Precise measurement of optical frequency with the help of electromagnetically induced transparency

We have studied electromagnetically induced transparency (EIT) spectra in a frequency span as wide as 300 MHz. This tunability of EIT spectra provides an opportunity to utilize the sub-natural spectra in measuring unknown laser frequency very accurately. EIT is observed when control and probe laser frequency detunings are equal. This correlation has been used to identify and measure unknown probe frequency with a very high degree of accuracy, subject to the condition that control laser frequency is known.     

$${f(\mathcal R)}$$ quantum cosmology

We have quantized a flat cosmological model in the context of the metric models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.     

Spin–gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin–gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin–gravity coupling plays in particular problems.     

A Categorical Framework for the Quantum Harmonic Oscillator

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures.     

Quantic Superpositions and the Geometry of Complex Hilbert Spaces

The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An in-depth analysis of superpositions is proposed, in which states are represented by one-dimensional subspaces, not by unit vectors as in Dirac’s notation. Superpositions must be considered when one cannot distinguish between possible paths, i.e., histories, leading to the current state of the system. In such a case the resulting state is some compound of the states that result from each of the possible paths. States can be compounded, i.e., superposed in such a way only if they are not orthogonal. Since different classical states are orthogonal, the claim implies no non-trivial superpositions can be observed in classical systems. The parameter that defines such compounds is a proportion defining the mix of the different states entering the compound. Two quantities, p and θ, both geometrical in nature, relate one-dimensional subspaces in complex Hilbert spaces: the first one is a measure of proximity relating two rays, the second one is an angle relating three rays. The properties of superpositions with respect to those two quantities are studied. The algebraic properties of the operation of superposition are very different from those that govern linear combination of vectors. This work was partially supported by the Jean and Helene Alfassa fund for research in Artificial Intelligence, by the Israel Science Foundation grant 183/03 on “Quantum and other cumulative logics” and by EPSRC Visiting Fellowship GR/T 24562 on “Quantum Logic”.     

Massive Radiation via Tunneling in a BTZ Black Hole

Hawking radiation can usefully be viewed as a semi-classical tunneling process that originates at the black hole horizon. Massive radiation from a BTZ black hole is investigated. The conservation of energy implies the effect of self-gravitation. Viewed as a tunneling process, the emission spectrum derivates from the pure thermal spectrum, but it is consistent with an underlying unitary theory. The result is the same as that of massless particles.     

Constructing Four-Photon States for Quantum Communication and Information Processing

We provide a method for constructing a set of four-photon states suitable for quantum communication applications. Among these states is a set of concatenated quantum code states that span a decoherence-free subspace that is robust under collective-local as well as global dephasing noise. This method requires only the use of spontaneous parametric down-conversion, quantum state post-selection, and linear optics. In particular, we show how this method can be used to produce all sixteen elements of the second-order Bell gem , which includes these codes states and is an orthonormal basis for the Hilbert space of four qubits composed entirely of states that are fully entangled under the four-tangle measure.     

Note on Generalized Quantum Gates and Quantum Operations

Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional Hilbert space (S. Gudder, Int. J. Theor. Phys. 47:268–279, 2008). In this note, we proved that the set of all generalized quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space ℋ. Meanwhile, we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on ℋ. This subject is supported by NSF of China (10571113).