We present an experimental technique that allows us to determine the zero-field intervals between high-$\ell$ states of Rb in a magneto-optical trap, in spite of the fact that we can only control the stray electric field in one direction. The technique is based on measuring a property of the atom that depends on the field, as opposed to its square. This approach allows the determination of the zero-field intervals and the magnitude of the stray field in the uncontrolled perpendicular direction. We use this technique to observe the microwave transitions of rubidium from the $(n+1)d_{5/2}$ states to the $ng$ and $nh$ states of $27\le n\le 30$. From the observed microwave transitions, we determine the quantum defects of the $ng$ and $nh$ states. Using the quantum defects of the $ng$ and $nh$ states and the adiabatic core polarization theory, we determine the ${\mathrm{Rb}}^{+}$ ionic dipole and quadrupole polarizabilities to be ${\alpha }_d=9.12\left(2\right)a_0^3$ and ${\alpha }_q=14\left(3\right)a_0^5$, respectively.

We analyze the imprint of nodal planes in high-order-harmonic spectra from aligned diatomic molecules in intense laser fields whose components exhibit orthogonal polarizations. We show that the typical suppression in the spectra associated to nodal planes is distorted, and that this distortion can be employed to map the electron's angle of return to its parent ion. This investigation is performed semianalytically at the single-molecule response and single-active orbital level, using the strong-field approximation and the steepest descent method. We show that the velocity form of the dipole operator is superior to the length form in providing information about this distortion. However, both forms introduce artifacts that are absent in the actual momentum-space wave function. Furthermore, elliptically polarized fields lead to larger distortions in comparison to two-color orthogonally polarized fields. These features are investigated in detail for ${\mathrm{O}}_2$, whose highest occupied molecular orbital provides two orthogonal nodal planes.

Cross sections for one- and two-photon detachment of ${\mathrm{O}}^{-}\left(1s^{2}2s^{2}2p^5{}^2\mathrm{P}^{\mathrm{o}}\right)$ have been determined in a joint experimental and theoretical study. The absolute measurement is based on the animated-crossed-beam technique, which is extended to the case of pulsed lasers, pulsed ion beams, and multiphoton detachment. The ab initio calculations employ $R$-matrix Floquet theory, with simple descriptions of the initial bound state and the residual oxygen atom which reproduce well the electron affinity and ground-state polarizability. For one-photon detachment, the measured and computed cross sections are in good mutual agreement, departing significantly from previous reference experiments and calculations. The generalized two-photon detachment cross section, measured at the Nd:YAG laser wavelength, is in good agreement with the $R$-matrix Floquet calculations. Long-standing discrepancies between theory and experiment are thus resolved.

We suggest a highly efficient method of ultrashort pulse formation from resonant XUV radiation due to sub-laser-cycle modulation of the excited state of non-hydrogen-like atoms by a nonionizing IR laser field. This modulation results in formation of the Raman-Stokes and anti-Stokes sidebands in coherently forward-scattered radiation, which, in turn, leads to formation of short pulses, when the phases of the sidebands are matched. This method is a generalization of a recently suggested technique [V. A. Antonov et al., Phys. Rev. A 88, 053849 (2013)] for a non-hydrogen-like medium. The possibility to form 2-fs XUV pulses in the gas of helium atoms and 990-as XUV pulses in the plasma of Li+ ions with efficiencies over 80% is shown.

In two recent papers exact Hermite-Gaussian solutions to relativistic wave equations were obtained for both electromagnetic and particle beams. The solutions for particle beams correspond to those of the Schrödinger equation in the nonrelativistic limit. Here, it will be shown that each beam particle has additional 4-momentum resulting from transverse localization compared to a free particle traveling in the same direction as the beam with the same speed. This will be referred to as the quantum 4-potential term since it will be shown to play an analogous role in relativistic Hamiltonian quantum mechanics as the Bohm potential in the nonrelativistic quantum Hamilton-Jacobi equation. Low-order localization effects include orbital angular momentum, Gouy phase, and beam spreading. Toward a more systematic approach for calculating localization effects at all orders, it will be shown that both the electromagnetic and quantum 4-potentials couple into the canonical 4-momentum of a particle in a similar way. This offers the prospect that traditional methods used to calculate the affect of an electromagnetic field on a particle can now be adapted to take localization effects into account. The prospects for measuring higher order quantum 4-potential related effects experimentally are also discussed alongside some questions to challenge the quantum information and quantum field theorists.

In two recent papers [Phys. Rev. A 90, 062121 (2014) and Phys. Rev. A, 91, 052110 (2015)] an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. Here we apply this method to more complicated examples of $S_4$ symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of three-dimensional representations of $S_4$ determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corresponding nonlocal game is analyzed.

Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional subdynamics. Each of the subdynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.

We develop a technique to find simultaneous measurements for noisy quantum observables in finite-dimensional Hilbert spaces. We use the method to derive lower bounds for the noise needed to make incompatible measurements jointly measurable. Using our strategy together with recent developments in the field of one-sided quantum information processing we show that the attained lower bounds are tight for various symmetric sets of quantum measurements. We use this characterisation to prove the existence of so called 4-Specker sets, i.e. sets of four incompatible observables with compatible subsets in the qubit case.

We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identifies the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$ locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)\mathrm{th}$ Bell-type inequality. When $m=2$, the corresponding inequality reduces to the one shown earlier [Q. Chen et al., Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$, the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality.

An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact on deep learning and other machine-learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggest it will do so with an instance-dependent effective temperature, different from its physical temperature. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this work, we propose a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a special class of a restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep-learning architectures. We also provide a comparison to $k$-step contrastive divergence (CD-$k$) with $k$ up to 100. Although assuming a suitable fixed effective temperature also allows us to outperform one-step contrastive divergence (CD-1), only when using an instance-dependent effective temperature do we find a performance close to that of CD-100 for the case studied here.

The present paper constitutes a development of our previous work devoted to calculations of the angular Fock coefficients ${\psi }_{k,p}(\alpha ,\theta )$. Explicit analytic representations for the edge components ${\psi }_{k,0}^{\left(0\right)}$ and ${\psi }_{k,0}^{\left(k\right)}$ with $k\le 8$ are derived. The methods developed enable such a calculation for arbitrary $k$. The single-series representation for subcomponent ${\psi }_{3,0}^{\left(2e\right)}$ missed in the author's previous paper is developed. It is also shown how to express some of the complicated subcomponents through hypergeometric and elementary functions. Using the operator FindSequenceFunction of Wolfram's Mathematica, simple explicit representations for some complicated mathematical expressions under consideration have been obtained.

General formulas for calculating the several leading long-range interactions among three identical atoms where two atoms are in identical $S$ states and the other atom is in a $P$ state are obtained using perturbation theory for the energies up to second order. The first-order (dipolar) interactions depend on the geometrical configurations of the three atoms. In second order, additive and nonadditive dispersion interactions are obtained. The nonadditive interactions depend on the geometrical configurations in marked contrast to the case where all three atoms are in identical $S$ states, for which the nonadditive (also known as triple-dipole or as Axilrod-Muto-Teller) dispersion interactions appear at the third order. The formalism is demonstrated by the calculation of the coefficients for the $\mathrm{Li}\left(2{}^{2}S\right)-\mathrm{Li}\left(2{}^{2}S\right)-\mathrm{Li}\left(2{}^{2}P\right)$ system using variationally generated atomic lithium wave functions in Hylleraas coordinates. The present dipolar coefficients and additive and nonadditive dispersion coefficients may be useful in constructing precise potential energy surfaces for this three lithium atom system.

We present a numerical implementation of the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method [Phys. Rev. A 88, 023402 (2013)] for atoms driven by a strong linearly polarized laser pulse. The present implementation treats the problem in its full dimensionality and introduces a gauge-invariant frozen-core approximation, an efficient evaluation of the Coulomb mean field scaling linearly with the number of basis functions, and a split-operator method specifically designed for stable propagation of stiff spatial derivative operators. We apply this method to high-harmonic generation in helium, beryllium, and neon and explore the role of electron correlations.

We consider the stability of systems subjected to periodic parametric driving in the context of ions confined by oscillating electric fields. The behavior of these systems can be understood in terms of a pseudopotential approximation and resonances arising from parametric excitation. We investigate the key properties of a way of operating a linear Paul trap with two radio frequencies that simultaneously confines two species with extremely different charge-to-mass ratios. The theoretical calculations have been verified by molecular dynamics simulations and normal modes analysis.

We study the transverse-field Ising model with interactions that are modulated in time. In a rotating frame, the system is described by a time-independent Hamiltonian with many-body interactions, similar to the cluster Hamiltonians of measurement-based quantum computing. In one dimension, there is a three-body interaction, which leads to string order instead of conventional magnetic order. We show that the string order is robust to power-law interactions that decay with the cube of distance. In two and three dimensions, there are five- and seven-body interactions. We discuss adiabatic preparation of the ground state as well as experimental implementation with trapped ions, Rydberg atoms, and polar molecules.

We consider a Fermi gas that is loaded onto a square optical lattice and subjected to a perpendicular artificial magnetic field, and determine its superfluid transition boundary by adopting a BCS-like mean-field approach in momentum space. The multiband structure of the single-particle Hofstadter spectrum is taken explicitly into account while deriving a generalized pairing equation. We present the numerical solutions as functions of the artificial magnetic flux, interaction strength, Zeeman field, chemical potential, and temperature, with a special emphasis on the roles played by the density of single-particle states and center-of-mass momentum of Cooper pairs.

Recently it was shown by Wolfe and Yelin [E. Wolfe and S. F. Yelin, Phys. Rev. Lett. 112, 140402 (2014)] that in the idealized Dicke model of superradiance there is no entanglement among any partitions of the system during the total evolution time of the system. This result immediately causes us to question if other measures from quantum information theory can explain the characteristic release of energy in a short time interval. In this work we identify the uncertainty of purely quantum origin as the property responsible for Dicke superradiance. The quantum uncertainty on the population of each emitter of the sample captured by the Wigner-Yanase skew information (WYSI) is proportional to the correlation radiation rate, which is the part of the total radiated power coming from dipole correlations and responsible for releasing in a short time a great intensity of radiation energy. We also show that the correlation measure called local quantum uncertainty, which is the minimization of the WYSI over all local observables, presents a double sudden change induced by the environment. The time window between these two sudden changes is used to define the interval in which symmetric global observables of the system behave classically for $N\to \infty$, although the emitters remain strongly quantum correlated.

Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realize coatings to achieve exotic effects like optical illusions and anomalous diffraction behavior. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.