The problem of constructing physically and mathematically well-defined Wigner functions for the canonical pair angle $\theta$ and angular momentum $p$ is solved. While a key element for the construction of Wigner functions for the planar phase space $\{(q,p)\in {\mathbb{R}}^2\}$ is the Heisenberg-Weyl group, the corresponding group for the cylindrical phase space $\{(\theta ,p)\in S^1\times \mathbb{R}\}$ is the Euclidean group $E\left(2\right)$ of the plane and its unitary representations. Here the angle $\theta$ is replaced by the pair $(cos\theta ,sin\theta )$, which corresponds uniquely to the points on the unit circle. The main structural properties of the Wigner functions for the planar and the cylindrical phase spaces are strikingly similar. A crucial role is played by the $sinc$ function, which provides the interpolation for the discontinuous quantized angular momenta in terms of the continuous classical ones, in accordance with the famous Whittaker cardinal function well known from interpolation and sampling theories. The quantum mechanical marginal distributions for the angle (continuous) and angular momentum (discontinuous) are, as usual, uniquely obtained by appropriate integrations of the $(\theta ,p)$ Wigner function. Among the examples discussed is an elementary system of simple cat states.

Quantum teleportation (QT) is a fundamentally remarkable communication protocol that also finds many important applications for quantum informatics. Given a quantum entangled resource, it is crucial to know to what extent one can accomplish the QT. This is usually assessed in terms of output fidelity, which can also be regarded as an operational measure of entanglement. In the case of multipartite communication when each communicator possesses a part of an $N$-partite entangled state, not all pairs of communicators can achieve a high fidelity due to the monogamy property of quantum entanglement. We here investigate how such a monogamy relation arises in multipartite continuous-variable (CV) teleportation, particularly when using a Gaussian entangled state. We show a strict monogamy relation, i.e., a sender cannot achieve a fidelity higher than optimal cloning limit with more than one receiver. While this seems rather natural owing to the no-cloning theorem, a strict monogamy relation still holds even if the sender is allowed to individually manipulate the reduced state in collaboration with each receiver to improve fidelity. The local operations are further extended to non-Gaussian operations such as photon subtraction and addition, and we demonstrate that the Gaussian cloning bound cannot be beaten by more than one pair of communicators. Furthermore, we investigate a quantitative form of monogamy relation in terms of teleportation capability, for which we show that a faithful monogamy inequality does not exist.

We analyze the entanglement properties for the not-completely-permutation-symmetric states of quantum systems composed of two subsystems with an equal but arbitrary finite local Hilbert space dimension. We investigate both pure and mixed states with such a symmetry obtained by relaxing the symmetry requirement of the axisymmetric states. For such states we discuss the entanglement classification with respect to stochastic local operations and classical communication and establish the entanglement quantitatively by means of concurrence and negativity. In particular, we determine the separability criterion in the frame of various methods, including the $k$-positive map witness, optimal Schmidt-number witnesses, and entanglement measures.

We present a precise calculation of the Lamb shift $(2P_{1/2}-2S_{1/2})$ in muonic ions ${\left({\mu }_3^6\text{Li}\right)}^{2+},{\left({\mu }_3^7\text{Li}\right)}^{2+}, {\left({\mu }_4^9\text{Be}\right)}^{3+},{\left({\mu }_4^{10}\text{Be}\right)}^{3+}, {\left({\mu }_5^{10}\text{B}\right)}^{4+},{\left({\mu }_5^{11}\text{B}\right)}^{4+}$. The contributions of orders ${\alpha }^3÷{\alpha }^6$ to the vacuum polarization, nuclear structure and recoil, and relativistic effects are taken into account. Our numerical results are consistent with previous calculations and improved by additional corrections. The obtained results can be used for the comparison with future experimental data, and extraction more accurate values of nuclear charge radii.

The electronic structure of the diatomic VO anion was explored by combining the photoelectron-imaging spectroscopy and high-level theoretical calculations. The electron affinity (EA) of VO is determined to be 1.244 ± 0.025 eV from the vibrationally resolved photoelectron spectrum acquired at 532 nm. The anisotropy parameter (β) for the EA defined peak is measured to be 1.59 ± 0.02, indicating that it is the 9σ electron attachment leading to the formation of the ground state of $\mathrm{V}{\mathrm{O}}^{-}$. The present imaging experiment provides direct evidence that the ground state of $\mathrm{V}{\mathrm{O}}^{-}$ is $X{}^3{\mathrm{\Sigma }}^{-}$ with a ${\left(3\pi \right)}^4{\left(8\sigma \right)}^2{\left(9\sigma \right)}^2{\left(1\delta \right)}^2$ electron configuration, which resolves the significant discrepancy in previous experiment and theory. In addition, the molecular orbitals and bonding involved in the anionic VO cluster are also examined based on the present high-level theoretical calculations.

We report the frequency measurements of the $2{}^{3}P\to 3{}^{3}D$ transitions in ${}^{3,4}\mathrm{He}$ at 588 nm using an optical frequency comb stabilized laser system. The Doppler-free spectra of the $2{}^{3}P\to 3{}^{3}D$ transitions are demonstrated in an rf discharged sealed-off helium cell using intermodulated fluorescence spectroscopy. The measured absolute frequency of the ${}^4\mathrm{He}2{{}^{3}P}_0\to 3{{}^{3}D}_1$ transition is 510 059 755.352(28) MHz, which is more precise than the previous measurement by two orders of magnitude. The ionization energies of the ${}^4\mathrm{He}2{{}^{3}P}_0$ and $2{{}^{3}S}_1$ states can be derived from our result and agree very well with the previous experimental values. More importantly, the Lamb shift of the $2{{}^{3}S}_1$ state can be deduced to be 4057.086(34) MHz, which is two times more precise than the previous result. In addition, the absolute frequencies of the $2{{}^{3}P}_{0,1/2}\to 3{{}^{3}D}_{1,3/2}, 2{{}^{3}P}_{0,1/2}\to 3{{}^{3}D}_{1,1/2}$, and $2{{}^{3}P}_{0,1/2}\to 3{{}^{3}D}_{2,3/2}$ transitions in ${}^3\mathrm{He}$ are measured. Our precision surpasses the theoretical calculations by more than one to two orders of magnitude. The hyperfine separations of the $3{}^{3}D$ states in ${}^3\mathrm{He}$ and the frequency differences between ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$ transitions are also presented.

The internal degrees of freedom provided by ultracold atoms provide a route for realizing higher dimensional physics in systems with limited spatial dimensions. Nonspatial degrees of freedom in these systems are dubbed “synthetic dimensions.” This connection is useful from an experimental standpoint but complicated by the fact that interactions alter the condensate ground state. Here we use the Gross-Pitaevskii equation to study the ground-state properties of a spin-1 Bose gas under the combined influence of an optical lattice, spatially varying spin-orbit coupling, and interactions at the mean-field level. The associated phases depend on the sign of the spin-dependent interaction parameter and the strength of the spin-orbit field. We find “charge”- and spin-density-wave phases which are directly related to helical spin order in real space and affect the behavior of edge currents in the synthetic dimension. We determine the resulting phase diagram as a function of the spin-orbit coupling and spin-dependent interaction strength, considering both attractive (ferromagnetic) and repulsive (polar) spin-dependent interactions, and we provide a direct comparison of our results with the noninteracting case. Our findings are applicable to current and future experiments, specifically with ${}^{87}\mathrm{Rb}, {}^7\mathrm{Li}, {}^{41}\mathrm{K}$, and ${}^{23}\mathrm{Na}$.

The recent experimental condensation of ultracold atoms in a triangular optical lattice with a negative effective tunneling parameter paves the way for the study of frustrated systems in a controlled environment. Here, we explore the critical behavior of the chiral phase transition in such a frustrated lattice in three dimensions. We represent the low-energy action of the lattice system as a two-component Bose gas corresponding to the two minima of the dispersion. The contact repulsion between the bosons separates into intra- and intercomponent interactions, referred to as $V_0$ and $V_{12}$, respectively. We first employ a Huang-Yang-Luttinger approximation of the free energy. For $V_{12}/V_0=2$, which corresponds to the bare interaction, this approach suggests a first-order phase transition, at which both the $\mathrm{U}\left(1\right)$ symmetry of condensation and the ${\mathbb{Z}}_2$ symmetry of the emergent chiral order are broken simultaneously. Furthermore, we perform a renormalization-group calculation at one-loop order. We demonstrate that the coupling regime $0<V_{12}/V_0\le 1$ shares the critical behavior of the Heisenberg fixed point at $V_{12}/V_0=1$. For $V_{12}/V_0>1$ we show that $V_0$ flows to a negative value, while $V_{12}$ increases and remains positive. This results in a breakdown of the effective quartic-field theory due to a cubic anisotropy and, again, suggests a discontinuous phase transition.

A ferromagnetic spin-1 condensate supports polar-core spin vortices (PCVs) in the easy plane phase. We derive a model for the dynamics of these PCVs using a variational Lagrangian approach. The PCVs behave as massive charged particles interacting under the two-dimensional Coulomb interaction, with the mass arising from interaction effects within the vortex core. We compare this model to numerical simulations of the spin-1 Gross-Pitaevskii equations and find semiquantitative agreement. In addition, the numerical results suggest that the PCV core couples to spin waves, and this affects the PCV dynamics even far from the core. We identify areas of further research that could extend the model of PCV dynamics presented here.

We present a theoretical framework for the study of surface-plasmon polariton (SPP) packets propagating along a lossy metal-dielectric interface within the paraxial approximation. Using a rigorous formulation based on the plane-wave spectrum formalism, we introduce a set of modes that constitute a complete basis set for the solutions of Maxwell's equations for a metal-dielectric interface in the paraxial approximation. The use of this set of modes allows us to fully analyze the evolution of the transversal structure of SPP packets beyond the single plane-wave approximation. As a paradigmatic example, we analyze the case of a Gaussian SPP mode, for which, exploiting the analogy with paraxial optical beams, we introduce a set of parameters that characterize its propagation.

We introduce an optomechanical scheme for the probabilistic preparation of single-phonon Fock states of mechanical modes based on photosubtraction. The quality of the produced mechanical state is confirmed by a number of indicators, including phonon statistics and conditional fidelity. We assess the detrimental effect of parameters such as the temperature of the mechanical system and address the feasibility of the scheme with state-of-the-art technology.

We present a theoretical study of the spatial Goos-Hänchen shift occurring at the interface between two photonic graphene lattices. Numerical simulations of light propagation in such a wave-guiding system are also presented to corroborate our findings. Our results show that the combined action of the honeycomb lattice structure and the discrete nature of wave-guiding systems give rise to a giant and negative Goos-Hänchen shift.

Nonlinear optical effects provide a natural way of light manipulation and interaction and form the foundation of applied photonics, from high-speed signal processing and telecommunication to ultrahigh-bandwidth interconnects and information processing. However, relatively weak nonlinear response at optical frequencies calls for operation at high optical powers or boosting efficiency of nonlinear parametric processes by enhancing local-field intensity with high-quality-factor resonators near cavity resonance, resulting in reduced operational bandwidth and increased loss due to multiphoton absorption. We present an alternative to this conventional approach, with strong nonlinear optical effects at low local intensities, based on period-doubling bifurcations near nonlinear cavity antiresonance and apply it to low-power optical frequency comb generation in a silicon chip.

We demonstrate how the emergence of extreme events strongly depends on the correlation length of the input field distribution. Observing the behavior of optical waves in turbulent photorefractive propagation with partially incoherent excitations, we find that rogue waves are strongly enhanced for a characteristic input correlation scale. Waveform analysis identifies this scale with a characteristic peak-intensity-independent wave size, suggesting a general role played by saturation in the nonlinear response in rogue phenomena.

The quantum Fisher information represents a continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of quantum Fisher information can be determined from linear-response theory through generalized covariances. We derive the generalized fluctuation-dissipation theorem that relates linear-response functions to generalized covariances and hence allows us to determine the quantum Fisher information from linear-response functions, which are experimentally measurable quantities. As an application, we examine the skew information, which is a quantum Fisher information, of a harmonic oscillator in thermal equilibrium, and show that the equality of the skew-information-based uncertainty relation holds.

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose performance is optimal when operating in the partially coherent regime, as opposed to the extremes of fully coherent or classical regimes. The algorithm builds on continuous-time quantum stochastic walks (QSWs) on graphs and the algorithmic performance is quantified by the distinguishing power between nonisomorphic graphs. The QSW explores the entire graph and acquires information about the underlying structure, which is extracted by monitoring stochastic jumps across an auxiliary edge. The resulting counting statistics of stochastic jumps is used to identify the spectrum of the dynamical generator of the QSW, serving as a novel graph invariant, based on which nonisomorphic graphs are distinguished. We provide specific examples of nonisomorphic graphs that are only distinguishable by QSWs in the presence of decoherence.

The valence-shell double ionization of atomic magnesium is calculated using a grid-based representation of the $3s^2$ electron configuration in the presence of a fully occupied frozen-core configuration of the remaining ten electrons. Atomic orbitals are constructed from an underlying finite-element discrete variable representation that facilitates accurate representation of the interaction between the inner-shell electrons with those entering the continuum. Length and velocity gauge results are compared with recent theoretical calculations and experimental measurements for the total double-, single-, and triple-differential cross sections, particularly at the photon energy of 55.49 eV for the last one. Comparison between the similar processes of double ionization of the $n{s}^2$ atoms helium, beryllium, and magnesium further illuminates the role of valence-shell electron correlation in atomic targets with heliumlike electronic configurations and symmetry.

We investigate the magnetic phases of a bilayer system of ultracold bosons in the presence of Raman-induced spin-orbit (SO) coupling and laser-assisted interlayer tunneling. We consider this bilayer system in the Mott-insulating regime where on-site two-body interactions exceed all the tunneling terms. In such a system there exists a rich set of spin textures including hetero-ferromagnetic, heterochiral magnetic, and chiral magnetic phases with interlayer antiferromagnetic. In particular, the heterochiral magnetic phase induced by SO coupling occurs extremely rarely in solid-state materials. We theoretically analyze the contribution of interlayer ferromagnetic interaction to the formation of these magnetic phases, including interactions that arise from laser-assisted tunneling, stagger “magnetic field,” and antisymmetric exchange, i.e., Dzyaloshinskii-Moriya interactions. Finally, we detail an experimental setup that produces the desired interactions in a system of cold alkali-metal atoms.