In the 1970s Smith and Tassie [G. B. Smith and L. J. Tassie, Ann. Phys. (NY) 65, 352 (1971)] and Bell and Ruegg [J. S. Bell and H. Ruegg, Nucl. Phys. B 98, 151 (1975); J. S. Bell and H. Ruegg, Nucl. Phys. B 104, 546 (1976)] independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry was revealed by Ginocchio [J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997)] as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean-field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also two- and one-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.

We investigate the quantum interference shifts between energetically close states, where the state structure is observed by laser spectroscopy. We report a compact and analytical expression that models the quantum interference induced shift for any admixture of circular polarization of the incident laser and angle of observation. An experimental scenario free of quantum interference can thus be predicted with this formula. Although this study is exemplified here for muonic deuterium, it can be applied to any other laser spectroscopy measurement of $ns-n^{\prime }p$ frequencies of a nonrelativistic atomic system, via an $ns\to n^{\prime }p\to n^{\prime \prime }s$ scheme.

We describe the methodology of our recently developed Monte Carlo rate equation (MCRE) approach, which systematically incorporates bound-bound resonances to model multiphoton ionization dynamics induced by high-fluence, high-intensity x-ray free-electron laser (XFEL) pulses. These resonances are responsible for ionization far beyond that predicted by the sequential single photon absorption model and are central to a quantitative understanding of atomic ionization dynamics in XFEL pulses. We also present calculated multiphoton ionization dynamics for Kr and Xe atoms in XFEL pulses for a variety of conditions, to compare the effects of bandwidth, pulse duration, pulse fluence, and photon energy. This comprehensive computational investigation reveals areas in the photon energy–pulse fluence landscape where resonances are critically important. We also uncover a mechanism, preservation of inner-shell vacancies (PIVS), whereby radiation damage is enhanced at higher XFEL intensities and identify the sequence of core-outer–Rydberg, core-valence, and core-core resonances encountered during multiphoton x-ray ionization.

We explore the effect of transverse confinement on the stability of a Bose-Einstein condensate loaded in a shaken one-dimensional or two-dimensional square lattice. We calculate the decay rate from two-particle collisions. We predict that if the transverse confinement exceeds a critical value, then, for appropriate shaking frequencies, the condensate is stable against scattering into transverse directions. We explore the confinement dependence of the loss rate, explaining the rich structure in terms of resonances.

We use a phase-only computer-generated hologram to encode both phase and amplitude of a power of Rayleigh speckles. This method allows us to generate speckles with enhanced and reduced contrast without any optimization process. We explore non-Rayleigh speckles and unveil, theoretically and experimentally, their first-order statistical properties. These speckles may find applications in syntheses of disordered optical potentials for cold atoms and colloidal particles, in speckle illumination imaging, and in wave interference studied through spatial intensity correlation.

We present methods for efficient characterization of an optical coherent state $|\alpha \rangle$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct steps: (i) before the first detection of a vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely; and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of $\alpha$. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve a certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of $\alpha$ in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in step (i).

Recently, a new type of quantum key distribution, called the round-robin differential-phase-shift (RRDPS) protocol [T. Sasaki et al., Nature (London) 509, 475 (2014)], was proposed, where the security can be guaranteed without monitoring any statistics. In this Rapid Communication, we investigate source imperfections and side-channel attacks on the source of this protocol. We show that only three assumptions are needed for the security, and no detailed characterizations of the source or the side-channel attacks are needed. This high robustness is another striking advantage of the RRDPS protocol over other protocols.

The Leggett-Garg inequality is a widely used test of the “quantumness” of a system and involves correlations between measurements realized at different times. According to its widespread interpretation, a violation of the Leggett-Garg inequality disproves macroscopic realism and noninvasiveness. Nevertheless, recent results point out that macroscopic realism is a model-dependent notion and that one should always be able to attribute to invasiveness a violation of a Leggett-Garg inequality. This opens some natural questions: How do we provide such an attribution in a systematic way? How can apparent macroscopic realism violation be recast into a dimensional-independent invasiveness model? The present work answers these questions by introducing an operational model where the effects of invasiveness are controllable through a parameter associated with what is called the measurability of the physical system. Such a parameter leads to different generalized measurements that can be associated with the dimensionality of a system, to measurement errors, or to back action.

The use of weak measurements for performing quantum tomography is enjoying increased attention due to several recent proposals. The claimed merits of using weak measurements in this context are varied, but are generally represented by novelty, increased efficacy, and foundational significance. We critically evaluate two proposals that make such claims and find that weak measurements are not an essential ingredient for most of their claimed features.

We present Bell-type tests of nonclassicality and non-Gaussianity for single-mode fields employing a generalized quasiprobability function. Our nonclassicality tests are based on the observation that two orthogonal quadratures in phase space (position and momentum) behave as independent realistic variables for a coherent state. Taking four (three) points at the vertices of a rectangle (right triangle) in phase space, our tests detect every pure nonclassical Gaussian state and a range of mixed Gaussian states. These tests also set an upper bound for all Gaussian states and their mixtures, which thereby provide criteria for genuine quantum non-Gaussianity. We optimize the non-Gaussianity tests by employing a squeezing transformation in phase space that converts a rectangle (right triangle) to a parallelogram (triangle), which enlarges the set of non-Gaussian states detectable in our formulation. We address fundamental and practical limits of our generalized phase-space tests by looking into their relation with decoherence under a lossy Gaussian channel and their robustness against finite data and nonoptimal choice of phase-space points. Furthermore, we demonstrate that our parallelogram test can identify useful resources for nonlocality testing in phase space.

We extend the generalized conservation law of light propagating in a one-dimensional $\mathcal{PT}\text{-symmetric}$ system, i.e., $|T-1|=\sqrt{R_L{R}_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\mathcal{PT}$ or $\mathcal{RT}$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss how a multimode $\mathcal{PT}\text{-symmetric}$ waveguide can be used to observe spontaneous symmetry breaking of the scattering matrix, which typically requires tuning the non-Hermiticity of the system (i.e., the strength of gain and loss). Here the advantage of using a multimode waveguide is the elimination of tuning any system parameters: the transverse mode order $m$ plays the role of the symmetry-breaking parameter, and one observes the symmetry breaking by simply performing a scattering experiment in each waveguide channel at a single frequency and fixed strength of gain and loss.

We design realizable time-dependent semiclassical pulses to invert the population of a two-level system faster than adiabatically when the rotating-wave approximation cannot be applied. Different approaches, based on the counterdiabatic method or on invariants, may lead to singularities in the pulse functions. Ways to avoid or cancel the singularities are put forward when the pulse spans few oscillations. For many oscillations an alternative numerical minimization method is proposed and demonstrated.

The statistical fluctuation problem is a critical factor in all quantum key distribution (QKD) protocols under finite-key conditions. The current statistical fluctuation analysis is mainly based on independent random samples, however, the precondition cannot always be satisfied because of different choices of samples and actual parameters. As a result, proper statistical fluctuation methods are required to solve this problem. Taking the after-pulse contributions into consideration, this paper gives the expression for the secure key rate and the mathematical model for statistical fluctuations, focusing on a decoy-state QKD protocol [Z.-C. Wei et al., Sci. Rep. 3, 2453 (2013)] with a biased basis choice. On this basis, a classified analysis of statistical fluctuation is represented according to the mutual relationship between random samples. First, for independent identical relations, a deviation comparison is made between the law of large numbers and standard error analysis. Second, a sufficient condition is given that the Chernoff bound achieves a better result than Hoeffding's inequality based on only independent relations. Third, by constructing the proper martingale, a stringent way is proposed to deal issues based on dependent random samples through making use of Azuma's inequality. In numerical optimization, the impact on the secure key rate, the comparison of secure key rates, and the respective deviations under various kinds of statistical fluctuation analyses are depicted.

We present a different kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $AB{C}_1...C_{N-2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and $C_1...C_{N-2}$, as well as under the partition $AB{C}_1$ and $C_2...C_{N-2}$, are established, which gives rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.

High-fidelity gate operations are a crucial function for quantum information processing. This problem is particularly challenging for hybrid systems where coherence and control time scales greatly differ by orders of magnitude among different elements. Here we propose decoherence-protected gate operations in an important class of hybrid system in the context of a spin qubit in semiconductor quantum dots coupled to a superconductor resonator. Our scheme is able to generate complex photon states for various applications even in the presence of practical imperfections: limited available control of the spin-photon hybrid system and demanding spin decoherence in current state-of-the-art devices.

Relativistic configuration-interaction calculations using hydrogenlike or Dirac-Fock spin orbitals of the transition from the ground state to some $n{p}_{1/2}$, $n{p}_{3/2}$ low-lying excited states for the alkali metals are presented. In these calculations each virtual spin orbital corresponds to a unique noninteger atomic number determined iteratively using the virtual-particle model. The virtual-particle model based on “condensed-space” idea is here adopted to many electron systems consisting of a single valence electron and the core. The transition energy and the oscillator strength values were computed for sodium, potassium, rubidium, cesium, and francium. Both hydrogenlike and Dirac-Fock basis functions have been used in the computations for comparison.

We compute the virial coefficients, the contact parameters, and the momentum distribution of a strongly interacting three-dimensional Bose gas by means of a virial expansion up to third order in the fugacity, which takes into account three-body correlations exactly. Our results characterize the nondegenerate regime of the interacting Bose gas, where the thermal wavelength is smaller than the interparticle spacing but the scattering length may be arbitrarily large. We observe a rapid variation of the third virial coefficient as the scattering length is tuned across the three-atom and the atom-dimer thresholds. The momentum distribution at unitarity displays a universal high-momentum tail with a log-periodic momentum dependence, which is a direct signature of Efimov physics. We provide a quantitative description of the momentum distribution at high momentum as measured by P. Makotyn et al. [Nat. Phys. 10, 116 (2014)], and our calculations indicate that the lowest trimer state might not be occupied in the experiment. Our results allow for a spectroscopy of Efimov states in the unitary limit.

The strong mixing of many-electron basis states in excited atoms and ions with open $f$ shells results in very large numbers of complex, chaotic eigenstates that cannot be computed to any degree of accuracy. Describing the processes which involve such states requires the use of a statistical theory. Electron capture into these “compound resonances” leads to electron-ion recombination rates that are orders of magnitude greater than those of direct, radiative recombination and cannot be described by standard theories of dielectronic recombination. Previous statistical theories considered this as a two-electron capture process which populates a pair of single-particle orbitals, followed by “spreading” of the two-electron states into chaotically mixed eigenstates. This method is similar to a configuration-average approach because it neglects potentially important effects of spectator electrons and conservation of total angular momentum. In this work we develop a statistical theory which considers electron capture into “doorway” states with definite angular momentum obtained by the configuration interaction method. We apply this approach to electron recombination with ${\mathrm{W}}^{20+}$, considering $2\times {10}^6$ doorway states. Despite strong effects from the spectator electrons, we find that the results of the earlier theories largely hold. Finally, we extract the fluorescence yield (the probability of photoemission and hence recombination) by comparison with experiment.

In this work we develop an approach for a molecular hydrogen ion (${\mathrm{H}}_2{}^{+}$) in the Born-Oppenheimer approximation while exposed to intense short-pulse radiation. Our starting point is the $R$-matrix-incorporating-time formulation for atomic hydrogen [L. A. A. Nikolopoulos et al., Phys. Rev. A 78, 063420 (2008)], which has proven to be successful at treating multielectron atomic systems efficiently and with a high accuracy [L. R. Moore et al., J. Mod. Opt. 58, 1132 (2011)]. The present study on ${\mathrm{H}}_2{}^{+}$ is performed with the similar objective of developing an ab initio method for solving the time-dependent Schrödinger equation for multielectron diatomic molecules exposed to an external time-dependent potential field. The theoretical formulation is developed in detail for the molecular hydrogen ion where all the multielectron and internuclei complications are absent. As in the atomic case, the configuration space of the electron's coordinates is separated artificially over two regions: the inner (I) and outer (II) regions. In region I the time-dependent wave function is expanded on the eigenstate basis corresponding to the molecule's Hamiltonian augmented by Bloch operators, while in region II a grid representation is used. We demonstrate the independence of our results from the introduced artificial boundary surface by calculating observables that are directly accessed experimentally and also by showing that gauge-dependent quantities are also invariant with the region I box size. We also compare our results with other theoretical works and emphasize cases where basis-set approaches are currently very computationally expensive or intractable in terms of computational resources.