We propose the concept of a plasma compressor capable of producing extremely short relativistic laser pulse, which is based on the studies of self-focusing of high-power laser pulses under the wake-wave excitation conditions. It is shown that, in the optimal regime, the compression of laser pulses up to a duration of one optical cycle is possible. We study the influence of hose instability on the process of pulse self-compression and have found that this instability is not important for a wide set of initial conditions. The matter is that the length of pulse distortion in both transverse and longitudinal directions is larger than the length of the pulse self-compression. Hose instability gives only negligible decrease of compression degree and weak deformation of pulse profile.

We construct faces of the convex set of all $2\otimes 4$ bipartite separable states, which are affinely isomorphic to the simplex ${\Delta }_9$ with 10 extreme points. Every interior point of these faces is a separable state which has a unique decomposition into 10 product states, even though the ranks of the state and its partial transpose are 5 and 7, respectively. We also note that the number 10 is greater than $2\times 4$, to disprove a conjecture on the lengths of qubit-qudit separable states. This face is inscribed in the corresponding face of the convex set of all PPT states so that subsimplices ${\Delta }_k$ of ${\Delta }_9$ share the boundary if and only if $k\le 5$. This enables us to find a large class of $2\otimes 4$ PPT entangled edge states with rank 5.

We propose to implement tunable interfaces for realizing universal quantum computation with topological qubits. One interface is between the topological and superconducting qubits, which can realize an arbitrary single-qubit gate on the topological qubit. When two qubits are involved, the interface between the topological qubits and a microwave cavity can induce a nontrivial two-qubit gate, which cannot be constructed based on braiding operations. The two interfaces, being tunable via an external magnetic flux, may serve as the building blocks towards universal quantum computation with topological qubits.

In this paper we obtain analytical solutions of the Dirac and the Klein-Gordon equations coupled to a strong electromagnetic wave in the presence of a plasma environment. These are a generalization of the familiar Volkov solutions. The contribution of the nonzero photon effective mass to the scalar and fermion wave functions, conserved quantities, and effective mass is demonstrated. The wave functions exhibit differences from Volkov solutions for nowadays available laser intensity.

The Leggett-Garg inequality (LGI) as a temporal analog of Bell's inequality, derived using the notion of realism, is studied in a hitherto unexplored context involving weak-interaction-induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of the LGI obtained from the relevant quantum mechanical results is significantly higher for oscillating neutrinos compared to that for kaons. Interestingly, the effect of CP noninvariance for the kaon oscillation is to enhance this violation, while, for neutrinos, the violation is sensitive to the value of mixing parameter.

We find that real and complex Bohmian quantum trajectories resulting from well-localized Klauder coherent states in the quasi-Poissonian regime possess qualitatively the same type of trajectories as those obtained from a purely classical analysis of the corresponding Hamilton-Jacobi equation. In the complex cases we treated the quantum potential results to a constant, such that the agreement is exact. For the real cases we provide conjectures for analytical solutions for the trajectories as well as the corresponding quantum potentials. The overall qualitative behavior is governed by the Mandel parameter determining the regime in which the wave functions evolve as solitonlike structures. We demonstrate these features explicitly for the harmonic oscillator and the Pöschl-Teller potential.

Positive operator valued measures representing phase observables for systems with arbitrary discrete, possibly degenerate, spectra are constructed. The general construction is presented and discussed using illustrative examples. The phase POVM shows intricate discontinuous dependence on the eigenfrequencies. Special discussion is devoted to the systems with degenerate energy spectrum, in which case the phase observable is nonunique. We present arguments that can be used to reduces this nonuniqueness.

In this paper, we propose an environment-assisted error correction scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an $N$-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an $N$-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum entangled state beyond the standard RU scheme.

We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a nonlinear Boolean function with a high probability are contextual. The class of contextual MBQCs includes an example which is of practical interest and has a superpolynomial speedup over the best-known classical algorithm, namely, the quantum algorithm that solves the “discrete log” problem.

A general approach to evaluation of two-center two-electron exponential integrals with arbitrary parameters is presented. The results for the Born-Oppenheimer potential for various excited states of molecular hydrogen with Kołos-Wolniewicz functions are obtained with precision exceeding previous values by about three orders of magnitude.

The Pauli exclusion principle gives an upper bound of 1 on natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of a kinematic nature, satisfied by these numbers [M. Altunbulak and A. Klyachko, Commun. Math. Phys. 282, 287 (2008)]. Here a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasipinned. For rank 6 and rank 7 approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank 8 approximation we find well-defined families of saturation conditions.

We present a theoretical study to determine the energies, widths, and wave functions of the neutral hydrogen atom under a constant electric field by the direct integration of the Hamiltonian in parabolic coordinates. We work in terms of the complex coordinate rotation to distinguish the resonances from the continuum sea, and the wave functions are expanded in a basis set of Laguerre-mesh polynomials. We obtain ab initio results for the first five atomic shells of neutral hydrogen for a field intensity up to ${10}^9$ V/m.

The nonradiative single-electron-capture (SEC) and double-electron-capture (DEC) processes for C${}^{4+}$(1$s^2$) colliding with He atoms are investigated by using the quantum-mechanical molecular-orbital close-coupling method. Total and state-selective electron-capture cross sections are calculated in the energy range of 10${}^{-6}$–6 keV/amu. For energies less than 2 keV/amu, the DEC dominates the electron-capture processes. As the energy increases, the SEC cross sections increase while the DEC cross sections decrease; when $E$ > 2 keV/amu, the SEC process becomes the dominant mechanism. It is found that the SEC processes mainly result from the electron capture to $n$ = 3 channels of C${}^{3+}$ ion for energy below 0.7 keV/amu and from $n$ = 2 channels for $E>0.7$ keV/amu. Compared with the available theoretical calculations, better agreement is achieved between the present results and the available measurements for total DEC and SEC cross sections. For state-resolved cross sections, excellent agreement is obtained for two-electron capture to C${}^{2+}$(2$s^2$), C${}^{2+}$(2$s$2$p$), and C${}^{2+}$(2$p^2$) and one-electron capture to C${}^{3+}$(2$s$) and C${}^{3+}$(2$p$) between the present calculations and the available theoretical and experimental results.

We consider a two-component gas of fermionic atoms confined to a quasi-two-dimensional (quasi-2D) geometry by a harmonic trapping potential in the transverse direction. We construct a mean-field theory of the BCS-BEC crossover at zero temperature that allows us to extrapolate to an infinite number of transverse harmonic oscillator levels. In the extreme BEC limit, where the confinement length exceeds the dimer size, we recover 3D dimers confined to two dimensions with weak repulsive interactions. However, even when the interactions are weak and the Fermi energy is less than the confinement frequency, we find that the higher transverse levels can substantially modify fermion pairing. We argue that recent experiments on pairing in quasi-2D Fermi gases [Y. Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)] have already observed the effects of higher transverse levels.

Boson-fermion pair correlations in a mixture are considered at zero temperature in the $T$-matrix approximation. Special attention is paid to the Luttinger theorem. In a strict random-phase approximation variant of the Nozières-Schmitt-Rink approach, it is shown that this theorem is respected also in the homogeneous infinite matter case. We calculate the corresponding occupation numbers of fermions and bosons and the condensate depletion. We also show that in the limit of very small boson density, our results are in good agreement with the results found in the literature for the Fermi polaron in strongly imbalanced Fermi-Fermi mixtures.

We study the soliton scattering by parity-time- (PT) symmetric potentials and demonstrate that, for a certain range of parameters, both single and multiple soliton scattering exhibit almost perfect unidirectional flow. We employ direct numerical simulations of the corresponding nonlinear Schrödinger equation combined with the analysis of the effective equations derived by the collective-coordinate approach and reveal that the physical mechanism behind this effect of the unidirectional scattering is related to the energy exchange between the soliton center of mass and its internal mode.

We theoretically analyze photonic-plasmonic coupling between a high-$Q$ whispering gallery mode (WGM) resonator and a core-shell nanoparticle. Blue and red shifts of WGM resonances are shown to arise from crossing of the photonic and plasmonic modes. Level repulsion in the hybrid system is further seen to enable sensitivity enhancements in WGM sensors: maximal when the two resonators are detuned by half the plasmon linewidth. Approximate bounds are given to quantify possible enhancements. Criteria for reactive vs resistive coupling are also established.

We investigate the light transmission through a nanoaperture in a metal film deposited on a planar metamaterial. An effect of an anomalously high light transmission (up to $800\%$) through the nanoaperture is revealed, which we associate with the enhancement of the field at the interface of the planar structure “metamaterial–metal-film” due to the appearance of an optical Tamm state. Our numerical results are in qualitative agreement with experimental data.

It is shown that there is a direct connection between the enhancement effects of chiroptical spectroscopic signals using perpendicular-polarization detection method and the amplifications of various weak effects, known as weak-value measurements, in quantum optics. In addition, the acceptable range of chiroptical weak values is discussed.

The recent progresses in single crystalline wide bandgap hexagonal disk have stimulated intense research attention on pursuing ultraviolet (UV) laser diodes with low thresholds. While whispering-gallery modes based UV lasers have been successfully obtained in GaN, ZnO nanorods, and nanopillars, the reported thresholds are still very high, due to the low-quality ($Q$) factors of the hexagonal resonances. Here we demonstrate resonances whose $Q$ factors can be more than two orders of magnitude higher than the hexagonal modes, promising the reduction of the energy consumption. The key to our finding is the avoided resonance crossing between superscar states along two sets of nearly degenerated triangle orbits, which leads to the formation of hexagram modes. The mode couplings suppress the field distributions at the corners and the deviations from triangle orbits simultaneously and therefore enhance the $Q$ factors significantly.