An introductory review on resource theories of generalized nonclassical light

Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols that optimize its usefulness in a given application in areas ranging from quantum information to computation. Moreover, the resource theories have transmuted radical quantum phenomena like coherence, nonclassicality and entanglement from being just intriguing to being helpful in executing realistic thoughts. A general quantum resource theoretical framework relies on the method of categorization of all possible quantum states into two sets, namely, the free set and the resource set. Associated with the set of free states there is a number of free quantum operations emerging from the natural constraints attributed to the corresponding physical system. Then, the task of quantum resource theory is to discover possible aspects arising from the restricted set of operations as resources. Along with the rapid growth of various resource theories corresponding to standard harmonic oscillator quantum optical states, significant advancement has been expedited along the same direction for generalized quantum optical states. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas including nonlinearity, PT -symmetric non-Hermitian theories, q-deformed bosonic systems, etc., to accomplish similar but elevated objectives of the standard quantum optics and information theories. In this article, we review the developments of nonclassical resource theories of different generalized quantum optical states and their usefulness in the context of quantum information theories.

A Versatile Quantum Simulator for Coupled Oscillators Using a 1D Chain of Atoms Trapped near an Optical Nanofiber

The transversely confined propagating light modes of a nanophotonic optical waveguide or nanofiber can effectively mediate infinite-range forces. We show that for a linear chain of particles trapped within the waveguide’s evanescent field, transverse illumination with a suitable set of laser frequencies should allow the implementation of a coupled-oscillator quantum simulator with time-dependent and widely controllable all-to-all interactions. Using the example of the energy spectrum of oscillators with simulated Coulomb interactions, we show that different effective coupling geometries can be emulated with high precision by proper choice of laser illumination conditions. Similarly, basic quantum gates can be selectively implemented between arbitrarily chosen pairs of oscillators in the energy as well as in the coherent-state basis. Key properties of the system dynamics and states can be monitored continuously by analysis of the out-coupled fiber fields.

Recent Progress in Confined Atoms and Molecules: Superintegrability and Symmetry Breakings

This review article has the antecedents of Jaskolski’s 1996 Physics Report Confined Many-electron Systems , the fifteen chapters on the Theory of Confined Quantum Systems in Vols. 57 and 58 of 2009 Advances in Quantum Chemistry, and the nine chapters of the 2014 Monograph “Electronic Structure of Confined Quantum Atoms and Molecules”. In this contribution the last two sets of reviews are taken as the points of reference to illustrate some advances in several lines of research in the elapsed periods. The recent progress is illustrated on the basis of a selection of references from the literature taking into account the confined quantum systems, the confining environments and their modelings; their properties and processes, emphasizing the changes due to the confinement; the methods of analysis and solutions, their results including confiability and accuracy; as well as applications in other areas. The updated and current works of the Reviewer are also presented. The complementary words in the title apply to the simplest atom in its free configuration and to the harmonic oscillator quantum dot because they admit more exact solutions than the number of their degrees of freedom; and to their many-electron and confined counterparts, due to their additional interactions and changes in boundary conditions.

Four-dimensional quantum oscillator and magnetic monopole with U(1) dynamical group

By using an appropriate transformation, it was shown that the quantum system of four-dimensional (4D) simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the Dirac magnetic monopole has the hidden algebra of U(1) symmetry and by reducing the dimensions of space, the U(1) × U(1) dynamical group for 4D harmonic oscillator quantum system was obtained. Using the group representation and based on explicit solution of the obtained differential equation, the spectrum of system was calculated.

Dirac equation with anisotropic oscillator, quantum E3′ and Holt superintegrable potentials and relativistic generalized Yang–Coulomb monopole system

The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum [Formula: see text], anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang–Coulomb monopole (YCM) superintegrable system (a [Formula: see text] non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.