Collective coherent population trapping in a thermal field

We analyzed the efficiency of coherent population trapping (CPT) in a superposition of the ground states of three-level atoms under the influence of the decoherence process induced by a broadband thermal field. We showed that in a single atom there is no perfect CPT when the atomic transitions are affected by the thermal field. The perfect CPT may occur when only one of the two atomic transitions is affected by the thermal field. In the case when both atomic transitions are affected by the thermal field, we demonstrated that regardless of the intensity of the thermal field the destructive effect on the CPT can be circumvented by the collective behavior of the atoms. An analytic expression was obtained for the populations of the upper atomic levels which can be considered as a measure of the level of thermal decoherence. The results show that the collective interaction between the atoms can significantly enhance the population trapping in that the population of the upper state decreases with increased number of atoms. The physical origin of this feature was explained by the semiclassical dressed atom model of the system. We introduced the concept of multiatom collective coherent population trapping by demonstrating the existence of collective (entangled) states whose storage capacity is larger than that of the equivalent states of independent atoms.Comment: Accepted for publication in Phys. Rev.

Coherent States of SU(l,1)SU(l,1) groups

This work can be considered as a continuation of our previous one (J.Phys., 26 (1993) 313), in which an explicit form of coherent states (CS) for all SU(N) groups was constructed by means of representations on polynomials. Here we extend that approach to any SU(l,1) group and construct explicitly corresponding CS. The CS are parametrized by dots of a coset space, which is, in that particular case, the open complex ball $CD^{l}$. This space together with the projective space $CP^{l}$, which parametrizes CS of the SU(l+1) group, exhausts all complex spaces of constant curvature. Thus, both sets of CS provide a possibility for an explicit analysis of the quantization problem on all the spaces of constant curvature.Comment: 22 pages, to be published in "Journal of Physics A

Classification of quantum relativistic orientable objects

Started from our work "Fields on the Poincare Group and Quantum Description of Orientable Objects" (EPJC,2009), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of 10 commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to usual 6 quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). We believe that the proposed approach can be useful for description of elementary spinning particles considering as orientable objects. In particular, their classification in the framework of the approach under consideration reproduces the usual classification but is more comprehensive. This allows one to give a group-theoretical interpretation to some facts of the existing phenomenological classification of known spinning particles.Comment: 24 page

Field on Poincare group and quantum description of orientable objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincare group $G$. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group $\Pi =G\times G$. All such transformations can be studied by considering a generalized regular representation of $G$ in the space of scalar functions on the group, $f(x,z)$, that depend on the Minkowski space points $x\in G/Spin(3,1)$ as well as on the orientation variables given by the elements $z$ of a matrix $Z\in Spin(3,1)$. In particular, the field $f(x,z)$ is a generating function of usual spin-tensor multicomponent fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.Comment: 46 page

3D cave model with sparse data

Speleology is the science that studies caves. Currently, with the development and reduction of the cost of technology, an integral component of speleology is rapidly developing - topographic survey of caves, which involves determining the shape and size of the cave. The data collected in caves using various instruments (for example: compass, eclimeter, laser rangefinders) must be processed and visualized. This requires the appropriate programs. One of such programs is Topo. Topo software allows you to process, edit and visualize the topographic data of the cave. An integral part of the visualization of the topographic survey of the cave is the display of its volumetric model. The volumetric model of a cave is needed to visualize it, to document the caves and to calculate such characteristics of the cave as length, surface area and volume. In addition, with the help of a volumetric model, it is possible to outline the most promising places for further research and search for the continuation of the cave. The aim of this work is to construct a three-dimensional surface of a cave in conditions of sparse data within the Topo program

Incomplete figure perception - the problem of invisible masking

Our previous findings (2002 Perception 31 Supplement, 116) suggested that the Gollin test of incomplete figure perception (Foreman and Hemmings, 1987 Perception 16 543 - 548) and the Mooney test of incomplete silhouette faces may be considered as signal masking problems, in this sense similar to the Poppelreuter test of contour figure extraction from noisy overlapping figures. We considered the incompleteness of a Gollin figure to be the result of its masking by multiplicative noise similar to the texture of transparent windows and opaque elements. The brightness and colour of the opaque elements are identical to the background and size of transparent windows corresponding with the size of fragments of the incomplete figure. In other words, incomplete figures are figures occluded by an 'invisible' mask. The purpose of this work has been to determine the statistical properties of the 'invisible' mask and to show their connection with thresholds of incompleteness of figures at recognition. We have made additional investigations, which show that the incompleteness thresholds depend on the level of similarity of the spatial-frequency bands of the figure and the 'invisible' mask. The thresholds are reduced when the 'invisible' mask changes to a visible one. We presented in psychophysical experiments incomplete figures with two sizes, covering the foveal or macular areas. We measured the thresholds of recognition of incomplete figures in normal participants and in neurological patients with 'filtration agnosia' and showed recognition-threshold differences for the different tests. This difference depends on the similarity between the spatial-frequency spectra of the visible (Poppelreuter) and 'invisible' (Gollin, Mooney) masks with those of the incomplete figure, and also with the localisation of visual system damage

The Gollin incomplete figure test as a masking problem

The Gollin test of incomplete figure perception is usually employed to measure the thresholds of recognition in children and adults, and to study a process which provides a basis for the perception of incomplete figures as Gestalts (Foreman and Hemmings, 1987 Perception 16 543 ^ 548). Here we suggest that this test, along with such tests as the Poppelreuter test of figure extraction, and the Mooney faces test, may be considered as a visual masking problem. Digital image processing allows us to measure the spatial properties and spatial-frequency spectrum of the absent part of the image as a mask. We compare incomplete masking with other traditional types of masking. Using a noise paradigm, we have measured the signal-to-noise ratio for incomplete figure perception in normal participants and in neurological patients. This is the most powerful aspect of this new approach. Clinically, the new paradigm may provide a quantitative measure of agnosia. We have developed the hypothesis that some forms of visual agnosia arise primarily from an especially high level of noise within higher visual processing, including memory systems. We classify this type of agnosia as ‘filtration agnosia’. The concept of incomplete figure perception as noise filtration is therefore important for clinical purposes

The optical-geometrical characteristics and thresholds of perception of fragmented outline figures

Measurements were made of the threshold of recognition of cumulatively forming line figures. The threshold value of the outline, expressed in pixels, depended on the length of the outline of the whole unfragmented figure. Relative threshold values were constant, and for the measures of figure fragments used in the present study, averaged 12.5%. A spatial frequency analysis of the test images was performed. Variation of the amplitude-frequency parameters of the spectra of the images of various figures with threshold fragmentation was minimal as compared with the variation of these parameters in figures with subthreshold or suprathreshold levels of fragmentation

Incomplete figure perception and invisible masking

The Gollin test (measuring recognition thresholds for fragmented line drawings of everyday objects and animals) has traditionally been regarded as a test of incomplete figure perception or ‘closure’, though there is a debate about how such closure is achieved. Here, figural incompleteness is considered to be the result of masking, such that absence of contour elements of a fragmented figure is the result of the influence of an ‘invisible’ mask. It is as though the figure is partly obscured by a mask having parameters identical to those of the background. This mask is ‘invisible’ only consciously, but for the early stages of visual processing it is real and has properties of multiplicative noise. Incomplete Gollin figures were modeled as the figure covered by the mask with randomly distributed transparent and opaque patches. We adjusted the statistical characteristics of the contour image and empty noise patches and processed those using spatial and spatial-frequency measures. Across 73 figures, despite inter-subject variability, mean recognition threshold was always approximately 15% of total contour in naive observers. Recognition worsened with increasing spectral similarity between the figure and the ‘invisible’ mask. Near threshold, the spectrum of the fragmented image was equally similar to that of the ‘invisible’ mask and complete image. The correlation between spectral parameters of figures at threshold and complete figures was greatest for figures that were most easily recognised. Across test sessions, thresholds reduced when either figure or mask parameters were familiar. We argue that recognition thresholds for Gollin stimuli in part reflect the extraction of signal from noise

The Gollin test and the optical properties of incomplete figures at threshold

The Gollin test is a developmental test for measuring visual perceptual skills (Gollin, 1960 Perceptual and Motor Skills 11 289 - 298). The aim of our work was to measure the thresholds of recognition of incomplete figures when presented for the first time to observers, and relate this to their contour lengths and 2-D Fourier spectra. We generated 73 contour images of familiar objects. They were presented as incomplete figures, beginning from 0% of contour to 100% via the random addition of small fragments. The observers' task was to recognise figures as quickly as possible. Their score was the percentage of contour displayed at the moment of recognition. We found that the value of the threshold, in terms of percentage of contour length displayed, was similar for all images, averaging 12%, irrespective of the total length of contour of the full figure. For both complete and incomplete figures at threshold we carried out 2-D Fourier transform analysis, measuring the centroids of their spectra. The energy spectrum of each figure was transformed into an averaged amplitude spatial-frequency profile, representing the total energy within each of three orientation profiles, and the centroid was then calculated. We found that the value of the centroid at threshold was similar across the figures employed, averaging 6.3 cycles deg-1. We showed that the centroid of the amplitude spatial-frequency spectrum of an image coincides with the maximum on the curve of human contrast sensitivity