Geometric quantum discord is a well-defined measure of quantum correlation if Schatten one-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior of the one-norm geometric quantum discord under the effect of decoherence. By starting from arbitrary Bell-diagonal mixed states under Markovian local noise, we provide the decays of the quantum correlation as a function of the decoherence parameters. In particular, we show that the one-norm geometric discord exhibits the possibility of double sudden changes and freezing behavior during its evolution. For nontrivial Bell-diagonal states under simple Markovian channels, these are new features that are in contrast with the Schatten two-norm (Hilbert-Schmidt) geometric discord. The necessary and sufficient conditions for double sudden changes as well as their exact locations in terms of decoherence probabilities are provided. Moreover, we illustrate our results by investigating decoherence in quantum spin chains in the thermodynamic limit.

We study the effects of imperfections on the fidelity of the Toffoli gate recently realized in a circuit QED setup using quantum control methods. The noise is introduced in the interqubits interactions. The coupling constants are no longer fixed; instead, they fluctuate around average values obeying some given probability density functions characterizing the dynamical-imperfection case. We also consider the static-imperfection case in which the values of the coupling constants are not exactly known. We obtain a more robust gate by modifying the quantum optimization problem using a weighted average of the fidelity over an interval of coupling values as the objective functional.

Previous analyses of conditional ${\phi }_{nl}$-phase gates for photonic qubits that treat cross-phase modulation (XPM) in a causal, multimode, quantum field setting suggest that a large ($\sim$$\pi$ rad) nonlinear phase shift is always accompanied by fidelity-degrading noise [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)]. Using an atomic $\vee$ system to model an XPM medium, we present a conditional phase gate that, for sufficiently small nonzero ${\phi }_{nl}$, has high fidelity. The gate is made cascadable by using a special measurement, i.e., principal-mode projection, to exploit the quantum Zeno effect and preclude the accumulation of fidelity-degrading departures from the principal-mode Hilbert space when both control and target photons illuminate the gate. The nonlinearity of the $\vee$ system we study is too weak for this particular implementation to be practical. Nevertheless, the idea of cascading through principal-mode projection is of potential use to overcome fidelity-degrading noise for a wide variety of nonlinear optical primitive gates.

We show that in any quantum direct communication protocol that is based on $\Psi$ and $\Phi$ Bell states, an eavesdropper can always tell $\Psi$ from $\Phi$ states without altering the transmission in any way in the message mode. This renders all protocols that make use of only one $\Psi$ state and one $\Phi$ state completely insecure in the message mode. All four-Bell-state protocols require a revision and this might be of importance for new implementations of entanglement-based cryptographic protocols. The detection rate of an eavesdropper is 25$\%$ per control transmission, i.e., a half of the rate in the two-state (ping-pong) protocol. An eavesdropper can detect control probes with certainty in the standard control transmission without a photon in the Alice-to-Bob's travel mode and with near certainty in a transmission with a fake photon in the travel mode. Resending of measured control photons via the travel mode would make an eavesdropper completely invisible.

A study of the formation of excitons as a problem of two Dirac particles in a gapped graphene layer and in two gapped graphene layers separated by a dielectric is presented. In the low-energy limit the separation of the center-of-mass and relative motions is obtained. Analytical solutions for the wave function and energy dispersion for both cases when the electron and the hole interact via a Coulomb potential are found. It is shown that the energy spectrum and the effective exciton mass are functions of the energy gaps as well as of the interlayer separation in the case of two-layer gapped graphene.

We show that multipulse excitation of Rydberg atoms with a sequence of short time-delayed femtosecond pulses results in strong $n$ selection of the final-state amplitudes. In the experiment, a 150 fs laser pulse, which alone populates $n$ levels from 22–32 in Li, is chopped into four time-delayed excitation pulses, which results in a strong modification of the $n$-level distribution. The mechanism demonstrated in the experiment is derived theoretically: With more pulses, it is shown that the population of a single or a few $n$ levels can be performed on demand and varied as long as the central laser frequency is given.

If the photon energy is much less than the electron binding energy, ionization of an atom by a strong optical field is often described in terms of electron tunneling through the potential barrier resulting from the superposition of the atomic potential and the potential associated with the instantaneous electric component of the optical field. In the strict tunneling regime, the electron response to the optical field is said to be adiabatic, and nonadiabatic effects are assumed to be negligible. Here, we investigate to what degree this terminology is consistent with a language based on the so-called adiabatic representation. This representation is commonly used in various fields of physics. For electronically bound states, the adiabatic representation yields discrete potential-energy curves that are connected by nonadiabatic transitions. When applying the adiabatic representation to optical strong-field ionization, a conceptual challenge is that the eigenstates of the instantaneous Hamiltonian form a continuum; i.e., there are no discrete adiabatic states. This difficulty can be overcome by applying an analytic-continuation technique. In this way, we obtain a rigorous classification of adiabatic states and a clear characterization of (non)adiabatic and (non)diabatic ionization dynamics. Moreover, we distinguish two different regimes within tunneling ionization and explain the dependence of the ionization probability on the pulse envelope.

We calculate the distributions in recoil momenta and the energy distributions for the high-energy nonrelativistic double photoionization of helium caused by the quasifree mechanism of the process. The distributions obtain local maxima at small values of the recoil momenta. This is in agreement with the earlier predictions and with recently obtained experimental data. We obtained also the angular correlations, which reach the largest value in the “back-to-back” configuration of the photoelectrons. Our analysis is valid in all high-energy nonrelativistic region. Particular equations are true up to the photon energies making several kilo-electron-volts. We present numerical results for the photon energies in the region of 1 keV, employed in the recent experiments.

Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.

The Sommerfeld and Brillouin forerunners generated in a single-resonance absorbing medium by an incident step-modulated pulse are theoretically considered in the double limit where the susceptibility of the medium is weak and the resonance is narrow. Combining direct Laplace-Fourier integration and calculations by the saddle-point method, we establish an explicit analytical expression of the transmitted field valid at any time, even when the two forerunners significantly overlap. We examine how their complete overlapping, occurring for shorter propagation distances, originates the formation of the unique transient currently named resonant precursor or dynamical beat. We obtain an expression of this transient identical to that usually derived within the slowly varying envelope approximation in spite of the initial discontinuity of the incident field envelope. The dynamical beats and $0\pi$ pulses generated by ultrashort incident pulses are also briefly examined.

We show how to measure the structural witnesses proposed previously [P. Krammer et al., Phys. Rev. Lett. 103, 100502 (2009)] for detecting entanglement in a spin chain using photon scattering. The procedure allows one to measure the two-point correlation function of the spin array. This proposal could be performed in existing experimental platforms, realizing ion chains in Paul traps or atomic arrays in optical lattices.

We propose an experiment to observe the topological phases associated with cyclic evolutions, generated by local SU(2) operations, on three-qubit entangled states prepared on different degrees of freedom of entangled photon pairs. The topological phases reveal the nontrivial topological structure of the local SU(2) orbits. We describe how to prepare states showing different topological phases and discuss their relation to entanglement. In particular, the presence of a $\pi /2$ phase shift is a signature of genuine tripartite entanglement in the sense that it does not exist for two-qubit systems.

We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits encoded on photonic degrees of freedom. We show how the spatial correlations between photons generated by spontaneous parametric down-conversion can be used to evidence the multiple topological phases acquired by entangled qudits and the role played by the Hilbert space dimension. A realistic experimental proposal is presented with numerical predictions of the expected results.

We present a study of the coloring problem (antiferromagnetic Potts model) of random regular graphs, submitted to quantum fluctuations induced by a transverse field, using the quantum cavity method and quantum Monte Carlo simulations. We determine the order of the quantum phase transition encountered at low temperature as a function of the transverse field and discuss the structure of the quantum spin-glass phase. In particular, we conclude that the quantum adiabatic algorithm would fail to solve efficiently typical instances of these problems because of avoided level crossings within the quantum spin-glass phase, caused by a competition between energetic and entropic effects.

Two schemes are proposed for the dissipative preparation of large $W$ states, of the order of ten qubits, within the context of cavity QED. By utilizing properties of the irreducible representations of su(3), we are able to construct protocols in which it is possible to restrict the open-system dynamics to a fully symmetric irreducible subspace of the total Hilbert space and hence obtain analytic solutions for effective ground-state dynamics of arbitrary-size ensembles of $\Lambda$ atoms within an optical cavity. In the proposed schemes, the natural decay processes of spontaneous emission and photon loss are no longer undesirable, but essential to the required dynamics. All aspects of the proposed schemes relevant to implementation in currently available optical cavities are explored, especially with respect to increasing system size.

It has long been known that the long-range asymptotic behavior of Hartree-Fock orbitals is different from that of the orbitals in the local potential. However, there is no consensus about observable physical effects associated with this asymptotics. Here we argue that a weaker decrease of the Hartree-Fock orbitals at large distances is responsible for the positron annihilation on the inner shell electrons, which is observed experimentally.

We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one-dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single- and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wells, pairwise tunneling of the bosons may be realized for specific system parameters. In contrast, the decay process (corresponding to a broad right well) is dominated by uncorrelated single-particle decay.

The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as an unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film, and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution.

A dramatic spectral modulation of third-order harmonic (TH) emission generated in a near-infrared femtosecond (fs) pulse filamentation, assisted by a two-dimensional plasma grating formed by two pump femtosecond pulses, is experimentally demonstrated when their spatiotemporal overlap is achieved. It is mainly attributed to strong cross-phase modulation induced by the fundamental wave of the probe pulse and two pump ones. The delay dynamic of TH spectra indicates the influence of two retarded nonlinear responses on the TH generation. The dependencies of TH generation on the energies of probe and pump pulses, relative field polarization angle are also studied.

We present an interaction scheme that exhibits a dynamical effect of virtual photons carried by a vacuum-field dressed two-level atom in the ultrastrong-coupling regime. We show that, with the aid of an external driving field, virtual photons provide a transition matrix element that enables the atom to evolve coherently and reversibly to an auxiliary level accompanied by the emission of a real photon. The process corresponds to a type of vacuum Rabi oscillation, and we show that the effective vacuum Rabi frequency is proportional to the amplitude of a single virtual photon in the ground state. Therefore, the interaction scheme could serve as a probe of ground-state structures in the ultrastrong-coupling regime.