Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. However, in practice, it is difficult to distribute quantum entanglement over a long distance, due to the absorption and noise in quantum channels. A solution to this challenge is a quantum repeater, which can extend the distance of entanglement distribution. In this scheme, the time consumption of classical communication and local operations takes an important place with respect to time efficiency. Motivated by this observation, we consider a basic quantum repeater scheme that focuses on not only the optimal rate of entanglement concentration but also the complexity of local operations and classical communication. First, we consider the case where two different two-qubit pure states are initially distributed in the scenario. We construct a protocol with the optimal entanglement-concentration rate and less consumption of local operations and classical communication. We also find a criterion for the projective measurements to achieve the optimal probability of creating a maximally entangled state between the two ends. Second, we consider the case in which two general pure states are prepared and general measurements are allowed. We get an upper bound on the probability for a successful measurement operation to produce a maximally entangled state without any further local operations.

Accurate intercombination transition rates ($A$), arising from the $2s^{2}2pnl$ ($n$ = 3, 4, 5; $l$ = $s,p,d$) and $2s2p^3$ configurations of ${\mathrm{N}}^{+}$, are reported. Wavefunctions for the studied states in ${\mathrm{N}}^{+}$ are determined using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method and account for the effects of valence, core-valence (CV), and core-core (CC) correlations. It is found that the combined CV and CC correlation effects are important for accurate predictions of intercombination rates of ${\mathrm{N}}^{+}$. A strong spin-orbit mixing between the states ${}^{3}P_1^o$ and ${}^{1}P_1^o$ of $2s^{2}2p3s$ causes that the intercombination rates on its states ${}^{1,3}P_1^o$ are exceedingly sensitive to electron correlations and other corrections. The strong visible intercombination lines of ${\mathrm{N}}^{+}$ arise from the $2s^{2}2p3s-2s^{2}2p3p$ and $2s^{2}2p3p-2s^{2}2p3d$ transitions. There are also strong infrared and ultraviolet intercombination lines that have important applications in plasma diagnosis of radiative cooling coefficient and abundance. Different systematic methods are used to evaluate the intercombination rates and their uncertainties. For relatively strong lines ($gf>0.01$) of $2s^{2}2p3l$($l$ = $s,p,d$), $2s^{2}2p4l$($l$ = $s,p,d$) and $2s^{2}2p5s$ the uncertainties are separately estimated to be within 7%, 12%, and 20%. The rates of extremely weak lines, $gf<{10}^{-6}$, are of interests in the temperature and density diagnostic in nebulae, but are remarkably difficult to accurately calculate. The present calculations have included appropriate electron correlations to deal with them and provide guidance for further studies.

It is shown that triple ionization (TI) of the ${\mathrm{Se}}^{2+}$ ion is mainly formed in two ways: (i) Auger cascade following single ionization of the $3p$ shell and (ii) direct double ionization (DDI) with subsequent autoionization. A good agreement with recent experimental measurements is obtained when one of electrons in the DDI process acquires all the excess energy. The study also reveals negligible contribution of the direct TI by electron impact to the process. Single-ionization cross sections of the excitation-autoionization process show large dependence on the levels of the ground configuration. The obtained results demonstrate that the ions in the parent beam mainly reside in the highest level of the ground configuration.

Positronium (Ps) scattering by noble-gas atoms (He, Ne, Ar, Kr, and Xe) is studied in the frozen-target approximation and with inclusion of the van der Waals interaction. Single-particle electron and positron states in the field of the target atom are calculated, with the system enclosed by a hard spherical wall. The two-particle Ps wave function is expanded in these states, and the Hamiltonian matrix is diagonalized, giving the Ps energy levels in the cavity. Scattering phase shifts, scattering lengths, and cross sections are extracted from these energies and compared with existing calculations and experimental data. Analysis of the effect of the van der Waals interaction shows that it cannot explain the recent experimental data of Brawley et al. for Ar and Xe [Phys. Rev. Lett. 115, 223201 (2015)].

Solving the time-dependent Schrödinger equation numerically within the framework of an ab initio model, the breakdown of the dipole approximation in modeling the ionization and excitation dynamics of a hydrogen atom exposed to an intense 1.36-keV x-ray laser pulse is investigated in some detail. The relative importance of the ${\mathit{A}}^2$ diamagnetic term in comparison with the $\mathit{A}·\mathit{p}$ contribution to the resulting beyond-dipole (nondipole) light-matter interaction is studied for laser pulse intensities ranging from the weak perturbative to the strong-field regime. It is found that the diamagnetic interaction represents by far the most important correction to the dipole approximation at higher field strengths, while nondipole corrections induced by the $\mathit{A}·\mathit{p}$ operator are generally small and largely independent of the laser intensity. The most profound finding of the present study was the discovery of a forward-backward asymmetry in the underlying electron ejection dynamics: Depending on the electron's kinetic energy in the final state, the photoelectron tends to be emitted in the laser propagation (forward) and/or counterpropagation (backward) directions, for energies corresponding to the low-energy and/or high-energy side of the multiphoton resonances, respectively.

We present low-frequency approximation (LFA) for high-order harmonic generation (HHG) process. LFA represents the lowest-order term of an expansion of the final-state interaction matrix element in powers of the laser-field frequency $\omega$. In this approximation the plane-wave recombination matrix element which appears in the strong-field approximation is replaced by the exact laser-free recombination matrix element calculated for the laser-field dressed electron momenta. First, we have shown that the HHG spectra obtained using the LFA agree with those obtained solving the time-dependent Schrödinger equation. Next, we have applied this LFA to calculate the HHG rate for inert gases exposed to a bicircular field. The bicircular field, which consists of two coplanar counter-rotating fields having different frequencies (usually $\omega$ and $2\omega$), is presently an important subject of scientific research since it enables efficient generation of circularly polarized high-order harmonics (coherent soft x rays). Analyzing the photorecombination matrix element we have found that the HHG rate can efficiently be calculated using the angular momentum basis with the states oriented in the direction of the bicircular field components. Our numerical results show that the HHG rate for atoms having $p$ ground state, for higher high-order harmonic energies, is larger for circularly polarized harmonics having the helicity $-1$. For lower energies the harmonics having helicity $+1$ prevails. The transition between these two harmonic energy regions can appear near the Cooper minimum, which, in the case of Ar atoms, makes the selection of high-order harmonics having the same helicity much easier. This is important for applications (for example, for generation of attosecond pulse trains of circularly polarized harmonics).

Wavelength scaling of high-order harmonic generation (HHG) in a non-Born-Oppenheimer treatment of ${\mathrm{H}}_2{}^{+}$ is investigated by numerical simulations of the time-dependent Schrödinger equation. The results show that the decrease in the wavelength-dependent HHG yield is reduced compared to that in the fixed-nucleus approximation. This slower wavelength scaling is related to the charge-resonance-enhanced ionization effect, which considerably increases the ionization rate at longer driving laser wavelengths due to the relatively larger nuclear separation. In addition, we find an oscillation structure in the wavelength scaling of HHG from ${\mathrm{H}}_2^{+}$. Upon decreasing the laser intensity or increasing the nuclear mass, the oscillation structure will shift towards a longer wavelength of the laser pulse. These results permit the generation of an efficient harmonic spectrum in the midinfrared regime by manipulating the nuclear dynamics of molecules.

A quantum system exhibiting $\mathcal{PT}$ symmetry is a Bose-Einstein condensate in a double-well potential with balanced particle gain and loss, which is described in the mean-field limit by a Gross-Pitaevskii equation with a complex potential. A possible experimental realization of such a system by embedding it into a Hermitian time-dependent four-mode optical lattice was proposed by Kreibich et al. [Phys. Rev. A 87, 051601(R) (2013)], where additional potential wells act as reservoirs and particle exchange happens via tunneling. Since particle influx and outflux have to be controlled explicitly, a set of conditions on the potential parameters had to be derived. In contrast to previous work, our focus lies on a full many-body description beyond the mean-field approximation using a Bose-Hubbard model with time-dependent potentials. This gives rise to additional quantum effects, such that the differences between mean-field and many-body dynamics are of special interest. We further present stationary analytical solutions for the embedded wells in the mean-field limit, different approaches for the embedding into a many-body system, and a very efficient method for the evaluation of hopping terms to calculate exact Bose-Hubbard dynamics.

We consider bosonic atoms loaded into optical lattices with cavity-mediated infinite-range interactions. Competing short- and global-range interactions cultivate a rich phase diagram. With a systematic field-theoretical perspective, we present an analytical construction of a global ground-state phase diagram. We find that the infinite-range interaction enhances the fluctuation of the number density. In the strong-coupling regime, we find four branches of elementary excitations, with two being “particlelike” and two being “holelike,” and that the excitation gap becomes soft at the phase boundary between compressible phases and incompressible phases. We derive an effective theory describing compressible superfluid and supersolid states. To complement this perturbative study, we construct a self-consistent mean-field theory and find numerical results consistent with our theoretical analysis. We map out the phase diagram and find that a charge density wave may undergo a structure phase transition to a different charge density wave before it finally enters into the supersolid phase driven by increasing the hopping amplitude.

We consider the fate of Bose-Einstein condensation with time-reversal symmetry and inversion symmetry in a spin-orbit-coupled bilayer system. When these two symmetry operators commute, all the single-particle bands are exactly twofold degenerate in the momentum space. The scattering in the twofold-degenerate rings can relax the spin-momentum locking effect from spin-orbit-coupling interaction and thus can realize the spin-polarized plane-wave phase even when the interparticle interaction dominates. When these two operators anticommute, the lowest two bands may have the same minimal energy, but with totally different spin structures. As a result, the competition between different condensates in these two energetically degenerate rings can give rise to different stripe phases with atoms condensed at two or four collinear momenta. We find that the crossover between these two cases is accompanied by the excited band condensation when the interference energy can overcome the increased single-particle energy in the excited band. This effect is not based on strong interaction and thus can be realized even with moderate interaction strength.

We study the classical correlation function of spatially incoherent beams with a phase aberration in the beam path. On the basis of our experimental measurements and in the optical coherence theory, we show that the effects of phase disturbances, independently of their kind and without need of coordinate inversion, can be canceled out if the same phase is aligned in the signal and reference beam path. These results can be useful for imaging and microscopy through random media.

Single atoms form a model system for understanding the limits of single-photon detection. Here, we develop a non-Markovian theory of single-photon absorption by a two-level atom to place limits on the absorption (transduction) time. We show the existence of a finite rise time in the probability of excitation of the atom during the absorption event which is infinitely fast in previous Markov theories. This rise time is governed by the bandwidth of the atom-field interaction spectrum and leads to a fundamental jitter in time stamping the absorption event. Our theoretical framework captures both the weak and strong atom-field coupling regimes and sheds light on the spectral matching between the interaction bandwidth and single-photon Fock state pulse spectrum. Our work opens questions whether such jitter in the absorption event can be observed in a multimode realistic single-photon detector. Finally, we also shed light on the fundamental differences between linear and nonlinear detector outputs for single-photon Fock-state vs coherent-state pulses.

We propose to couple the optical orientational nonlinearities of liquid crystals with their ability to self-organize to tailor them to control space-variant-polarized optical fields in a nonlinear manner. Experimental demonstration is made using a liquid crystal light valve that behaves like a light-driven geometric phase optical element. We also unveil two original nonlinear optical processes, namely self-induced separability and nonseparability. These results contribute to the advancement of nonlinear singular optics that is still in its infancy despite 25 years of effort, which may foster the development of nonlinear protocols to manipulate high-dimensional optical information both in the classical and quantum regimes.

The most typical ingredient of topologically protected quantum states is magnetic fluxes. In a system of spins, complex-valued interaction parameters give rise to a flux, if their phases do not add up to zero along a closed loop. Here we apply periodic driving, a powerful tool for quantum engineering, to a trapped-ion quantum simulator in order to generate such spin-spin interactions. We consider a simple driving scheme, consisting of a repeated series of locally quenched fields, and demonstrate the feasibility of this approach by studying the dynamics of a small system. An emblematic hallmark of the flux, accessible in experiments, is the appearance of chiral spin currents. Strikingly, we find that in parameter regimes where, in the absence of fluxes, phonon excitations dramatically reduce the fidelity of the spin model simulation, the spin dynamics remains widely unaffected by the phonons when fluxes are present. Our work provides a realistic experimental recipe to engineer the minimal building block of a topological quantum system with a currently existing ion trap apparatus.

We report an experimental observation of the interatomic Coulombic decay (ICD) and radiative charge-transfer (RCT) processes in a Ne dimer $\left(e,2e\right)$ following a 380-eV electron impact. By detecting the $\mathrm{N}{\mathrm{e}}^{+}-\mathrm{N}{\mathrm{e}}^{+}$ cation pair and one of the emitted electrons in coincidence, the fingerprint of the ICD process initiated by the inner-valence ionization of Ne is obtained. Furthermore, the experimental results and ab initio calculations together unambiguously confirm the occurrence of the RCT process, and we show that most of the low-energy electrons produced in ionization of the Ne dimers are due to the ICD, which strongly suggests the importance of the ICD in causing radiation damage in a biological medium.

Using a superconducting circuit QED device, we present a theoretical study of real-time quantum state estimation via the quantum Bayesian approach. Suitable conditions under which the quantum Bayesian approach can accurately update the density matrix of the qubit are analyzed. We also consider the correlation between some basic and physically meaningful parameters of the circuit QED and the performance of the Bayesian approach. Our results advance the understanding of the quantum Bayesian approach.

We address parameter estimation in two-level systems exhibiting level anticrossing and prove that universally optimal strategies for parameter estimation may be designed. In fact, we find a parameter-independent measurement scheme, leading to the ultimate quantum precision, independently of the value of the parameter of interest. Optimal estimation may be achieved also at high temperature, depending on the structure of the two-level Hamiltonian. Finally, we discuss parameter estimation based on dynamical strategies, and a number of specific applications.

We investigate a parity-time ($\mathcal{PT}$)-symmetric system that consists of two symmetrically coupled asymmetric dimers. The enclosed magnetic flux controls the $\mathcal{PT}$ phase transition. The system can reenter the exact $\mathcal{PT}$-symmetric phase from a broken $\mathcal{PT}$-symmetric phase with large non-Hermiticity. Two-state coalescence may have one or two defective eigenstates. The topology of exceptional points is reflected by the phase rigidity scaling exponents. The topology changes when exceptional points coincide. The geometric phases accumulate when encircling the exceptional points and vary as the magnetic flux. The magnetic flux is favorable for the realization of high-order exceptional points. A triple point of different quantum phases has an order of 4. The perturbation around the four-state coalescence leads to a fourth-root mode frequency splitting; the sensing sensitivity is significantly enhanced.

We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises, such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two times longer than conventional maximally entangled states.