Creation of pure multi-mode entangled states in a ring cavity

Practical schemes for creation of multi-mode squeezed (entangled) states of atomic ensembles located inside a high-Q ring cavity are discussed. It is assumed that the cavity is composed of two degenerate mutually counter-propagating modes that can simultaneously couple to the atomic ensembles with the same coupling strengths. The ensembles are composed of ultra-cold atoms which are modeled as four-level systems driven by two laser fields, both co-propagating with one of the cavity directions. We illustrate a procedure that constructs multi-mode squeezed states from the vacuum by a unitary transformation associated with the collective dynamics of the atomic ensembles subjected to driving lasers of a suitably adjusted amplitudes and phases. The lasers pulses together with the cavity dissipation prepare the collective modes in a desired stationary squeezed state.     

Scalable preparation of three-atom and four-atom W states via atom-cavity-laser interaction

We propose the optical generation of W states for three atomic and four atomic qubits, with each qubit trapped in a separate cavity and coupled to the cavity laser. A single-photon source and two classical fields are employed in the present scheme. By encoding the quantum information of each qubit on the degenerate ground states of the atom, we obtain the atomic entanglement that is relatively stable against spontaneous emission. It is demonstrated that the three- and four-atomic W states can be produced deterministically via a proper manipulation of the atom-cavity interaction sequence and time. Generalization of the present scheme to prepare multi-atomic W states is also discussed.     

Valence of “divalent” rare earth metals

It is generally recognized that light rare earths change their valence from 2 to 3 when forming a bulk metal while remaining divalent at the surface. However, performed DFT calculations ultimately indicate that the higher-binding-energy peaks in photoemission spectra (like the −5.3 eV peak for Sm), characteristic of the trivalent 4fⁿ⁻¹5d¹ configuration, correspond not to the ground state, but to excited states induced by radiation. This means that the trivalent state is not inherent for the bulk of divalent rare earths, and therefore they do not become trivalent.     

Nitrogen bonding in aluminum oxynitride films

Assignment of oxidation states of N_1s in XPS spectra of aluminum oxynitride by curve fitting is difficult. The XPS curve fitting was previously discussed in the paper published in J. Non-Cryst. Solids, 224 (1998) 31, in which O_1s photoelectrons from GeO₂ glass were used to illustrate how to fit the XPS spectra. Three different ways were pointed out to eliminate the ambiguity caused by curve fitting such as comparing the data to data from standard samples, investigating the continuous surface modifications caused by slowly sputtering the surface, and monitoring the continuous surface modifications due to gradual increases in surface species under heating, cooling, or irradiation. Our recent work in aluminum oxynitride films provides another example of how to fit the XPS spectra of N_1s by three different oxidation states of N⁺, N²⁺, and N³⁺, by comparison of the measured data to data from previously published results, and by the gradual changes of spectra as functions of the oxygen contents in the films. Three oxidation states in different nitrogen bonding in the aluminum oxynitride, AlO₂N, Al₂O₅N₂, and AlO₃N, were clearly deduced.     

A combined experimental and theoretical analysis of Fe-implanted TiO2 modified by metal plasma ion implantation

Photocatalyst titanium dioxide (TiO₂) thin films were prepared using sol-gel process. To improve the photosensitivity of TiO₂ at visible light, transition metal of Fe was implanted into TiO₂ matrix at 20 keV using the metal plasma ion implantation process. The primary phase of the Fe-implanted TiO₂ films is anatase, but X-ray diffraction revealed a slight shift of diffraction peaks toward higher angles due to the substitutional doping of iron. The additional band gap energy levels were created due to the formation of the impurity levels (Fe-O) verified by X-ray photoelectron spectroscopy, which resulted in a shift of the absorption edge toward a longer wavelength in the absorption spectra. The optical band gap energy of TiO₂ films was reduced from 3.22 to 2.87 eV with an increase of Fe ion dosages from 0 to 1 × 10¹⁶ ions/cm². The band gap was determined by the Tauc plots. The photocatalysis efficiency of Fe-implanted TiO₂ was assessed using the degradation of methylene blue under ultraviolet and visible light irradiation. The calculated density of states for substitutional Fe-implanted TiO₂ was investigated using the first-principle calculations based on the density functional theory. A combined experimental and theoretical Fe-implanted TiO₂ film was formed, consistent with the experimentally observed photocatalysis efficiency of Fe-implanted TiO₂ in the visible region.     

Spectral theory of one-channel operators and application to absolutely continuous spectrum for Anderson type models

A one-channel operator is a self-adjoint operator on ${?}^2(\mathbb{G})$ for some countable set $\mathbb{G}$ with a rank 1 transition structure along the sets of a quasi-spherical partition of $\mathbb{G}$. Jacobi operators are a very special case. In essence, there is only one channel through which waves can travel across the shells to infinity. This channel can be described with transfer matrices which include scattering terms within the shells and connections to neighboring shells. Not all of the transfer matrices are defined for some countable set of energies. Still, many theorems from the world of Jacobi operators are translated to this setup. The results are then used to show absolutely continuous spectrum for the Anderson model on certain finite dimensional graphs with a one-channel structure. This result generalizes some previously obtained results on antitrees.     

Atomic motion in Se nanoparticles embedded into a porous glass matrix

By neutron diffraction it was shown that nanostructured Se confined within a porous glass matrix exists in a crystalline as well as in an amorphous state. The spontaneous crystallization of crystalline Se from confined amorphous phase was observed. The root-mean-square amplitudes of the atomic motions in the bulk as well as in confinement are found to be essentially different in a basal plane and in the perpendicular direction along the hexagonal axis. The atomic motions in the confined Se differ from the atomic motions in the bulk at low temperatures. The results shows an unusual “freezing" of the atomic motion along the chains, while the atomic motions in the perpendicular plane still keep. This “freezing" is accompanied by the deformation of nanoparticles and the appearance of inner stresses. This effect is attributed to the interaction of confined nanoparticle with the cavity walls.     

Continuum variable entangled state generated by an asymmetric beam splitter

For an asymmetric beam-splitter a new kind of entangled state is introduced, we then derive the integration measure with which such states can make up a complete and orthonormal representation in two-mode Fock space. We then show how to use in finding new squeezing operator and new squeezed state, whose generation can relies on the asymmetric beamsplitter.     

Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system

We derive some new results concerning the Cauchy problem and the existence of bound states for a class of coupled nonlinear Schrödinger-gKdV systems. In particular, we obtain the existence of strong global solutions for initial data in the energy space H¹(R)×H¹(R), generalizing previous results obtained in Tsutsumi (1993) [11], Corcho and Linares (2007) [13] and Dias et al. (submitted for publication) [14] for the nonlinear Schrödinger-KdV system.