We present a method to generate an extremely short unipolar half-cycle pulse based on resonant propagation of a few-cycle pulse through asymmetrical media with periodic subwavelength structure. Moreover, single- and few-cycle gap solitons with different frequencies are found to split from one incident few-cycle ultrashort pulse. These solitons with various frequencies provide evidence for the generation of different parametric waves during the strong light-matter coupling in asymmetrical media under the extreme nonlinear optics condition. Because of the pulse self-shaping process during the course of resonant propagation, the generated low-frequency sideband and another broadband continuum sideband ranging from the visible to the near-infrared regime couple together, which results in the generation of the subfemtosecond unipolar half-cycle pulse. A time-frequency analysis is preformed which corroborates the mechanism. The generated unipolar half-cycle pulse might be utilized to control and probe the ultrafast electronic dynamics.

We demonstrate high-order harmonic generation in a wave form synthesized by a multicycle 800-nm chirped laser pulse and a chirp-free laser pulse. Compared with the case of using only a chirped pulse, both the harmonic cutoff and the extreme ultraviolet supercontinuum can be extended when a weak chirp-free pulse is combined with the chirped pulse. When chirp-free pulse intensity grows, the cutoff energy and bandwidth of the supercontinuum grow as well. It is found that the broad supercontinuum can be achieved for a driving pulse with long duration even though the driving pulse reaches 10 optical cycles. An isolated attosecond pulse with duration of about 59 as is obtained, and after appropriate phase compensation with a duration of about $11$ as. In addition, by performing time-frequency analyses and the classical trajectory simulation, the difference in supercontinuum generation between the preceding wave form and a similar wave form synthesized by an $800$-nm fundamental pulse and a $1600$-nm subharmonic pulse is investigated.

An $N$-level quantum model is proposed in which the energies are represented by an $N$-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials $G(n,a,x)$ is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians $H\ne H^{†}$. We managed to (i) start from elementary secular equation $G(N,a,E_n)=0$, (ii) keep our $H$, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric $\Theta \ne I$, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared $N$-site lattice.

We propose a scheme for entanglement distribution among different single atoms trapped in separated cavities. In our scheme, by reflecting an input coherent optical pulse from a cavity with a single trapped atom, a controlled phase-shift gate between the atom and the coherent optical pulse is achieved. Based on this gate and homodyne detection, we construct an $n$-qubit parity gate and show its use for the distribution of a large class of entangled states in one shot, including the GHZ state $|{\mathrm{GHZ}}_n\rangle$, $W$ state $|W_n\rangle$, Dicke state $|D_{n,k}\rangle$, and certain sums of Dicke states $|G_{n,k}\rangle$. We also show that such a distribution could be performed with high success probability and high fidelity even in the presence of channel loss.

For each odd prime power $q$, let $4⩽n⩽q^2+1$. Hermitian self-orthogonal $[n,2,n-1]$ codes over ${\mathbf{F}}_{q^2}$ with dual distance three are constructed by using finite field theory. Hence, $[[n,n-4,3]]{}_q$ quantum maximal-distance-separable (MDS) codes for $4⩽n⩽q^2+1$ are obtained.

Electron-hydrogen scattering in weakly coupled hot-dense plasmas has been investigated using the convergent-close-coupling method. The Yukawa-type Debye-Hückel potential has been used to describe the plasma screening effects. The target structure, excitation dynamics, and ionization process change dramatically as the screening is increased. Excitation cross sections for the $1s\to 2s,2p,3s,3p,3d$ and $2s\to 2p,3s,3p,3d$ transitions and total and total ionization cross sections for the scattering from the $1s$ and $2s$ states are presented. Calculations cover the energy range from thresholds to high energies ($250$ eV) for various Debye lengths. We find that as the screening increases, the excitation and total cross sections decrease, while the total ionization cross sections increase.

The single-body Schrödinger equation with complex potentials has been studied intensively. In this work, we investigate the dynamical process for Bose-Einstein condensed gases, based on the many-body Schrödinger equation with complex potentials. It is shown that a weakly imaginary periodic potential may induce perfect quantum coherence between different condensates, even without considering interatomic interactions. This imaginary-potential-induced quantum coherence may be tested with present experimental techniques. We also consider the quantum coherence in the presence of both the imaginary periodic potential and interatomic interactions.

We present a scheme for obtaining entangled photons and quantum phase gates in a room-temperature four-state tripod-type atomic system with two-mode active Raman gain (ARG). We analyze the linear and nonlinear optical responses of this ARG system and show that the scheme is fundamentally different from those based on electromagnetically induced transparency and hence can avoid significant probe-field absorption as well as a temperature-related Doppler effect. We demonstrate that highly entangled photon pairs can be produced and rapidly responding polarization qubit phase gates can be constructed based on the unique features of the enhanced cross-phase-modulation and superluminal probe-field propagation of the system.

We theoretically investigate the opto-mechanical interactions between a dielectric nanoparticle and the resonantly enhanced optical field inside a high $Q$, small-mode-volume optical cavity. We develop an analytical method based on open system analysis to account for the resonant perturbation due to particle introduction and predict trapping potential in good agreement with three-dimensional (3D) finite-difference time-domain (FDTD) numerical simulations. Strong size-dependent trapping dynamics distinctly different from free-space optical tweezers arise as a consequence of the finite cavity perturbation. We illustrate single nanoparticle trapping from an ensemble of monodispersed particles based on size-dependent trapping dynamics. We further discover that the failure of the conventional dipole approximation in the case of resonant cavity trapping originates from a new perturbation interaction mechanism between trapped particles and spatially localized photons.

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increases (decreases) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.

Energies and wave functions for quasibound states of a relativistic particle interacting with the field of a quadratic isotropic potential $V(r)=m{\omega }^2{r}^2/2$ are obtained using a power expansion method. The stabilization of autoionizing resonances is performed by introducing the spherical confinement of finite radius $R_b$. For comparison, the problem is investigated also in the framework of direct perturbation theory (DPT). It has been shown that the substantial degeneracy of nonrelativistic levels of the isotropic harmonic oscillator is completely removed. The relativistic effects, spin effects, fine-structure splittings, and radial densities of probability for several states are studied.

Geometric phases and information flows of a two-level system coupled to its environment are calculated and analyzed. The information flow is defined as a cumulant of changes in trace distance between two quantum states, which is similar to the measure for non-Markovianity given by Breuer. We obtain an analytic relation between the geometric phase and the information flow for pure initial states, and a numerical result for mixed initial states. The geometric phase behaves differently depending on whether there are information flows back to the two-level system from its environment.

We present a class of two-dimensional (2D) systems which shows a counterintuitive property that contradicts a semiclassical intuition: A 2D quantum particle “prefers” tunneling through a barrier rather than traveling above it. Viewing the one-particle 2D system as a system of two 1D particles, it is demonstrated that this effect occurs due to a specific symmetry of the barrier that forces excitations of the interparticle degree of freedom that, in turn, lead to the appearance of an effective potential barrier even though there is no “real” barrier. This phenomenon cannot exist in 1D.

We show that a local Hamiltonian of spin-$\frac{3}{2}$ particles with only two-body nearest-neighbor Affleck-Kennedy-Lieb-Tasaki and exchange-type interactions has a unique ground state, which can be used to implement universal quantum computation merely with single-spin measurements. We prove that the Hamiltonian is gapped, independent of the system size. Our result provides a further step toward utilizing systems with condensed-matter-type interactions for measurement-based quantum computation.

We provide a class of optimal nondecomposable entanglement witnesses for $4N\times 4N$ composite quantum systems or, equivalently, another construction of nondecomposable positive maps in the algebra of $4N\times 4N$ complex matrices. This construction provides natural generalization of the Robertson map. It is shown that their structural physical approximations give rise to entanglement breaking channels.

We propose an architecture based on superconducting qubits and resonators for the implementation of a variety of exotic lattice systems, such as spin and Hubbard models in higher or fractal dimensions and higher-genus topologies. Spin systems are realized naturally using qubits, while superconducting resonators can be used for the realization of Bose-Hubbard models. Fundamental requirements for these designs, such as controllable interactions between arbitrary qubit pairs, have recently been implemented in the laboratory, rendering our proposals feasible with current technology.

We study the set of random matrix product states (RMPS) introduced by Garnerone, de Oliveira, and Zanardi [S. Garnerone, T. R. de Oliveira, and P. Zanardi, Phys. Rev. A 81, 032336 (2010)] as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical investigation of the properties of RMPS. We calculate the average state of the ensemble in the nonhomogeneous case, and numerically check the validity of this result. We also suggest using RMPS as a tool to approximate properties of general quantum random states. The numerical simulations presented here support the accuracy and efficiency of this approximation. These results suggest that any generalized canonical state can be approximated with high probability by the reduced density matrix of a RMPS, if the average matrix product states coincide with the associated microcanonical ensemble.

We investigate whether a two-qubit quantum gate can be implemented in a scattering process involving a flying and a static qubit. To this end, we focus on a paradigmatic setup made out of a mobile particle and a quantum impurity, whose respective spin degrees of freedom couple to each other during a one-dimensional scattering process. Once a condition for the occurrence of quantum gates is derived in terms of spin-dependent transmission coefficients, we show that this can be actually fulfilled through the insertion of an additional narrow potential barrier. An interesting observation is that under resonance conditions this procedure enables a gate only for isotropic Heisenberg (exchange) interactions and fails for an $\mathit{XY}$ interaction. We show the existence of parameter regimes for which gates able to establish a maximum amount of entanglement can be implemented. The gates are found to be robust to variations of the optimal parameters.

It was shown by T. Morimae [Phys. Rev. A 81, 060307(R) (2010)] that the gate fidelity of an inaccurate one-way quantum computation is upper bounded by a decreasing function of the amount of entanglement in the register. This means that a strong entanglement causes the low gate fidelity in the one-way quantum computation with inaccurate measurements. In this paper, we derive similar entanglement-fidelity relations for the inaccurate ancilla-driven quantum computation. These relations again imply that a strong entanglement in the register causes the low gate fidelity in the ancilla-driven quantum computation if the measurements on the ancilla are inaccurate.

We present experimental atomic lifetimes for $12$ levels in Sb i. The levels belong to the $5$$p$${}^2$(${}^{3}P$)$6$$s$ ${}^{2}P$, ${}^{4}P$, and $5$$p^2$(${}^{3}P)5d$ ${}^{4}P$, ${}^{4}F$, and ${}^{2}F$ terms. The lifetimes were measured using time-resolved laser-induced fluorescence. In addition, we report calculations of transition probabilities in Sb i using a multiconfigurational Dirac-Hartree-Fock method. The physical model was tested through comparisons between theoretical and experimental lifetimes for 5$d$ and 6$s$ levels. The lifetimes of the $5$$d$ ${}^4{F}_{3/2,5/2,7/2}$ levels ($19.5$, $7.8$, and $54$ ns, respectively) depend strongly on the $J$ value. This is explained by different degrees of level mixing for the different levels in the ${}^{4}F$ term.