Based on color-locking noisy field correlation, the subtle Markovian field correlation effects in three stochastic models have been investigated in studying the Raman- and Rayleigh-enhanced four-wave mixing (FWM). Homodyne and heterodyne detections of the Raman attosecond sum-frequency polarization beats (ASPB), the Rayleigh ASPB, and the coexisting Raman and Rayleigh ASPB have also been investigated, respectively. Raman- and Rayleigh-enhanced FWM processes strongly compete with each other in ASPB. The heterodyne detected signal of ASPB potentially offers rich dynamic information about the homogeneous broadening material phase of the third-order nonlinear susceptibility.

We introduce a class of spatial complex-variable-function Gaussian (CVF Gaussian) beams, which are the product of an arbitrary analytic complex variable function and a Gaussian function, in strongly nonlocal nonlinear media (SNNM). The CVF Gaussian beam rotates generally during propagation. By choosing the input power of the beam, we can obtain a CVF Gaussian breather or a CVF Gaussian soliton. We reveal that a stable CVF Gaussian beam can exist in SNNM with different forms, including rotating dipoles, rotating elliptic doughnuts, and rotating figure eights.

We demonstrate the existence of localized optical vortex and necklace solitons in three-dimensional (3D) highly nonlocal nonlinear media, both analytically and numerically. The 3D solitons are constructed with the help of Kummer’s functions in spherical coordinates and their unique properties are discussed. The procedure we follow offers ways for generation, control, and manipulation of spatial solitons.

Zahariev and Wang [Phys. Rev. A, 70, 042503 (2004)] discuss the density functional theory of noninteger average particle numbers. Among their many results is one we dispute: that the exact exchange-correlation potential (more precisely, the exact functional derivative of the exchange-correlation energy with respect to the density) cannot have a discontinuity as the particle number crosses an integer, in contradiction to works by two of us (J.P.P. and M.L.) in collaboration with co-workers [Phys. Rev. Lett. 49, 1691 (1982); Phys. Rev. Lett.51, 1884 (1983)] and by Sham and Schlüter [Phys. Rev. Lett. 51, 1888 (1983)]. We point to a counterexample to Zahariev and Wang’s claim, which two of us (E.S. and J.P.P.) have presented in a separate paper: A rigorous proof that, in the absence of external magnetic fields, the exchange-correlation potential jumps by the difference between the ionization potential $\left(I\right)$ and electron affinity $\left(A\right)$ when the particle number crosses 1, given that $I⩾A$. We point out that Zahariev and Wang’s derivation neglects an order-of-limits problem. We also prove that $I>A$ for any one-electron system in the absence of magnetic fields.

In a recent paper [Raabe and Welsch, Phys. Rev. A 71, 013814 (2005)] an electromagnetic energy-momentum tensor is suggested as an alternative to the Abraham-Minkowski tensor and is applied to calculations of Casimir forces in planar geometries. We argue that the universality of the suggested tensor is doubtful; application of the Raabe-Welsch theory to a simple example in classical electrodynamics shows that their proposed tensor is unable to describe the situation in a simple way. We also show that modified Casimir forces acting on the cavity medium as prescribed by these authors suffer from problems of definiteness and peculiar properties which call for experimental support before this theory can be regarded as acceptable.

The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of bosons to higher Bloch bands, coupled with contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss the implications for cold-atom experiments where expansion of the Mott lobes by fermions has been conclusively established.

We develop a systematic approach to establish Bell inequalities for qubits based on the Cauchy-Schwarz inequality. We also use the concept of distinct “roots” of the Bell function to classify some well-known Bell inequalities for qubits. As applications of the approach, we present three unique and tight Bell inequalities for four and three qubits, respectively.

We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MOE). We show that all proven MOE relations using concurrence can be rephrased in terms of CREN. Furthermore, we show that higher-dimensional (qudit) extensions of MOE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MOE in terms of concurrence. We further test the CREN version of MOE for qudits by considering fully or partially coherent mixtures of a qudit $W$-class state with the vacuum and show that the CREN version of MOE for qudits is satisfied in this case as well. The CREN version of MOE for qudits is thus a strong conjecture with no obvious counterexamples.

We present a linear optical scheme for the implementation of a three-qubit quantum gate that can be considered as a generalization of the two-qubit partial-SWAP gate. The gate leaves unchanged all fully symmetric states of three qubits, and all states antisymmetric with respect to the transposition of some pair of qubits acquire a phase shift $\varphi$. The gate operates in the coincidence basis and requires one auxiliary pair of photons prepared in the maximally entangled Bell state. By altering parameters of the proposed interferometric scheme, we can also obtain a quantum filter that attenuates amplitudes of the three-qubit states according to their permutation symmetry properties.

We consider a two-chain, spin-$\frac{1}{2}$ antiferromagnetic Heisenberg spin ladder in an external magnetic field $H$. The spin ladder is known to undergo second-order quantum phase transitions (QPTs) at two critical values $H_{c1}$ and $H_{c2}$ of the magnetic field. There are now known examples of strongly coupled (where the rung exchange interaction is much stronger than the nearest-neighbor intrachain exchange interaction) organic ladder compounds in which QPTs have been experimentally observed. In this paper, we investigate whether well-known bipartite entanglement meaures such as one-site von Neumann entropy, two-site von Neumann entropy, and concurrence develop special features close to the quantum critical points. As suggested by an earlier theorem, the first derivatives of the measures with respect to magnetic field are expected to diverge as $H\to H_{c1}$ and $H\to H_{c2}$. Based on numerical diagonalization data and a mapping of the strongly coupled ladder Hamiltonian onto the $XXZ$ chain Hamiltonian, for which several analytical results are known, we find that the derivatives of the entanglement measures diverge as $H\to H_{c2}$ but remain finite as $H\to H_{c1}$. The reason for this discrepancy is analyzed. We further calculate two recently proposed quantum information theoretic measures, the reduced fidelity and reduced fidelity susceptibility, and show that these measures provide appropriate signatures of the QPTs occuring at the critical points $H=H_{c1}$ and $H=H_{c2}$.

We rigorously analyze Knill’s Fibonacci scheme for fault-tolerant quantum computation, which is based on the recursive preparation of Bell states protected by a concatenated error-detecting code. We prove lower bounds on the threshold fault rate of $0.67\times {10}^{-3}$ for adversarial local stochastic noise, and $1.25\times {10}^{-3}$ for independent depolarizing noise. In contrast to other schemes with comparable proved accuracy thresholds, the Fibonacci scheme has a significantly reduced overhead cost because it uses postselection far more sparingly.

The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.

We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules (${}^2\Sigma$, ${}^3\Sigma$, and ${}^2\Pi$) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. 129, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. 280, 19 (2009)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He-CaH $\left(X{}^2\Sigma ^{+}\right)$, He-${\mathrm{O}}_2$ $\left(X{}^3\Sigma ^{–}\right)$, and He-OH $\left(X{}^2\Pi _{\Omega }\right)$ systems at thermal collision energies. Since the cross sections can be obtained for different orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He-OH system, weak for the He-CaH collisions, and strong for the He-${\mathrm{O}}_2$. While odd $\Delta M$ transitions dominate the He-OH $[J=3∕2,f\to J^{\prime },e/f]$ integral cross sections in a magnetic field parallel to the relative velocity vector, even $\Delta M$ transitions prevail in the case of the He-CaH $\left(X^2{\Sigma }^{+}\right)$ and He-${\mathrm{O}}_2$ $\left(X{}^3\Sigma ^{-}\right)$ collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions $N=1,J=0\to N^{\prime }$, $J^{\prime }$ with $J^{\prime }=N^{\prime }$.

We show how to combine finite elements and the discrete-variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of ${\mathrm{H}}_2^{+}$, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.

We study the merging of two independent Bose-Einstein condensates with arbitrary initial phase difference, in the framework of a one-dimensional time-dependent Gross-Pitaevskii model. The role of the initial phase difference in the process is discussed, and various types of phase-sensitive excitations are identified.

We propose a two-photon correlated emission laser to generate entanglement amplifier for bright light source. The coherence between upper and lower levels is generated in a Raman-driven scheme using two external classical fields. The proposed scheme is practically more suitable for the macroscopic entanglement of photons of the two modes of the cavity field.

We have proposed and experimentally demonstrated tunable cavity-linewidth narrowing by means of coupled-active-resonator-induced dispersion. We have theoretically studied the coupling-resonator-induced-dispersion phenomenon in the general case of $N$ coupled resonators and especially the case of two or three resonators. In the case of two resonators we have experimentally shown that the strong dispersion induced by the coupling of resonators can lead to cavity ringdown effect enhancement. In the case of three resonators, we propose a coupling scheme allowing the quality $\left(Q\right)$ factor of a critically coupled resonator to be increased and actively modulated by using two additional coupled resonators. We have experimentally tested the feasibility of the proposition by using a model system consisting of ${\mathrm{Er}}^{3+}$-doped fiber coupled resonators. These experimental results demonstrate the possibility of $Q$-factor tailoring by the use of active artificial photonic media.

We put forward a scheme for tailoring the optical response of a four-level coherent media allowing the realization of competing giant nonlinearities of cubic-quintic type, with focusing and defocusing behavior for low and large field amplitudes, respectively. Numerical simulations of the beams propagation through tailored media show evidence of two-dimensional optical solitons with liquid-light dynamics, which can be observed in the frame of current experiments.

We explore the nature of the classical propagation of light through media with strong frequency-dependent dispersion in the presence of a gravitational field. In the weak field limit, gravity causes a redshift of the optical frequency, which the slow-light medium converts into a spatially varying index of refraction. This results in the bending of a light ray in the medium. We further propose experimental techniques to amplify and detect the phenomenon using weak value measurements. Independent heuristic and rigorous derivations of this effect are given.

We consider one-dimensional solitons in a binary Bose-Einstein condensate with linear coupling between the components, trapped in an optical-lattice potential. The inter- and intraspecies interactions may be either repulsive or attractive. The main effects considered here are spontaneous breaking of the symmetry between components in symmetric and antisymmetric solitons, and spatial splitting between the components. These effects are studied by means of a variational approximation and numerical simulations.