The Huttner-Barnett model is extended to a magnetodielectric medium by adding a matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The electric and magnetic susceptibilities of the medium are explicitly derived and shown to satisfy the Kramers-Kronig relations. It is shown that the results obtained in this extended model are equivalent to their counterparts obtained in the phenomenological methods.

We characterize all coexistent pairs of qubit effects. This gives an exhaustive description of all pairs of events allowed, in principle, to occur in a single qubit measurement. The characterization consists of three disjoint conditions, which are easy to check for a given pair of effects. Known special cases are shown to follow from our general characterization theorem.

We examine the thermal pairwise entanglement in a symmetric system of $n$ spins fully connected through anisotropic $XYZ$-type couplings embedded in a transverse magnetic field. We consider both the exact evaluation together with that obtained with the static $\text{path}+\text{random}$ phase approximation (RPA) and the ensuing mean $\text{field}+\text{RPA}$. The latter is shown to provide an accurate analytic description of both the parallel and antiparallel thermal concurrence in large systems. We also analyze the limit temperature for pairwise entanglement, which is shown to increase for large fields and to decrease logarithmically with increasing $n$. Special finite-size effects are also discussed.

Motivated by the desire to better understand the class of quantum operations on bipartite systems that completely preserve positivity of partial transpose (PPT operations) and its relation to the class LOCC (local operations and classical communication), we present some results on deterministic bipartite pure-state transformations by PPT operations. Restricting our attention to the case in which we start with a rank $\mathit{K}$ maximally entangled state, we give a necessary condition for transforming it into a given pure state, which we show is also sufficient when $\mathit{K}$ is 2 and the final state has Schmidt rank 3. We show that it is sufficient for all $\mathit{K}$ and all final states provided a conjecture about a certain family of semidefinite programs is true. We also demonstrate that the phenomenon of catalysis can occur under PPT operations and that, unlike LOCC catalysis, a maximally entangled state can be a catalyst. Finally, we give a necessary and sufficient condition for the possibility of transforming a rank $\mathit{K}$ maximally entangled state to an arbitrary pure state by PPT operations assisted by some maximally entangled catalyst.

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically, it is shown that singular points at the border of the set of unentangled states originate singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down-conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.

We present a general formulation of the quantum-defect theory for systems with an attractive $1/r^{\alpha }$ type of asymptotic potentials with $\alpha >2$. Its structural differences from the standard theory for $\alpha \le 2$, or from the semiclassical theory, is fully explained through a systematic understanding of quantum reflection above the threshold, and quantum connection formulas below the threshold.

The discrepancies in the power spectrum of the light scattered by a coherently driven three-level atom are identified with the help of two methods [see, A. S. Manka et al., Phys. Rev. A 43, 3748 (1991); M. R. Ferguson et al., Phys. Rev. A 54, 2379 (1996)]. Moreover, the most prominent differences are the negative values as well as the greatly distorted profile in the spectrum. It is shown that the inhomogeneity or homogeneity of the two-time correlation Bloch vector equation is responsible for such discrepancies.

Motivated by the prospect of optical lattice experiments with two-component Fermi gases consisting of different atomic species such as Li and K, we calculate the energies for $N$ fermions under harmonic confinement as a function of the mass and trap imbalance, i.e., as a function of the ratio between the masses and frequencies of species one and two, using microscopic approaches. Our energies for $N=2-6$ can be used to determine the energetically most favorable configuration for a given number of atoms per species of a deep lattice in which each lattice site is approximately harmonic and in which tunneling between neighboring sites can be neglected. We also determine and interpret the excitation gap for unequal-mass systems with up to $N=13$ atoms for equal oscillator lengths.

We analytically investigate solitons counterpropagating in a longitudinally modulated Kerr medium by means of the Hirota bilinear approach. We show that Hirota solvability (partial integrability of the system) physically corresponds to the exact mutual cancellation of the effects of all the underlying nonlinear gratings. This cancellation is achieved in two different situation: either through a suitable choice of the field profile or by means of a peculiar tailoring of the nonlinear modulation. In the first situation we obtain both bright and dark one-soliton solutions whose intensity ratio between forward and backward propagating beams is set by the nonlinear modulation. In the second situation, we derive two-soliton solutions obtained by nonlinearly dressing two independent linear grating eigenmodes sharing the same propagation constant.

Classical wave optical analogs of coherent population transfer via a continuum, recently demonstrated for laser-driven atoms and molecules in the atomic physics context, are theoretically proposed for light waves propagating in waveguide-based photonic structures. In particular, it is shown that exploitation of the optical analogs of two-photon Rabi oscillations and stimulated Raman adiabatic passage via continuous states enables efficient transfer of light waves between two channel optical waveguides side coupled to a slab waveguide.

We demonstrate explicitly that a single-photon waveform, conditionally prepared by detecting the trigger photon of the photon pair born in the process of spontaneous parametric down-conversion, becomes broadened and chirped as the result of propagation through a single-mode optical fiber. The pulselike broadening of the single-photon waveform, due to the group velocity dispersion of the optical fiber, is shown to be controllable in a nonlocal way by spectrally filtering the trigger photon.

In connection with the experiments recently achieved on doped crystals, biological samples, doped optical fibers, and semiconductor heterostructures, we revisit the theory of the propagation of a pulse-modulated light in a saturable absorber. Explicit analytical expressions of the transmitted pulse are obtained, enabling us to determine the parameters optimizing the time-delay of the transmitted pulse with respect to the incident pulse. We finally compare the maximum fractional delay or figure of merit so attainable to those which have been actually demonstrated in the experiments.

Prompted by the recent measurements of Predojević et al., we have calculated the excitation of the $3s4s$ ${{}^{1}S}_0$ and $3s4p$ ${{}^{1}P}_1$ states of magnesium by electron impact at 20, 40, 60, and 100 eV in the relativistic distorted-wave approximation. Results are presented for the differential and integrated cross sections and compared with previous experimental and theoretical data.

We introduce a suit of simple entangling protocols for generating tripartite Greenberger-Horne-Zeilinger and W states in systems with anisotropic exchange interaction $g(XX+YY)+\tilde{g}ZZ$. An interesting example is provided by macroscopic entanglement in Josephson phase qubits with capacitive $(\tilde{g}=0)$ and inductive $(0<\mid \tilde{g}∕g\mid <0.1)$ couplings.

We report a theoretical study of Feshbach resonances in ${}^6\mathrm{Li}+{}^{23}\mathrm{Na}$ and ${}^7\mathrm{Li}+{}^{23}\mathrm{Na}$ mixtures at ultracold temperatures using accurate interaction potentials in a full quantum coupled-channel calculation. Feshbach resonances for $l=0$ in the initial collisional open channel ${}^6\mathrm{Li}(f=1∕2,m_f=1∕2)+{}^{23}\mathrm{Na}(f=1,m_f=1)$ are found to agree with previous measurements, leading to precise values of the singlet and triplet scattering lengths for the ${}^{6,7}\mathrm{Li}+{}^{23}\mathrm{Na}$ pairs. We also predict additional Feshbach resonances within experimentally attainable magnetic fields for other collision channels.

We study the pair-breaking effect of rotation on a cold Fermi gas in the BCS-BEC crossover region. In the framework of BCS theory, which is supposed to be qualitatively correct at zero temperature, we find that in a trap rotating around a symmetry axis, three regions have to be distinguished: (A) a region near the rotational axis where the superfluid stays at rest and where no pairs are broken, (B) a region where the pairs are progressively broken with increasing distance from the rotational axis, resulting in an increasing rotational current, and (C) a normal-fluid region where all pairs are broken and which rotates like a rigid body. Due to region B, density and current do not exhibit any discontinuities.

We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N}\times \sqrt{N}$. The previous quantum-walk based algorithms take $O\left(\sqrt{N}\text{ln}N\right)$ steps to solve this problem, and it is an open question whether the performance can be improved. We present an algorithm which solves the problem in $O\left(\sqrt{N\text{ln}N}\right)$ steps, thus giving an $O\left(\sqrt{\text{ln}N}\right)$ improvement over the known algorithms. The improvement is achieved by controlling the quantum walk on the lattice using an ancilla qubit.

We provide a detailed proof of an analytical lower bound of entanglement quantified by concurrence for arbitrary bipartite quantum states. It is shown that though the bound does not allow one to detect bound entanglement, it is tight for some mixed states and can detect most of the free entanglement. On the other hand, it is known that the entanglement monogamy inequality proposed by Coffman, Kundu, and Wootters is, in general, not true for higher-dimensional quantum states. Inducing from the lower bound of concurrence, we find a proper form of entanglement monogamy inequality for arbitrary pure quantum states.

Which state loses less quantum information between Greenberger-Horne-Zeilinger (GHZ) and $W$ states when they are prepared for two-party quantum teleportation through a noisy channel? We address this issue by solving analytically a master equation in the Lindblad form with introducing the noisy channels that cause the quantum channels to be mixed states. It is found that the answer to this question is dependent on the type of noisy channel. If, for example, the noisy channel is $\left(L_{2,x},L_{3,x},L_{4,x}\right)$ type, where the $L$'s denote the Lindblad operators, the GHZ state is always more robust than the $W$ state, i.e., the GHZ state preserves more quantum information. In, however, the $\left(L_{2,y},L_{3,y},L_{4,y}\right)$-type channel the situation becomes completely reversed. In the $\left(L_{2,z},L_{3,z},L_{4,z}\right)$-type channel, the $W$ state is more robust than the GHZ state when the noisy parameter $\left(\kappa \right)$ is comparatively small while the GHZ state becomes more robust when $\kappa$ is large. In isotropic noisy channel we found that both states preserve an equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.

We analyze a recently proposed physical implementation of a quantum computer based on polar molecules with “switchable” dipoles, i.e., dipole moments that can be switched “on” and “off”. Conditional dipole-dipole interaction is an efficient tool for realizing two-qubit quantum gates necessary to construct universal gates. A set of general requirements for a molecular system is presented, which would provide an optimal combination of quantum gate times, coherence times, number of operations, high gate accuracy, and experimental feasibility. We proceed with an analysis of a two-qubit phase gate realization based on switchable dipole-dipole interactions between polar molecules in an optical lattice architecture. We consider one of the schemes proposed in our previous work [Phys. Rev. A 74, 050301(R) (2006)], using specific molecules, such as CO and NF. We suggest suitable electronic states and transitions, and investigate requirements for the laser pulses driving them. Finally, we analyze possible sources of decoherence and list practical difficulties of the scheme.