sensing paradigm which permits sampling of a signal at its intrinsic information rate which could be much lower than Nyquist rate, while guaranteeing good quality reconstruction for signals sparse in a linear transform domain. We explore the application of CS formulation to music signals. Since music signals comprise of both tonal and transient nature, we examine several transforms such as discrete cosine transform (DCT), discrete wavelet transform (DWT), Fourier basis and also non-orthogonal warped transforms to explore the effectiveness of CS theory and the reconstruction algorithms. We show that for a given sparsity level, DCT, overcomplete, and warped Fourier dictionaries result in better reconstruction, and warped Fourier dictionary gives perceptually better reconstruction. “MUSHRA” test results show that a moderate quality reconstruction is possible with about half the Nyquist sampling.

Identification of coherent synchronous generators in a multi- machine power system using support vector clustering

This paper illustrates the application of a new technique, based on Support Vector Clustering (SVC) for the direct identification of coherent synchronous generators in a large interconnected Multi-Machine Power Systems. The clustering is based on coherency measures, obtained from the time domain responses of the generators following system disturbances. The proposed clustering algorithm could be integrated into a wide-area measurement system that enables fast identification of coherent clusters of generators for the construction of dynamic equivalent models. An application of the proposed method is demonstrated on a practical 15 generators 72-bus system, an equivalent of Indian Southern grid in an attempt to show the effectiveness of this clustering approach. The effects of short circuit fault locations on coherency are also investigated.

Gap-Dependent Quasiparticle Dynamics and Coherent Acoustic Phonons in CaFe2As2 across Spin Density Wave Phase Transition

We report ultrafast quasiparticle (QP) dynamics and coherent acoustic phonons in undoped CaFe2As2 iron pnictide single crystals exhibiting spin-density wave (SDW) and concurrent structural phase transition at temperature T-SDW similar to 165K using femtosecond time-resolved pump-probe spectroscopy. The contributions in transient differential reflectivity arising from exponentially decaying QP relaxation and oscillatory coherent acoustic phonon mode show large variations in the vicinity of T-SDW. From the temperature-dependence of the QP recombination dynamics in the SDW phase, we evaluate a BCS-like temperature dependent charge gap with its zero-temperature value of similar to(1.6 perpendicular to 0.2)k(B)T(SDW), whereas, much above T-SDW, an electron-phonon coupling constant of similar to 0.13 has been estimated from the linear temperature-dependence of the QP relaxation time. The long-wavelength coherent acoustic phonons with typical time-period of similar to 100 ps have been analyzed in the light of propagating strain pulse model providing important results for the optical constants, sounds velocity and the elastic modulus of the crystal in the whole temperature range of 3 to 300 K.

Adiabatic eigenfunction-based approach for coherent excitation transfer: An almost analytical treatment of the Fenna-Matthews-Olson complex

We suggest a method of studying coherence in finite-level systems coupled to the environment and use it for the Hamiltonian that has been used to describe the light-harvesting pigment-protein complex. The method works with the adiabatic states and transforms the Hamiltonian to a form in which the terms responsible for decoherence and population relaxation are separated out. Decoherence is then accounted for nonperturbatively and population relaxation using a Markovian master equation. Almost analytical results can be obtained for the seven-level system, and the calculations are very simple for systems with more levels. We apply the treatment to the seven-level system, and the results are in excellent agreement with the exact numerical results of Nalbach et al. Nalbach, Braun, and Thorwart, Phys. Rev. E 84, 041926 (2011)]. Our approach is able to account for decoherence and population relaxation separately. It is found that decoherence causes only damping of oscillations and does not lead to transfer to the reaction center. Population relaxation is necessary for efficient transfer to the reaction center, in agreement with earlier findings. Our results show that the transformation to the adiabatic basis followed by a Redfield type of approach leads to results in good agreement with exact simulation.

Visualization of coherent structures in turbulent subsonic jet using planar laser induced fluorescence of acetone

In this paper, we present the molecular density distribution measurement in turbulent nitrogen jet (Re approximate to 3 x 10(3)), using acetone as molecular tracer. The tracer was seeded in the nitrogen jet by purging through the liquid acetone at ambient temperature. Planar laser sheet of 266 nm wavelength from frequency quadrupled, Q-switched, Nd:YAG laser was used as an excitation source. Emitted fluorescence images of jet flow field were recorded on CMOS camera. The dependence of planar laser induced fluorescence (PLIF) intensity on acetone vapor density was used to convert PLIF image of nitrogen jet into the density image on pixel-by-pixel basis. Instantaneous quantitative density image of nitrogen jet, seeded with acetone, was obtained. The arrowhead-shaped coherent turbulent structures were observed in the present work. It was found that coherent structures were non-overlapping with separate boundaries. Breaking of coherent structures into turbulence was clearly observed above four times jet width.

Cluster labeling for multilingual scatter/gather using comparable corpora

Scatter/Gather systems are increasingly becoming useful in browsing document corpora. Usability of the present-day systems are restricted to monolingual corpora, and their methods for clustering and labeling do not easily extend to the multilingual setting, especially in the absence of dictionaries/machine translation. In this paper, we study the cluster labeling problem for multilingual corpora in the absence of machine translation, but using comparable corpora. Using a variational approach, we show that multilingual topic models can effectively handle the cluster labeling problem, which in turn allows us to design a novel Scatter/Gather system ShoBha. Experimental results on three datasets, namely the Canadian Hansards corpus, the entire overlapping Wikipedia of English, Hindi and Bengali articles, and a trilingual news corpus containing 41,000 articles, confirm the utility of the proposed system.