Discrete-Gauss states are a new class of Gaussian solutions of the free Schrödinger equation owning discrete rotational symmetry. They are obtained by acting with a discrete deformation operator onto Laguerre-Gauss modes. We present a general analytical construction of these states and show the necessary and sufficient condition for them to host embedded dark beam structures. We unveil the intimate connection between discrete rotational symmetry, orbital angular momentum, and the generation of focusing dark beams. The distinguishing features of focusing dark beams are discussed. The potential applications of discrete-Gauss states in advanced optical trapping and quantum information processing are also briefly discussed.

We propose a complex Ginzburg-Landau equation (CGLE) with localized linear gain as a two-dimensional model for pattern formation proceeding via spontaneous breaking of the axial symmetry. Starting from steady-state solutions produced by an extended variational approximation, simulations of the CGLE generate a vast class of robust solitary structures. These are varieties of asymmetric rotating vortices carrying the topological charge (TC), and four- to ten-pointed revolving stars, whose angular momentum is decoupled from the TC. The four- and five-pointed stars feature a cyclic change of their structure in the course of the rotation.

We use the third- and fourth-order autocorrelation functions $g^{\left(3\right)}({\tau }_1,{\tau }_2)$ and $g^{\left(4\right)}({\tau }_1,{\tau }_2,{\tau }_3)$ to detect the nonclassical character of the light transmitted through a photonic-crystal nanocavity containing a strongly coupled quantum dot probed with a train of coherent light pulses. We contrast the value of $g^{\left(3\right)}(0,0)$ with the conventionally used $g^{\left(2\right)}\left(0\right)$ and demonstrate that, in addition to being necessary for detecting two-photon states emitted by a low-intensity source, $g^{\left(3\right)}$ provides a more clear indication of the nonclassical character of a light source. We also present preliminary data that demonstrates bunching in the fourth-order autocorrelation function $g^{\left(4\right)}({\tau }_1,{\tau }_2,{\tau }_3)$ as the first step toward detecting three-photon states.

We analyze the ultimate bounds on the phase sensitivity of an interferometer, given the constraint that the state input to the interferometer's initial 50:50 beam splitter $B$ is a product state of the two input modes. Requiring a product state is a natural restriction: If one were allowed to input an arbitrary, entangled two-mode state $|\Xi \rangle$ to the beam splitter, one could generally just as easily input the state $B|\Xi \rangle$ directly into the two modes after the beam splitter, thus rendering the beam splitter unnecessary. We find optimal states for a fixed photon number and for a fixed mean photon number.

A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting “modular” position and momentum operators and their complementary counterparts, originally introduced by Aharonov and co-workers. We provide a precise argument as to why these relations are superior to the standard Heisenberg uncertainty relation at expressing the complementarity between spatial localization and the appearance of fringes. We further support the argument with explicit computations involving wave functions specifically tailored to the interference setup. Conceptually developing the idea of Aharonov and co-workers, we show how the modular momentum should reflect the given experimental setup, yielding a refined observable that accurately captures the fine structure of the interference pattern.

Dynamical decoupling is a promising approach to protect quantum information from decoherence. It averages out the noise by flipping the qubits. In this paper, we demonstrate the protection of geometric gates by using dynamical decoupling with trapped ions. Specifically, a universal set of geometric gates is proposed with trapped ions and these gates are commutative with the decoupling group of the system. Our scheme combines the robust advantages of quantum holonomies and dynamical decoupling and hence can combat both control errors and decoherence. We also investigate the effects of dynamical decoupling pulse errors on the proposed geometric gates.

Majorana fermionic quantum computation (MFQC) was proposed by S. B. Bravyi and A. Yu. Kitaev [Ann. Phys. (NY) 298, 210 (2002)], who indicated that a (nontopological) fault-tolerant quantum computer built from Majorana fermions may be more efficient than that built from distinguishable two-state systems. However, until now scientists have not known how to realize a MFQC in a physical system. In this paper we propose a possible realization of MFQC. We find that the end of a line defect of a $p$-wave superconductor or superfluid in a honeycomb lattice traps a Majorana zero mode, which becomes the starting point of MFQC. Then we show how to manipulate Majorana fermions to perform universal MFQC, which possesses possibilities for high-level local controllability through individually addressing the quantum states of individual constituent elements by using timely cold-atom technology.

The measurement of a quantum two-level system, or a qubit in modern terminology, often involves an electromagnetic field that interacts with the qubit, before the field is measured continuously and the qubit state is inferred from the noisy field measurement. During the measurement, the qubit may undergo spontaneous transitions, further obscuring the initial qubit state from the observer. Taking advantage of some well-known techniques in stochastic detection theory, here we propose a signal processing protocol that can infer the initial qubit state optimally from the measurement in the presence of noise and qubit dynamics. Assuming continuous quantum-nondemolition measurements with Gaussian or Poissonian noise and a classical Markov model for the qubit, we derive analytic solutions to the protocol in some special cases of interest using Itō calculus. Our method is applicable to multihypothesis testing for robust qubit readout and relevant to experiments on qubits in superconducting microwave circuits, trapped ions, nitrogen-vacancy centers in diamond, semiconductor quantum dots, or phosphorus donors in silicon.

The properties of the electronic ground state of the polar and paramagnetic europium–$S\text{-state-atom}$ molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium–alkali-metal-atom, $\mathrm{Eu}X(X=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs})$, europium–alkaline-earth-metal-atom, $\mathrm{Eu}Y(Y=\mathrm{Be},\mathrm{Mg},\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})$, and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances $C_6$ are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields.

We have studied collisions between 22.5 keV ${\mathrm{He}}^{2+}$ ions and mixed clusters $\left[\right({\mathrm{C}}_{60}\left){}_m\right({\mathrm{C}}_{24}$${\mathrm{H}}_{12}\left){}_n\right]$ of $m$ ${\mathrm{C}}_{60}$ and $n$ coronene molecules where $m$ and $n$ range up to about ten. Surprisingly, the cluster fragmentation behavior in distant collisions is dramatically different for pure coronene clusters ($m=0$) and clusters containing a single ${\mathrm{C}}_{60}$ molecule $(m=1)$. In the latter case, the clusters may be ionized without also being fragmented on the experimental time scale of tens of microseconds. This does not occur for pure coronene clusters, but is a main characteristic of pure fullerene clusters. For ion trajectories penetrating the mixed cluster, we observe covalent bond formations between ${\mathrm{C}}_{59}$ or ${\mathrm{C}}_{58}$ and ${\mathrm{C}}_{60}$, but not between coronene fragments and ${\mathrm{C}}_{60}$, or between ${\mathrm{C}}_{60}$ fragments and coronene. These results are explained by means of classical molecular dynamics simulations of collisions inside the fragmenting mixed clusters.

We report on the selective addressing of an individual atom in a pair of single-atom microtraps separated by $3\mu$m. Using a tunable light shift, we render the selected atom off-resonant with a global Rydberg excitation laser which is resonant with the other atom, making it possible to selectively block this atom from being excited to the Rydberg state. Furthermore we demonstrate the controlled manipulation of a two-atom entangled state by using the addressing beam to induce a phase shift onto one component of the wave function of the system, transferring it to a dark state for the Rydberg excitation light. Our results are an important step towards implementing quantum information processing and quantum simulation with large arrays of Rydberg atoms.

We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic Bose-Einstein condensate contained within an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasiprobability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.

We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by the delta function $\delta \left(x\right)$ and a spatially uniform SDF quintic term. This system gives rise to the most general family of 1D Townes solitons, with the entire family being unstable. However, it is completely stabilized by a finite-width regularization of the $\delta$ function. The results are produced by means of numerical and analytical methods. We also consider the system with a symmetric pair of regularized $\delta$ functions, which gives rise to a wealth of symmetric, antisymmetric, and asymmetric solitons, linked by a bifurcation loop, that accounts for the breaking and restoration of the symmetry. Soliton families in two-dimensional (2D) versions of both the single- and double-$\delta$-functional systems are also studied. The 1D and 2D settings may be realized for spatial solitons in optics and in Bose-Einstein condensates.

Plasmonic fields are usually considered nonchiral because of the transverse magnetic polarization of surface plasmon modes. We, however, show here that an optical lattice created from the intersection of two coherent surface plasmons propagating on a smooth metal film can generate optical chirality in the interfering near field. We reveal in particular the emergence of plasmonic potentials relevant to the generation of near-field chiral forces. This draws promising perspectives for performing enantiomeric separation schemes within the near field.

High-energy-resolution photoexcited $K{N}_{2,3}$ x-ray-emission measurements were carried out on krypton with the excitation energy tuned around the $1s4p$ and $1s3d$ double-excitation thresholds. Comprehensive two-dimensional resonant inelastic x-ray-scattering maps were recorded for the range of excitation and emission energies corresponding to both types of double excitations. The double-excitation signal could be clearly resolved from the dominant $1s$ ionization signal. The latter was subtracted from the measured maps, yielding isolated $1s4p$ and $1s3d$ photoexcitation spectra. Both two-electron excitation spectra are well described by a model spectrum built of consecutive bound-bound discrete transitions and shake-up and shake-off channels giving precise energies and intensities of the corresponding contributions. The obtained results are compared with other existing experimental values based on x-ray-absorption measurements and theoretical predictions.

Numerical experiments are performed using a recently published formalism [Phys. Rev. A 88, 013419 (2013)] for computing the transient absorption of an attosecond x-ray probe by a molecule in a nonstationary valence-excited state. This study makes use of an all-electron correlated electronic-structure model to compute electronic dynamics ensuing after a localized excitation on a model chromophore group. Simulated absorption of a delayed attosecond pulse is then used to investigate the presence of an extra valence electron or vacancy around atoms of a given element as a function of time, by tuning the carrier frequency to the associated core-valence energy gap. We show correlations between the predicted absorption of such pulses and visualizations of the particle and hole locations in test molecules. Given the strong role played by the relative orientation of the molecules and the probe polarization, results are presented for a few different alignment schemes. For the molecules studied, effective pump-induced alignment is sufficient to recover easily interpreted information.

Transport in complex systems is characterized by a fractal dimension—the walk dimension—that indicates the diffusive or anomalous nature of the underlying random walk process. Here we report on the experimental retrieval of this key quantity, using light waves propagating in disordered media. The approach is based on measurements of the time-resolved transmission, in particular on how the lifetime scales with sample size. We show that this allows one to retrieve the walk dimension and apply the concept to samples with varying degree of fractal heterogeneity. In addition, the method provides the first experimental demonstration of anomalous light dynamics in a random medium.

Spatially periodic and localized structures in the transverse plane of a medium displaying electromagnetically induced transparency in an optical cavity and under the action of two pumps are investigated. The system supports a multitude of different complex spatial structures depending on the chosen initial condition. We explore regimes of multistable patterns, filaments, stable defects, scrolling structures, nested patterns, fronts, and the spontaneous occurrence of multiple cavity solitons. To simulate realistic conditions of operation, we replace periodic boundary conditions with pumps of finite size. Many of the multistable features are recovered apart from the scrolling of patterns with defects.

We present an efficient way for measuring the entanglement of atoms. The concurrence of atomic entanglement can be obtained according to the probability of picking up the singlet states of the atoms. In this protocol, we require the phenomenon of optical Faraday rotation, but the entangled atoms do not need to be in contact with each other and the atomic entanglement can be distributed nonlocally. Moreover, our way of measuring the concurrence for atoms can also be suitable for other solid systems, such as quantum dots inside microcavities and the nitrogen-vacancy (N-V) defect centers in diamonds, which can also induce the optical Faraday rotation. All these advantages provide important applications in future distributed quantum computations.

We investigate the entanglement, CHSH nonlocality, fully entangled fraction, and symmetric extendibility of two-qubit states that have a single maximally mixed marginal. Within this set of states, the steering ellipsoid formalism has recently highlighted an interesting family of so-called maximally obese states. These are found to have extremal quantum correlation properties that are significant in the steering ellipsoid picture and for the study of two-qubit states in general.