In this paper, we construct a $\mathcal{PT}$-symmetric periodic structure with one-dimensional two-material waveguide networks and primarily investigate reflectionlessness. The formation conditions for reflectionlessness is presented in terms of the incident wave frequency and the number of unit cells. We show that, for this optical system, the orientation of unidirectional reflectionlessness can be controlled by tuning the spacing between waveguides with loss and gain. We also show the energy distribution when reflectionless light propagates through this $\mathcal{PT}$-symmetric optical structure. Finally, we find that unidirectional invisibility of the $\mathcal{PT}$-symmetric periodic structure could be achieved easily by adjusting the number of unit cells. Our results could be potentially important for developing a new generation of functional optical devices with singular directional responses.

The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include amplifying small signals, investigating quantum paradoxes, and elucidating fundamental quantum phenomena such as geometric phase. A key characteristic of the weak value is that it can be complex, in contrast to a standard expectation value. However, typically only either the real or imaginary component of the weak value is determined in a given experimental setup. Weak measurements can be used to, in a sense, simultaneously measure noncommuting observables. This principle was used in the direct measurement of the quantum wave function. However, the wave function's real and imaginary components, given by a weak value, are determined in different setups or on separate ensembles of systems, putting the procedure's directness in question. To address these issues, we introduce and experimentally demonstrate a general method to simultaneously read out both components of the weak value in a single experimental apparatus. In particular, we directly measure the polarization state of an ensemble of photons using weak measurement. With our method, each photon contributes to both the real and imaginary parts of the weak-value average. On a fundamental level, this suggests that the full complex weak value is a characteristic of each photon measured.

We address the problem of deriving the set of quantum correlations for every Bell and Kochen-Specker (KS) contextuality scenario from simple assumptions. We show that the correlations that are possible according to quantum theory are equal to those possible under the assumptions that there is a nonempty set of correlations for every KS scenario and a statistically independent realization of any two KS experiments. The proof uses tools of the graph-theoretic approach to correlations and deals with Bell nonlocality and KS contextuality in a unified way.

A minimal set of measurement operators for quantum state tomography has in the nondegenerate case ideally eigenbases which are mutually unbiased. This is different for the degenerate case. Here we consider the situation where the measurement operators are projections on individual pure quantum states. This corresponds to maximal degeneracy. We present numerically optimized sets of projectors and find that they significantly outperform those which are taken from a set of mutually unbiased bases.

This work addresses the modeling of the resonant neutralization of positive alkali-metal ions near metal surfaces. Usually the charge, induced by a positive ion, is taken into account by means of point image charge, located symmetrically to the image plane. Such an approach describes the ion level shift near the metal surfaces and gives reasonable values of the alkali-metal ion neutralization probability on the surfaces with a projected band gap, e.g., Au(111), Cu(111), and Ag(111). In this paper, we show that the induced charge is better described by means of a negatively charged plane located near the surface. This charged plane forms a potential barrier, the inclusion of which in the numerical model significantly reduces the calculated electron transfer probability and allows us to reach quantitative agreement with experimental data for free-electron surfaces, e.g., Cu(110). This repulsive potential barrier generates ion-induced states, by means of which the resonant neutralization of positive alkali-metal ions on free-electron surfaces occurs. Ion-induced states are not so important for surfaces with a projected band gap, because in this case ion neutralization occurs via well-known surface states.

In this paper we propose an optimization procedure for quality-factor (Q-factor) enhancement in dielectric oligomers. The oligomers are introduced as linear periodic chains of dielectric elements the individual Q factors of which are optimized via multipolar conversion in an avoided crossing of two resonant eigenfrequencies. It is demonstrated that when such dielectric elements are assembled into an infinite periodic array the coupling between individual resonances gives rise to an in-$\mathrm{\Gamma }$ optical bound state in the continuum (BIC) unprotected by symmetry. By setting up the oligomers of finite numbers of dielectric elements we observe high quality resonances which occur as traces of the infinite array band structure. The resulting high quality resonances exhibit light localization spots of a few squared wavelengths with Q factors $Q>{10}^4$. The localization is provided by similarity of the field pattern to that of the BIC with the losses at the edges of the array suppressed due to an almost flat BIC host band. The scaling law of the Q factor against the dielectric permittivity is derived.

Nonlinear non-Hermitian systems with saturable nonlinearities give rise to versatile phenomena that have no counterparts in linear systems. Here, we theoretically and experimentally demonstrate saturable nonlinearity (saturable absorption and gain) of erbium ions doped in silica microcavities at different concentrations. Our results show that when the doped concentration is low, the single isolated model agrees well with the experimental results, and also can be used as a basic description of highly doped samples to analyze the saturable nonlinearity. Yet, for highly doped microcavities we find that the clustering effect shall be also taken into account in order to match experimental data and to achieve a reasonable agreement. To confirm our finding, we experimentally characterize the saturable nonlinearity for ion concentrations varying from $1.0$ to $5.0\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$. Our experiment shows excellent consistency with the theory, which in turn suggests other potential applications of the theory based on saturable nonlinearity, including optical bistability and nonlinear parity-time symmetry.

We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero measure set of qubit states. We prove that the maximal maskable set of states on the Bloch sphere with respect to any masker is the ones on a spherical circle. Any states on a spherical circle on the Bloch sphere are maskable, which also proves the conjecture on maskable qubit states given by Modi et al. [Phys. Rev. Lett. 120, 230501 (2018)]. we provide explicitly operational unitary maskers for all maskable sets. As applications, different protocols for secret sharing are introduced.

Orthogonally polarized two-color fields, typically with a frequency ratio of 2:1, only rarely of 3:1, have been utilized for a variety of purposes. Driving high-order harmonic generation (HHG), the former yield linearly and the latter elliptically polarized harmonics. With emphasis on the 3:1 frequency ratio, we investigate the shape of the HHG spectrum for the fundamental frequency being in the midinfrared range (2200 nm). Depending on the relative phase between the two field components, a plethora of spectral shapes can be realized. For a suitable phase, the harmonic power can be concentrated within the highest 10% of the spectrum. The results are analyzed in terms of quantum orbits. For the 3:1 case, the scheme suggests an efficient table-top source of elliptically polarized soft x rays.

The paradigm of Schrödinger's cat illustrates how quantum states preclude the assignment of definite properties to a macroscopic object (realism). In this work, we develop a method to investigate the indefiniteness of cat states using currently available cold atom technology. The method we propose uses the observation of a statistical distribution to demonstrate the macroscopic distinction between dead and alive states and uses the determination of the interferometric sensitivity (Fisher information) to detect the indefiniteness of the cat state's vital status. We show how combining the two observations can provide information about the structure of the quantum state without the need for full quantum state tomography and propose a measure of the indefiniteness based on this structure. We test this method using a cat state proposed by Gordon and Savage [Phys. Rev. A 59, 4623 (1999)] which is dynamically produced from a coherent state. As a control, we consider a set of states produced using the same dynamical procedure acting on an initial thermal distribution. Numerically simulating our proposed method, we show that as the temperature of this initial state is increased, the produced state undergoes a quantum to classical crossover where the indefiniteness of the cat state's vital status is lost, while the macroscopic distinction between dead and alive states of the cat state is maintained.

For a pair of observables, they are called “incompatible” if and only if their commutator does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here, we explore one possible route towards this goal through uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we propose to measure the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, i.e., state independent. In particular, we focus on the incompatibility of spin-$1/2$ systems as an illustration. For an arbitrary, including nonorthogonal, setting of a finite number Pauli-spin operators, the incompatibility is analytically solved; the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, our measure of incompatibility represents a versatile tool for applications such as testing the entanglement of bipartite states, and EPR-steering criteria.

One of the challenges of photon-based quantum teleportation is that both a source of entangled photons and an entangled basis measurement are required. For qubits, one can perform a probabilistic entangled basis measurement using linear optics, making the scheme efficient. However, for photonic qudits, an equivalent scheme remains difficult to devise. In this paper, we generalize the probabilistic photonic qubit teleportation protocol to qudits. The method relies on producing permutation entangled states nondeterministically which are superpositions of permutations of the spatial and qudit states of the photons. Our scheme nondeterministically teleports a photonic qudit using only entangled photon sources, linear optics, and photon detectors, and should be experimentally realizable for small qudit dimensions.

The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realized in systems which support Hamiltonian evolution rather than discrete gates. We explore an alternative approach in which slowly varying measurements are used to mimic adiabatic evolution. We show that, for certain Hamiltonians, which remain frustration free all along the adiabatic path, the necessary measurements can be implemented through the measurement of random terms from the Hamiltonian. This offers a potentially more viable method of realizing adiabatic evolution in gate-based quantum computer architectures.

The approach suggested previously to treat the mean energy loss of charged projectiles in terms of induced currents is extended to describe the energy-loss straggling. It has been shown that, provided the perturbed wave function of electrons is known, the phenomenon can be represented in a form of distributions of densities of energy and energy squared within the target volume. These distributions satisfy respective continuity equations with the source terms defining the local deposition of energy and energy squared. The approach is applied to treat the canonical phenomenon, the stopping in a uniform electron gas, and provides a possibility to account for the spatial correlation of electrons. Two types of approximations for the perturbed state of electrons are considered, the impulse and continuum distorted-wave approximations. Together with the effect of electron correlations, these nonperturbative approaches permit one to evaluate the higher-order correction over the projectile charge. The origin of this correction is similar to the origin of Barkas correction in the stopping power; it can be argued also that there is no place in straggling for the Bloch correction. These properties, i.e., nonlinear electron response and electron correlations, can result in significant effects, both capable of changing dramatically the straggling at small projectile energies. However, in the case of positively charged projectiles, the two effects mainly compensate for one another. For negatively charged projectiles, due to the impossibility of close approaches of the collision partners, both effects are effectively smeared out.

In strong-field ionization, interferences between electron trajectories create a variety of interference structures in the final momentum distributions. Among them, the interferences between electron pathways that are driven directly to the detector and those that rescatter significantly with the parent ion lead to holography-type interference patterns that have received great attention in recent years. In this work, we study the influence of the laser magnetic-field component onto the holographic interference pattern, an effect beyond the electric-dipole approximation, in experiment and theory. The experimentally observed nondipole signatures are analyzed via quantum trajectory Monte Carlo simulations. We provide explanations for the experimentally demonstrated asymmetry in the holographic interference pattern and its nonuniform photoelectron energy dependence as well as for the variation of the topology of the holography-type interference pattern along the laser-field direction. Analytical scaling laws of the interference features are derived, and their direct relation to either the focal-volume-averaged laser intensities, or to the peak intensities are identified. The latter, in particular, provides direct access to the peak intensity in the focal volume.

Doppler cooling with lasers is essential to ion trapping and is also a preliminary step toward achieving ultracold ions. It requires substantial technological effort to experimentally monitor the ion temperature in the cooling process. Based on the simplified three-level $\mathrm{\Lambda }$ configuration, we analytically explore an one-dimensional Doppler cooling process of trapped ions, exemplified by ${}^{40}{\mathrm{Ca}}^{+}$, by solving the friction coefficient in Doppler cooling with respect to a thermal bath; in particular, for a bath with large heating rate. We propose a practical method for measuring the Rabi frequency by the Doppler cooling window, which helps for monitoring the final temperature of the Doppler-cooled ions. With our approach, the obtained results are analytical in the case of a weak thermal bath, whereas for the strong thermal bath numerical treatment is partially needed due to the involvement of the Doppler shift and a large Lamb-Dicke parameter. Our analytic treatments are applied to understand many experimental observations, such as configuration phase transition, phonon lasers, and thermodynamics regarding hot trapped ions, and could help for further our understanding three-dimensional Doppler cooling in realistic ion-trap experiments.

The indistinguishability of particles is an important feature of quantum mechanics. To account for indistinguishability, identical particles are described as inherently correlated. In this paper we study a method of transforming these correlations into operationally accessible entanglement with single-particle subtractions. We provide specific protocols to turn the bosonic symmetrization into various classes of entanglement. Moreover, we explain why analogous schemes cannot work for fermions. These results provide a new perspective on manipulating quantum states with heralded subtraction.

We present the results of an analysis of noiselike pulses generated in passively mode-locked fiber lasers with anomalous dispersion. The master equation used for the analysis takes into account the gain saturation, the quadratic frequency dispersion of the gain and the refractive index, and the cubic-quintic nonlinearity of the losses and refractive index. Reasons for the stabilization of noiselike pulses are investigated. It is found that the space-time localization of a noiselike pulse is associated with the suppression of single solitons located outside this pulse. The mechanism of such competition between single solitons and a noiselike pulse is determined.

Recently, it was demonstrated both theoretically and experimentally on the D-Wave quantum annealer that transverse-field quantum annealing does not find all ground states with equal probability. In particular, it was proposed that more complex driver Hamiltonians beyond transverse fields might mitigate this shortcoming. Here, we investigate the mechanisms of (un)fair sampling in quantum annealing. While higher-order terms can improve the sampling for selected small problems, we present multiple counterexamples where driver Hamiltonians that go beyond transverse fields do not remove the sampling bias. Using perturbation theory we explain why this is the case. In addition, we present large-scale quantum Monte Carlo simulations for spin glasses with known degeneracy in two space dimensions and demonstrate that the fair-sampling performance of quadratic driver terms is comparable to standard transverse-field drivers. Our results suggest that quantum annealing machines are not well suited for sampling applications, unless postprocessing techniques to improve the sampling are applied.

A recent experimental study of the energy losses of various ions in titanium nitride, in the low-energy range [M. A. Sortica et al., Sci. Rep. 9, 176 (2019)], showed a striking departure of the measured values from those predicted by density functional theory. They suggested electron promotion in atomic collisions between dressed atoms as an explanation. In this Rapid Communication, we investigate the process of energy loss of slow ions in TiN using theoretical formulations that are based, on one side, on self-consistent models of nonlinear screening and quantum scattering theory, and on the other, on ab initio computations of the electron-density profile of titanium nitride. Two theoretical approaches are considered to determine the average energy transfer: One is based on the local-density approximation for the inhomogeneous electron gas corresponding to the calculated density of TiN, and the other is based on the Penn model for the convolution of the inhomogeneous electron-gas response based on a measured electron-loss function. Both approaches produce very similar results and are in remarkable agreement with the experimental data, indicating that the observed enhancement in the energy-loss values is due to the contribution of a range of electron densities in the TiN compound.