A New Kind of Bipartite Coherent-Entangled State and?Its?Applications in Quantum Optics

A new kind of bipartite coherent-entangled state (CES) is introduced in the two-mode Fock space which exhibits the properties of both coherent state and entangled state. The set of CESs make up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the CES is proposed by using a beam splitter. Some applications of the CES are also presented in quantum optics.     

A New Quantum State

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Quantum State Generated by Parity-Squeezing Combinatorial Operator and Its Wigner Function and?Husimi Function

In this paper, a parity-squeezing combinatorial operator S ₁ with its normally ordered form is introduced, it is then applied to generate the even-odd squeezed coherent state, its Wigner function and Husimi function can be conveniently calculated by virtue of the coordinate representation of S ₁.     

A Kind Tripartite Entangled State Representation and?Its Application in Quantum Teleportation

We discuss entanglement for a tripartite system by setting up a new state vector representation |p,χ ₁,χ ₂〉 in three-mode Fock space. The Schmidt decomposition of |p,χ ₁,χ ₂〉 is presented and its application in teleporting a bipartite entangled state or a two-mode squeezed state to a pair of receivers is analyzed.     

New Form of Legendre Polynomials Obtained by Virtue of Excited Squeezed State and IWOP Technique in Quantum Optics

Using the technique of integration within an ordered product of operators and the intermediate coordinatemomentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.     

Teleported State and Its Fidelity in Quantum Teleportation of Continuous Variables

When given an unknown quantum state which may be either a pure or a mixed state in the coherent state representation.we show that explicit expressions for the teleported state and its fidelity in the teleportation process(S.L.Braunstein and H.J.Kimble 1998 Phys.Rev.Lett.80 869) can be obtained without explicit expansions for the two-mode squeezed vacuum state and the Bell basis in a specified representation.     

New Three—Mode Einstein—Podolsky—Rosen Entangled State Prepresentation and Its Application in Squeezing Theory

By extending the Einstein-Podolsky-Rosen bipartite entanglement to the tripartite case,we construct the common eigenvector of the tripartite centre-of -mass coordinate and two mass-weighted relative momenta,which is a new entangled state of continuum variables.The classical dilation transform of varibles in such a state induces new entangled state of continum variables,The classical dilation transform of variables in such a state induces a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.     

Rota–Baxter Algebras and New Combinatorial Identities

The word problem for an arbitrary associative Rota–Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects are indicated.      

Formalism and Interpretation in Quantum Theory

Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.     

Nonlinear Dicke Quantum Phase Transition and Its Quantum Witness in a Cavity-Bose–Einstein-Condensate System

We investigate nonlinear Dicke quantum phase transition(QPT) induced by inter-atomic nonlinear interaction and its quantum witness in a cavity-Bose–Einstein-condensate(BEC) system. It is shown that inter-atomic nonlinear interaction in a cavity BEC system can induce first-order Dicke QPT. It is found that this nonlinear Dicke QPT can happen in an arbitrary coupling regime of the cavity and atoms. It is demonstrated that the quantum speed limit time can witness the Dicke QPT through its sudden change at the critical point of the QPT.     

Multi-Partite EPR Entangled State Representation for Continuous Variables and Its Application in Squeezing Theory

By extending the Einstein-Podolsky-Rosen (EPR) bipartite entanglement to an n-partite case, we construct the common eigenstate of the n-partite total coordinate and relative momenta for the continuous variables. The entanglement property of the state is shown. The classical dilation transform of variables in such a state induces a new n-mode squeezing operator related to an n-mode bosonic operator realization of SU(1,1) Lie algebra.     

A New Way for the Extension of Quantum Theory: Non-Bohmian Quantum Potentials

Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics. Of course, at the nuclear level, because of some complications, it is not clear that we can claim the same confidence. One way of taking these complications and corrections into account seems to be a modification of the standard quantum theory. In this paper and its follow ups we consider a straightforward way of extending quantum theory. Our method is based on a Bohmian approach. We show that this approach has the essential ability for extending quantum theory, and we do this by introducing “non-Bohmian” forms for the quantum potential.     

Optics of Intense Light and Its Applications

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A Quasi-Symmetric Coupled Quantum Well and Its Electric-Optical Properties

We propose a novel coupled quantum well structure, i.e. a quasi-symmetric coupled quantum well (QSCQW). Based on the demands of optical switching devices for quantum well materials, the QSCQW configuration is further optimized. Consequently, in the case of low applied electric field 25kV/cm and low absorption loss 100cm^-1, a large field-induced refractive index change (for TE mode, n = 0.0106; for TM mode, n = 0.0115) is obtained in the QSCQW structure at the operation wavelength 1550hm. The value is in one or two order of magnitude larger than that in a rectangular quantum well and about 50% larger than that of five-step asymmetric coupled quantum well structure under the same working conditions. The refractive index change obtained with the optimized QSCQW under so low absorption loss and applied electric field is very attractive for semiconductor optical switching devices. This manifests that the QSCQW structure has a great potential for applications in ultra-fast and low-voltage optical switches and in travelling wave modulators.     

Fermionization,Convergent Perturbation Theory,and Correlations in the Yang–Mills Quantum Field Theory in Four Dimensions

We show that the Yang–Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function E(x,y) of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as

Bianchi I Quantum Cosmology in the Bergmann–Wagoner Theory

The Wheeler–DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for the Bianchi type I cosmology. Exact solutions are found for two selfinteracting potentials and arbitrary coupling function. The WKB wavefunctions are obtained and a family of solutions satisfying the Hawking–Page regularity conditions of wormholes are found.     

Quantum State Transfer in Trapped-Ion-Cavity Systems

We study the information transfer and entanglement transfer in a system consisting of single trapped ions in cavities by the three-mode cross-Kerr-like interaction among the cavity field （photons）, the centre-of-mass motion （phonons） and the internal state of the trapped ion in the Lamb-Dicke and large detuning regime.     

Zitterbewegung and Quantum Jumps in Relativistic Schrödinger Theory

Within the general framework of the relativistic Schrödinger theory, a new waveequation is identified which stands between Dirac's four-component spinorequation and the scalar one-component Klein–Gordon equation. It is atwo-component, first-order wave equation in pseudo-Riemannian spacetime which onone hand can take account of the Zitterbewegung (similar to the Dirac theory),but on the other hand describes spinless particles (just like the Klein–Gordontheory). In this way it is demonstrated that spin and Zitterbewegung areindependent phenomena despite the fact that both effects refer to a certain kindof internal motion. An extra variable for the internal motion can be introduced(similarly as in the Dirac theory) so that the new wave equation is reduced tothe Klein–Gordon case when the internal variable takes its trivial value and theinternal motion is not excited. The internal degree of freedom admits the occurenceof quasi-pure states (i.e., a special subset of the mixtures), which undergo atransition to a pure state in finite time. If the initial configuration is already apure state, this transition occurs in the form of a sudden jump to the final purestate. The coupling of the new wave field to gravity via the Einstein equationsmakes the Zitterbewegung manifest through the corresponding trembling of theextension of a Friedmann–Robertson–Walker universe.     

Fantappié-Arcidiacono Spacetime and Its Consequences in Quantum Cosmology

Einstein’s gravitational theory gave rise to a new conception of the Universe and Cosmology has been enclosed in the realm of Science and not only of Philosophy as before the Einstein work. Despite this, the presence of the Big Bang singularity, flatness and horizon problems led to the statement that Standard Cosmological Model, based on General Relativity and Standard Model of particle physics, is inadequate to describe the Universe in extreme regimes. Due to this facts, alternative gravitational theories and alternative approaches to cosmology have been proposed during the years. One of the most fruitful approach has been that of Projective Relativity and, in this paper, we analyze the developments of this theory. Projective Relativity, initially proposed by Fantappié and subsequently developed by Arcidiacono, has been recently revisited by prof. Ignazio Licata and other authors. The cosmological consequences of such extension appear relevant. In the following, we analyze the effects of the group approach on the metrics and on the dynamics and we will consider its properties in connection with varying speed of light.     

Hydrodynamical Reformulation and Quantum Limit of The Barut–Zanghi Theory

One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited for a hydrodynamical reformulation of the BZ theory. Working out a probabilistic fluid, we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to quantize the BZ theory: by employing this time the tensorial language, more popular in first-quantization. Quantizing the BZ theory, however, does notlead to the Dirac equation, but rather to a nonlinear, Dirac–like equation, which can be regarded as the actual quantum limit of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical Weyssenhoff fluid, while the Hamilton-Jacobi equation (linking mass, spin,and zbw frequency together) appears to be nothing but a special case of the de Broglie energy–frequency relation. Finally, after having discussed the remarkable relation existing between the gauge transformation U(1) and ageneral rotation on the spin plane, we clarify and comment on the two-valuedeness nature of the fremionic wave-function, as well as on the parity and charge conjugation transformations.