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

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

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