We consider a quantum emitter (“atom”) radiating in a one-dimensional photonic waveguide in the presence of a single mirror, resulting in a delay differential equation for the atomic amplitude. We carry out a systematic analysis of the non-Markovian (NM) character of the atomic dynamics in terms of refined, recently developed notions of quantum non-Markovianity such as indivisibility and information backflow. NM effects are quantified as a function of the round-trip time and phase shift associated with the atom-mirror optical path. We find, in particular, that unless an atom-photon bound state is formed a finite time delay is always required in order for NM effects to be exhibited. This identifies a finite threshold in the parameter space, which separates the Markovian and non-Markovian regimes.

We show how two distrustful parties, “Bob” and “Charlie,” can share a secret key with the help of a mutually trusted “Alice” counterfactually; that is, with no information-carrying particles traveling between any of the three.

The low-energy and weak-field limit of the Dirac equation can be obtained by an order-by-order block diagonalization approach to any desired order in the parameter $\pi /mc$ $(\pi$ is the kinetic momentum and $m$ is the mass of the particle). In previous work, it has been shown that, up to the order of ${(\pi /mc)}^8$, the Dirac-Pauli Hamiltonian in the Foldy-Wouthuysen (FW) representation may be expressed as a closed form and consistent with the classical Hamiltonian, which is the sum of the classical relativistic Hamiltonian for orbital motion and the Thomas-Bargmann-Michel-Telegdi Hamiltonian for spin precession. In order to investigate the exact validity of the correspondence between classical and Dirac-Pauli spinors, it is necessary to proceed to higher orders. In this paper, we investigate the FW representation of the Dirac and Dirac-Pauli Hamiltonians using Kutzelnigg's diagonalization method. We show that the Kutzelnigg diagonalization method can be further simplified if nonlinear effects of static and homogeneous electromagnetic fields are neglected (in the weak-field limit). Up to the order of ${(\pi /mc)}^{14}$, we find that the FW transformation for both Dirac and Dirac-Pauli Hamiltonians is in agreement with the classical Hamiltonian with the gyromagnetic ratio given by $g=2$ and $g\ne 2$, respectively. Furthermore, with higher-order terms at hand, it is demonstrated that the unitary FW transformation admits a closed form in the low-energy and weak-field limit.

We consider a system composed of a qubit interacting with a quartic (undriven) nonlinear oscillator (NLO) through a conditional displacement Hamiltonian. We show that even a modest nonlinearity can enhance and stabilize the quantum entanglement dynamically generated between the qubit and the NLO. In contrast to the linear case, in which the entanglement is known to oscillate periodically between zero and its maximal value, the nonlinearity suppresses the dynamical decay of the entanglement once it is established. While the entanglement generation is due to the conditional displacements, as noted in several works before, the suppression of its decay is related to the presence of squeezing and other complex processes induced by two- and four-phonon interactions. Finally, we solve the respective Markovian master equation, showing that the previous features are preserved also when the system is open.

We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields.

Our theoretical examination of second- and third-harmonic generation from metal-based nanostructures predicts that nonlocal and quantum-tunneling phenomena can significantly exceed expectations based solely on local, classical electromagnetism. Mindful that the diameter of typical transition-metal atoms is approximately 3 Å, we adopt a theoretical model that treats nanometer-size features and/or subnanometer-size gaps or spacers by taking into account (i) the limits imposed by atomic size to fulfill the requirements of continuum electrodynamics, (ii) spillage of the nearly free electron cloud into the surrounding vacuum, and (iii) the increased probability of quantum tunneling as objects are placed in close proximity. Our approach also includes the treatment of bound charges, which add crucial, dynamical components to the dielectric constant that are neglected in the conventional hydrodynamic model, especially in the visible and UV ranges, where interband transitions are important. The model attempts to inject into the classical electrodynamic picture a simple, perhaps more realistic description of the metal surface by incorporating a thin patina of free electrons that screens an internal, polarizable medium.

Recent high-precision measurements in a three-slit diffraction experiment [Sinha et al., Science 329, 418 (2010)] have been performed as an explicit test of the validity of Born's rule for quantum probabilities. This experiment aims to establish an upper limit to the possibility of higher-order interference, which, if observed, could support generalization of quantum probability theory. We reproduce this three-slit experiment using position-resolved detection, compare our results to a computational model, and find significant limitations to the normalization scheme proposed by Sinha et al. that influence interpretation. We further show that the dependence of the measurements on detector size and position must be taken into account for proper interpretation of results and meaningful comparison with other experimental schemes.

We study the generation of propagation invariant photons with orbital angular momentum by spontaneous parametric down conversion (SPDC) using a Bessel-Gauss pump beam. The angular and conditional angular spectra are calculated for an uniaxial crystal optimized for type I SPDC with standard Gaussian pump beams. It is shown that, as the mean value of the magnitude of the transverse wave vector of the pump beam increases, the emission cone is deformed into two non-coaxial cones that touch each other along a line determined by the orientation of the optical axis of the nonlinear crystal. At this location, the conditional spectrum becomes maximal for a pair of photons, one of which is best described by a Gaussian-like photon with a very small transverse wave vector, and the other a Bessel-Gauss photon with a distribution of transverse wave vectors similar in amplitude to that of the incident pump beam. A detailed analysis is then performed of the angular momentum content of SPDC photons by the evaluation of the corresponding transition amplitudes. As a result, we obtain conditions for the generation of heralded single photons which are approximately propagation invariant and have orbital angular momentum. A discussion is given about the difficulties in the interpretation of the results in terms of conservation of optical orbital angular momentum along the vector normal to the crystal surface. The angular spectra and the conditional angular spectra are successfully compared with available experimental data recently reported in the literature.

We investigate entropic uncertainty relations for two or more binary measurements, for example, spin-$\frac{1}{2}$ or polarization measurements. We argue that the effective anticommutators of these measurements, i.e., the anticommutators evaluated on the state prior to measuring, are an expedient measure of measurement incompatibility. Based on the knowledge of pairwise effective anticommutators we derive a class of entropic uncertainty relations in terms of conditional Rényi entropies. Our uncertainty relations are formulated in terms of effective measures of incompatibility, which can be certified in a device-independent fashion. Consequently, we discuss potential applications of our findings to device-independent quantum cryptography. Moreover, to investigate the tightness of our analysis we consider the simplest (and very well studied) scenario of two measurements on a qubit. We find that our results outperform the celebrated bound due to Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)] and provide an analytical expression for the minimum uncertainty which also outperforms some recent bounds based on majorization.

The electron capture process for the ${\mathrm{Si}}^{3+}$(3$s)$ + H(1$s)$ collisions is investigated by the quantum-mechanical molecular orbital close-coupling (MOCC) method and by the two-center atomic orbital close-coupling (AOCC) method in the energy range of 10${}^{-5}$–10 keV/u and 0.8–200 keV/u, respectively. Total and state-selective cross sections are presented and compared with the available theoretical and experimental results. The present MOCC and AOCC results agree well with the experimental measurements, but show some discrepancy with the calculations of Wang et al. [Phys. Rev. A 74, 052709 (2006)] at $E$ > 40 eV/u because of the inclusion of rotational couplings, which play important roles in the electron capture process. At lower energies, the present results are about three to five times smaller than those of Wang et al. due to the difference in the molecular data at large internuclear distances. The energy behaviors of the electron capture cross sections are discussed on the basis of identified reaction mechanisms.

We consider the process of atomic ionization driven by a laser pulse with varying ellipticity. We study the distribution of the momenta of the photoelectrons, ionized by a strong laser field, emitted in the direction perpendicular to the polarization plane (transverse distribution). We show that with changing laser pulse ellipticity, the transverse distribution evolves from the singular cusplike distribution for the close to linear polarization to the smooth Gaussian-like structure for the close to circular polarization. In the latter case, when the ellipticity parameter $\epsilon \to 1$, the strong-field approximation formula for the transverse momentum distribution becomes quantitatively correct.

Incoherent dispersive shock waves and collapselike singularities have been recently predicted to occur in the spectral evolution of an incoherent optical wave that propagates in a noninstantaneous nonlinear medium. Here we extend this work by considering the generalized nonlinear Schrödinger equation. We show that self-steepening significantly affects these incoherent spectral singularities: (i) It leads to a delay in the development of incoherent dispersive shocks, and (ii) it arrests the incoherent collapse singularity. Furthermore, we show that the spectral collapselike behavior can be exploited to achieve a significant enhancement (by two orders of magnitudes) of the degree of coherence of the optical wave.

Noncommutative phase space plays an essential role in particle physics and quantum gravity at the Planck scale. However, direct experimental evidence or observation to demonstrate the existence of noncommutative phase space is still lacking. We study a quantum ring in noncommutative phase space based on the Seiberg-Witten map and give the effective magnetic potential and field coming from the noncommutative phase space, which induces the persistent current in the ring. We introduce two variables as two signatures to detect the noncommutative phase space and propose an experimental scheme to detect the noncommutative phase space as long as we measure the persistent current and the external magnetic flux.

Multiplex two-photon excitation spectroscopy is demonstrated at Doppler-limited resolution. We describe first Fourier-transform two-photon spectroscopy of an atomic sample with two mode-locked laser oscillators in a dual-comb technique. Each transition is uniquely identified by the modulation imparted by the interfering comb excitations. The temporal modulation of the spontaneous two-photon fluorescence is monitored with a single photodetector, and the spectrum of all excited transitions is revealed by a Fourier transform.

We propose a quantum algorithm in an embedding ion-trap quantum simulator for the efficient computation of $N\text{-qubit}$ entanglement monotones without the necessity of full tomography. Moreover, we discuss possible realistic scenarios and study the associated decoherence mechanisms.

Based on a microwave-photon quantum processor with two superconducting resonators coupled to one transmon qutrit, we construct the controlled-phase (c-phase) gate on microwave-photon-resonator qudits, by combination of the photon-number-dependent frequency-shift effect on the transmon qutrit by the first resonator and the resonant operation between the qutrit and the second resonator. This distinct feature provides us a useful way to achieve the c-phase gate on the two resonator qudits with a higher fidelity and a shorter operation time, compared with the previous proposals. The fidelity of our c-phase gate can reach $99.51\%$ within 93 ns. Moreover, our device can be extended easily to construct the three-qudit gates on three resonator qudits, far different from the existing proposals. Our controlled-controlled-phase gate on three resonator qudits is accomplished with the assistance of a transmon qutrit and its fidelity can reach $92.92\%$ within 124.64 ns.

We consider quantum-key-distribution implementations in which the receiver's apparatus is fixed and does not depend on his choice of basis at each qubit transmission. We show that, although theoretical quantum key distribution is proven secure, such implementations are totally insecure against a strong eavesdropper that has one-time (single) access to the receiver's equipment. The attack we present here, the “fixed-apparatus attack,” causes a potential risk to the usefulness of several recent implementations.

Finding optimal and noise robust probe states is a key problem in quantum metrology. In this paper we propose Markov dynamics as a possible mechanism for generating such states, and show how the Heisenberg scaling emerges for systems with multiple “dynamical phases” (stationary states), and noiseless channels. We model noisy channels by coupling the Markov output to “environment” ancillas, and consider the scenario where the environment is monitored to increase the quantum Fisher information of the output. In this setup we find that the survival of the Heisenberg limit depends on whether the environment receives “which phase” information about the memory system.