We consider effects of interspecies attraction on two-component gap solitons (GSs) in the binary BEC with intraspecies repulsion, trapped in the one-dimensional optical lattice (OL). Systematic simulations of the coupled Gross-Pitaevskii equations corroborate an assumption that, because the effective mass of GSs is negative, the interspecies attraction may split the two-component soliton. Two critical values, ${\kappa }_1$ and ${\kappa }_2$, of the OL strength $\left(\kappa \right)$ are identified. Two-species GSs with fully overlapping wave functions are stable in strong lattices $(\kappa >{\kappa }_1)$. In an intermediate region, ${\kappa }_1>\kappa >{\kappa }_2$, the soliton splits into a double-humped state with separated components. Finally, in weak lattices $(\kappa <{\kappa }_2)$, the splitting generates a pair of freely moving single-species GSs. We present and explain the dependence of ${\kappa }_1$ and ${\kappa }_2$ on the number of atoms (total norm), and on the relative strength of the competing interspecies attraction and intraspecies repulsion. The splitting of asymmetric solitons, with unequal norms of the two species, is briefly considered too. It is found and explained that the splitting threshold grows with the increase of the asymmetry.

We elucidate a ray picture of coherence for vectorial electromagnetic waves by using the Stokes parameters for light rays defined by the optical Wigner function. Paraxial propagation is formulated as a complementary Huygens principle. We show that the degrees of coherence are averages of the phase difference where the weights are the Stokes parameters for light rays. We analyze the van Cittert–Zernike theorem for vectorial waves in terms of ray propagation. We show that simple polarization measurements in a Young interferometer determine the degrees of coherence for vectorial electromagnetic waves.

Ghost imaging with classical incoherent light by third-order correlation is investigated. We discuss the similarities and the differences between ghost imaging by third-order correlation and by second-order correlation, and analyze the effect from each correlation part of the third-order correlation function on the imaging process. It is shown that the third-order correlated imaging includes richer correlated imaging effects than the second-order correlated one, while the imaging information originates mainly from the correlation of the intensity fluctuations between the test detector and each reference detector, as does ghost imaging by second-order correlation.

We study the joint spectral properties of photon pairs generated by spontaneous parametric down-conversion in a one-dimensional nonlinear photonic crystal in a collinear, degenerate, type-II geometry. We show that the photonic crystal properties may be exploited to compensate for material dispersion and obtain photon pairs that are nearly factorable, in principle, for arbitrary materials and spectral regions, limited by the ability to fabricate the nonlinear crystal with the required periodic variation in the refractive indices for the ordinary and extraordinary waves.

We evaluate the Casimir-Polder potential between two atoms in the presence of an infinite perfectly conducting plate and at nonzero temperature. In order to calculate the potential, we use a method based on equal-time spatial correlations of the electric field, already used to evaluate the effect of boundary conditions on interatomic potentials. This method also gives a transparent physical picture of the role of a finite temperature and boundary conditions on the Casimir-Polder potential. We obtain an analytical expression of the potential both in the near and far zones, and consider several limiting cases of interest, according to the values of the parameters involved, such as atom-atom distance, atoms-wall distance, and temperature.

We study the effects of the preparation of input states in a quantum tomography experiment. We show that maps arising from a quantum process tomography experiment (called process maps) differ from the well-known dynamical maps. The difference between the two is due to the preparation procedure that is necessary for any quantum experiment. We study two preparation procedures: stochastic preparation and preparation by measurements. The stochastic preparation procedure yields process maps that are linear, while the preparations using von Neumann measurements lead to nonlinear processes and can only be consistently described by a bilinear process map. A process tomography recipe is derived for preparation by measurement for qubits. The difference between the two methods is analyzed in terms of a quantum process tomography experiment. A verification protocol is proposed to differentiate between linear processes and bilinear processes. We also emphasize that the preparation procedure will have a nontrivial effect for any quantum experiment in which the system of interest interacts with its environment.

How much unavoidable randomness is generated by a positive-operator-valued measure (POVM)? We address this question using two complementary approaches. First, we study the variance of a real variable associated with the POVM outcomes. In this context we introduce an uncertainty operator which measures how much additional noise is introduced by carrying out a POVM rather than a von Neumann measurement. We illustrate this first approach by studying the variances of joint estimates of ${\sigma }_x$ and ${\sigma }_z$ for spin-$1∕2$ particles. We show that for unbiased measurements the sum of these variances is lower bounded by $1$. In our second approach we study the entropy of the POVM outcomes. In particular, we try to establish lower bounds on the entropy of the POVM outcomes. We illustrate this second approach by examples.

Anholonomies in the parametric dependences of the eigenvalues and the eigenvectors of Floquet operators that describe unit time evolutions of periodically driven systems, e.g., kicked rotors, are studied. First, an example of the anholonomies induced by a periodically pulsed rank-1 perturbation is given. As a function of the strength of the perturbation, the perturbed Floquet operator of the quantum map and its spectrum are shown to have a period. However, we show examples where each eigenvalue does not obey the periodicity of the perturbed Floquet operator and exhibits an anholonomy. Furthermore, this induces another anholonomy in the eigenspaces, i.e., the directions of the eigenvectors, of the Floquet operator. These two anholonomies are previously observed in a family of Hamiltonians [T. Cheon, Phys. Lett. A 248, 285 (1998)] and are different from the phase anholonomy known as geometric phases. Second, the stability of Cheon’s anholonomies in periodically driven systems is established by a geometrical analysis of the family of Floquet operators. Accordingly, Cheon’s anholonomies are expected to be abundant in systems whose time evolutions are described by Floquet operators. As an application, a design principle for quantum state manipulations along adiabatic passages is explained.

Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-$\frac{1}{2}$ systems subject to precession by different magnetic fields the achievement of orthogonalization is demonstrated for every scenario but a special one. This discrimination between evolutions is experimentally much simpler than procedures proposed earlier based on either sequential or parallel application of the unknown unitaries. A lower bound for the orthogonalization time is proposed in terms of the properties of the two Hamiltonians.

The Siegert-state expansion approach is applied to the solution of the time-dependent Schrödinger equation describing a model one-dimensional laser-atom interaction problem in the Kramers-Henneberger frame. Our method is mathematically rigorous and numerically exact even though a very restricted spatial box is considered, since the use of Siegert states as a basis in the expansion eliminates unphysical reflections from the boundary of the box and the Kramers-Henneberger frame enables us to fully take the interaction with the laser field into account. The method is demonstrated by calculations of above-threshold ionization spectra generated by strong high-frequency laser pulses. We found an oscillating substructure of multiphoton peaks caused by an interference of photoelectron wave packets produced at different times during the pulse which becomes especially pronounced in the stabilization regime. An interpretation of this effect in terms of the high-frequency Floquet theory is given.

We study the effects of interaction between bosons and fermions in Bose-Fermi mixtures loaded in an optical lattice. We concentrate on the destruction of a bosonic Mott phase driven by repulsive interaction between bosons and fermions. Once the Mott phase is destroyed, the system enters a superfluid phase where the movements of bosons and fermions are correlated. We show that this phase has simultaneous correlations reminiscent of a conventional superfluid and of a pseudospin density wave order.

Manipulation of the bifurcation structure of nonlinear optical systems via intracavity photonic crystals is demonstrated. In particular, subcritical regions between spatially periodic states are stabilized by modulations of the material’s refractive index. An family of dissipative solitons within this bistability range due to the intracavity photonic crystal is identified and characterized in both one and two transverse dimensions. Nontrivial snaking of the modulated-cavity soliton solutions is also presented.

The propagation of a laser beam of intensity $I$ in a nonlinear medium with a refractive index $n\left(I\right)$ of arbitrary form is studied. In particular, the influence of the functional form $n=n\left(I\right)$ on self-focusing and self-trapping is investigated. Starting from the propagation equations and using symmetry considerations and the Bogoliubov renormalization group approach, we derive a general equation relating the self-focusing distance, the intensity, and $n\left(I\right)$. For different polynomial dependences of $n\left(I\right)$ on $I$, we construct analytical solutions for the spatial intensity profile $I\left(\mathbf{r}\right)$ for an initially collimated Gaussian beam inside the medium. We also explicitly analyze the case of nonlinear self-focusing accompanied by multiphoton ionization. For particular (already studied) cases, we considerably improve the accuracy of the results with respect to previous semianalytical studies and obtain very good agreement with recent numerical simulations.

Bose-Einstein coalescence of independent photons at the surface of a beam splitter is the physical process that allows linear optical quantum gates to be built. When distinct parametric down-conversion events are used as an independent photon source, distinguishability arises form the energy correlation of each photon with its twin. We derive upper bound for the entanglement which can be generated under these conditions.

We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from three dimensions (3D) to one dimension (1D). There, using the nonpolynomial Schrödinger mean-field model, we find that the anomalous mode of the Bogoliubov spectrum has an eigenfrequency which coincides with the soliton oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that substantial deviations (of the order of 10% or more) from the characteristic frequency ${\omega }_z∕\sqrt{2}$ (${\omega }_z$ being the longitudinal trap frequency) are possible even in the purely 1D regime.

We present a protocol for growing graph states, the resource for one-way quantum computing, when the available entanglement mechanism is highly imperfect. The distillation protocol is frugal in its use of ancilla qubits, requiring only a single ancilla qubit when the noise is dominated by one Pauli error, and two for a general noise model. The protocol works with such scarce local resources by never postselecting on the measurement outcomes of purification rounds. We find that such a strategy causes fidelity to follow a biased random walk, and that a target fidelity is likely to be reached more rapidly than for a comparable postselecting protocol. An analysis is presented of how imperfect local operations limit the attainable fidelity. For example, a single Pauli error rate of $20\%$ can be distilled down to $\sim 10$ times the imperfection in local operations.

We investigate the stability of an attractive Bose-Einstein condensate in a one-dimensional lattice in the presence of radial confinement. We find that the system is dynamically unstable for low quasimomenta and becomes stable near the band edge, in a specular fashion with respect to the repulsive case. For low interactions the instability occurs via long-wavelength excitations that produce an oscillating density pattern in both real and momentum space instead of spoiling the condensate coherence. This behavior is illustrated by simulations for the expansion of the condensate in a moving lattice.

We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called generalized Hartman effect, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the generalized Hartman effect. We compare our results with the nonrelativistic ones and discuss their interpretation.

We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (e-print arXiv:quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in polynomial time. Moreover, our approach allow us to formulate a condition for the composability of simulable quantum circuits. We use this condition to show that any circuit composed of a constant number of approximate quantum Fourier transform circuits and log depth circuits with limited interaction range can also be efficiently simulated.