An adiabatic scheme for separation of the three-dimensional (3D) nuclear dynamics on the ground electronic Born-Oppenheimer potential energy surface of an ${\mathrm{H}}_2\mathrm{O}$ molecule in hyperspherical coordinates is presented. It is found that the three vibrational modes are weakly coupled and the 3D vibrational wave function can be approximated as a product of three separable functions: one represented by the hyperradius and two by the two hyperangles individually. This framework is then used for investigation of the formation and the role of a saddlelike barrier arising in the two hyperspherical angles that is to moderate the OH $+$ H dissociation process. In order to test the validity of the framework, vibrational states with energies up to 19 500 ${\mathrm{cm}}^{-1}$ are constructed under the assumptions of adiabaticity and separability and compared to full three-dimensional high-precision numerical calculations yielding remarkable correspondence. As a result we present a simple construction scheme for separated molecular vibration states as the first step towards theoretical investigation of laser-driven molecular dynamics of triatomic molecules.

The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5–1000 K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

A method is proposed to produce atomic ensembles with sub-Poissonian atom-number distributions. The method consists of removing the excess atoms using the interatomic interactions induced by Rydberg dressing. The selective removal of atoms occurs via spontaneous decay into untrapped states using an electromagnetically induced transparency scheme. Ensembles with the desired number of atoms can be produced almost deterministically. Numerical simulations predict a strong reduction of the atom-number fluctuations, with the variance 20 times less than the Poisson noise level (the predicted Fano factor is $F\simeq 0.05$). Strikingly, the method is suitable for both fermions and bosons. It solves the problem of the atom-number fluctuations in bosons, whose weak interactions have usually been an obstacle to controlling the number of atoms.

Understanding the effect of interactions in the phase evolution of expanding atomic Bose-Einstein condensates is fundamental to describing the basic phenomenon of matter wave interference. Many theoretical and experimental works tackled this problem, always with the implicit assumption that the mutual interaction between two expanding condensates rigidly modifies the phase evolution through an effective force. In this paper, we present a combined experimental and theoretical investigation of the interference profile of expanding ${}^{87}\mathrm{Rb}$ condensates, with a specific focus on the effect of interactions. We come to the different conclusion that the mutual interaction produces local modifications of the condensate phase only in the region where the wave packets overlap.

Structured light characterized by spatially inhomogeneous optical fields found rich applications in optical communication, sensing, microscopy, manipulation, and quantum information. While generation of structured light has been extensively studied in linear optics, the nonlinear optical process, particularly in two-dimensional (2D) materials, is an emerging alternative for generating structured light at shorter wavelengths. In this work, we theoretically demonstrate that radially and azimuthally polarized beams and vortex beams carrying orbital angular momentum could be generated at second-harmonic frequencies by using 2D material-based metasurfaces comprising the same transition-metal dichalcogenide meta-atoms. Manipulation of translations and orientations of anisotropically nonlinear meta-atoms exhibiting a threefold rotation-symmetrical crystalline structure induces strong nonlinear spin-orbital coupling, which enables simultaneous control of spatial phase and polarization in second-harmonic generation. The nonlinear transition-metal dichalcogenide metasurface proposed is promising for on-chip integration of nonlinear generation of structured light.

We show theoretically that highly dispersive optical media characterized by a Kerr nonlinear response may support the existence of quartic and dipole solitons in the presence of the self-steepening effect. The existence and stability properties of these localized pulses are examined in the presence of all the material parameters. Regimes for the modulation instability of a continuous-wave signal propagating inside the nonlinear medium are investigated and an analytic expression for the gain spectrum is obtained and shown to be dependent on the self-steepening parameter in addition to second- and fourth-order group velocity dispersion parameters. Self-similar soliton solutions are constructed for a generalized nonlinear Schrödinger equation with distributed second-, third-, and fourth-order dispersions, self-steepening nonlinearity, and gain or loss describing ultrashort pulse propagation in the inhomogeneous nonlinear media via the similarity transformation method. The evolutional dynamics of the self-similar structures are investigated in a periodic distributed waveguide system and an exponential dispersion decreasing waveguide.

We reformulate the single-molecule analysis in an electron microscope in terms of a quantum-state discrimination problem, and discuss its implementation through electron-beam shaping. Our approach relies on the use of new electron-optical elements to efficiently extract the “which-molecule” information from the state of each electron. The optimal observables are formally derived, and subsequently implemented by suitably designed phase elements in a generalized orbital angular momentum sorter. As a representative example, we simulate the discrimination between model proteins and benchmark the performance of the sorter against that of the best known real-space approach.

In this paper we study, in the time domain, the interaction between localized surface plasmons and photons in arbitrarily shaped metal nanoparticles, by using the Hopfield approach to quantize the plasmon modes, where the electron oscillations are represented by a harmonic matter field linearly coupled to the electromagnetic radiation. The plasmon-photon coupling gives rise to dressed plasmon modes. We have found that the radiation does not induce a significant coupling among the different quasielectrostatic plasmon modes for particles of size up to the plasma wavelength, but causes a frequency shift and an exponential decay in time of the modes. By solving the equations governing the expectation values of the plasmon creation and annihilation operators, we obtain a closed-form full-wave expression for the decay rate and for the frequency shift of the plasmon modes. It is nonperturbative and it only depends on the surface charge distribution of the quasielectrostatic plasmon modes. We validate the expression against the Mie theory for a nanosphere of radius comparable to the plasma wavelength. Eventually, we investigate the decay rate and the frequency shift of the plasmon modes in isolated and interacting nanoparticle of noncanonical shape, as their size increases up to the plasma wavelength.

We construct implementations of the PR-box using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state space model. We construct all quantum qubit channels that maximally violate a given CHSH inequality, we show that they all are entanglement-breaking channels, that they have certain block-diagonal structure, and we present some examples of such channels.

We perform a systematic investigation of variational forms (wave-function Ansätze), to determine the ground-state energies and properties of two-dimensional model fermionic systems on triangular lattices (with and without periodic boundary conditions), using the variational quantum eigensolver (VQE) algorithm. In particular, we focus on the nature of the entangler blocks which provide the most efficient convergence to the system ground state inasmuch as they use the minimal number of gate operations, which is key for the implementation of this algorithm in noisy intermediate-scale quantum computers. Using the concurrence measure, the amount of entanglement of the register qubits is monitored during the entire optimization process, illuminating its role in determining the efficiency of the convergence. Finally, we investigate the scaling of the VQE circuit depth as a function of the desired energy accuracy. We show that the number of gates required to reach a solution within an error $\varepsilon$ follows the Solovay-Kitaev scaling, $O\left[{log}_{10}^c(1/\varepsilon )\right]$, with an exponent $c=1.31\pm 0.13$.

We study the performance of efficient quantum state tomography methods based on neural-network quantum states using measured data from a two-photon experiment. Machine-learning-inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. While the power of these methods has been demonstrated on synthetic data, applications to real experimental data remain scarce. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states, i.e., to positive semidefinite density matrices, greatly improves the quality of the reconstructed states but renders the learning procedure more demanding. Including additional, possibly unjustified, constraints, such as assuming pure states, facilitates learning, but also biases the estimator.

We report measurements of the isotope shift of the mass 104, 105, 106, 108, and 110 stable palladium isotopes for transitions from the metastable state $4d^9{(}^2{D}_{5/2})5s,{}^2{[5/2]}_3\to 4d^9{(}^2{D}_{5/2})5p,{}^2{[7/2]}_4^o$ at 340 nm, and $4d^9{(}^2{D}_{5/2})5s,{}^2{[5/2]}_3\to 4d^9{(}^2{D}_{5/2})5p,{}^2{[3/2]}_2^o$ at 363 nm. For ${}^{105}\mathrm{Pd}$, we determine the hyperfine structure of both transitions. The measurements were performed by saturation absorption spectroscopy in a custom-built hollow cathode lamp and will serve as a reference for collinear laser spectroscopy of short-lived neutron-rich palladium isotopes. We also report on the observation of a population inversion for the 363-nm transition under certain discharge conditions.

Neutral uranium (U i) is a very difficult atom for theoretical calculations due to a large number (six) of valence electrons, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can efficiently treat valence-core correlations and relativistic effects, but because the formalism was developed for a Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for the $+6$ charge of such a potential. Much more efficient is the relativistic configuration-interaction (RCI) approach, which uses a relatively accurate starting DHF potential that includes some valence electrons to make the valence-electron Hamiltonian diagonally dominated for some states. Here we report calculations of U i hyperfine constants of several low-energy states using the RCI method with the starting potential that includes four $f$ valence electrons. With this starting potential, it is possible to use the single-configuration approximation or small basis sets to obtain quite accurate results for hyperfine-structure constants. In fact, by scaling the nuclear magnetic moment, the agreement for five levels was within 5% and a new magnetic moment can be recommended, 0.43(2). When two states are mixed, it is difficult to predict the exact mixing fractions, so in this case we proposed a method in which the mixing fraction is found by optimization of one parameter in the MBPT correction to obtain correct $g$ factors. The resulting hyperfine constants are significantly improved. Finally, the CI-MBPT approach was also tested, with some success for low-energy states, with the limited basis set. The methods investigated here can be further developed to include more extensive data sets to improve accuracy and can be applied to other atoms and for calculations of other properties, for example, relevant to fundamental symmetry tests.

It has been shown that for nonlinear atomic ionization, transfer of the degree of circular polarization from incident to fluorescence light is maximum at the Cooper minimum [J. Hofbrucker, A. V. Volotka, and S. Fritzsche, Phys. Rev. A 100, 011401(R) (2019)]. However, it is still a challenge to produce and detect circularly polarized light at xuv and x-ray photon energies. We here show that transfer of linear polarization is strongly enhanced at the Cooper minimum in two-photon ionization and can be readily detected using current free-electron laser facilities by measurements of the degree of linear polarization of the characteristic $L{\alpha }_1$ and $L{\alpha }_2$ lines. Two-photon ionization of a $2p_{3/2}$ electron of a tungsten atom is proposed to demonstrate the presented phenomena and realization of such an experiment is discussed in detail.

Motivated by a recent experiment [J. H. Han et al., Phys. Rev. Lett. 122, 065303 (2019)], we investigate the many-body physics of interacting fermions in a synthetic Hall tube, using a state-of-the-art density-matrix renormalization-group numerical method. Since the interleg couplings of this synthetic Hall tube generate an interesting spin-tensor Zeeman field, exotic topological and magnetic properties occur. In particular, four quantum phases, such as nontopological spin-vector and -tensor paramagnetic insulators, and topological and nontopological spin-mixed paramagnetic insulators, are predicted by calculating the entanglement spectrum, entanglement entropies, energy gaps, and local magnetic orders with three spin vectors and five spin tensors. Moreover, the topologically magnetic phase transitions induced by the interaction as well as the interleg couplings are also revealed. Our results establish a way to explore many-body (topological) states induced by both the spiral spin-vector and -tensor Zeeman fields.

$Q$-switching instability restricts pulse shortening in Kerr-lens mode-locked lasers (KLMLs). However, $Q$-switching suppression in KLMLs has not been discussed to date because of the difficulty of treating the Kerr-lens effect theoretically. We investigated parameter ranges for stable Kerr-lens mode locking (KLM) against $Q$ switching theoretically and experimentally. We found the parameters and ranges required to suppress $Q$ switching in hard- and soft-aperture KLMLs. In soft-aperture KLMLs, both intracavity power and spatial mode matching between a pump beam and a cavity mode were found to be critical. These findings were verified experimentally using an Yb:${\mathrm{Y}}_2{\mathrm{O}}_3$ KLML. Our results provide cavity design criteria for stable KLMLs against $Q$ switching.

To manipulate the wave front of the harmonic wave, nonlinear photonic crystals (NPCs) have been employed in constructing nonlinear holography. Through designing a multi-channel ${\chi }^2$ structure, nonlinear multiplexing holography is reported here in NPCs. We propose a multi-channel nonlinear holography in an orbital-angular-momentum- (OAM-)multiplexing NPC. In experiment, three images encoded in a single NPC are reconstructed in second-harmonic waves distinctively, when the necessary Fourier-domain OAM-matching conditions are met, respectively. Our method not only conceptually extends nonlinear holography, but also provides a multifunctional platform for high-capacity security storage.