We examine heralded nondeterministic noiseless amplification based on the quantum scissors device, which has been shown to increase the one-photon amplitude of a state at the expense of the vacuum-state amplitude. Here we propose using the same basic design to perform perfect amplification in a basis set of up to two photons. The device is much more efficient than several one-photon amplifiers working in tandem. When used to amplify coherent states this advantage is shown either using fidelity or in terms of probability of successful action, or more strikingly in a combination of the two.

We present a scheme to realize three-dimensional Dirac-like fermions with an edge-centered cubic optical lattice. We propose a method to construct the optical edge-centered cubic crystals and then determine the parameters required for the description of the systems with a tight-binding model. Interestingly, we show that the low-energy quasiparticles are three-dimensional massive or massless Dirac-like fermions determined by the parameters of the system. In addition, two three-dimensional degenerate flat bands lie between the upper and the lower branches of the Dirac dispersion. Furthermore, we demonstrate that the Dirac dispersion relation and the flat bands can be verified by the density profile measurement.

Horodecki formulated a remarkable criterion for separability, which is called the range criterion. This range criterion was mostly used to show that some states with positive partial transpose are entangled. In this Brief Report, we show that the range criterion is also useful to find a convex combination of product states for a separable state. For this purpose, we give an example of density matrix, which is separable in a $2\otimes 3$ system and entangled in a $3\otimes 2$ system at the same time. Then we illustrate the usefulness of the range criterion with this example.

We report an experimental demonstration of quantum Deutsch’s algorithm using a linear-optical system. By employing photon polarization and spatial modes, we implement all balanced and constant functions for a quantum computer. The experimental system is very stable, and the experimental data are in excellent accordance with the theoretical results.

We describe theoretically a scheme for observing conical emission, a transverse nonlinear optical effect, in an atomic vapor with all excitation fields below the saturation level of the involved atomic transitions. The scheme relies on the giant Kerr nonlinearities possible under electromagnetically induced transparency to introduce a radially varying phase shift to a weak probe field by a weak signal field. The probe’s far-field diffraction pattern shows multiple concentric rings around the probe beam’s axis, characteristic of conical emission.

We study the quantum dynamics of cold Bose atoms in a double well. It is shown that self-trapping as well as population oscillations are common phenomena associated with nonlinear interactions. For larger $U/t$, multiparticle tunneling is damped and the quantum dynamics is dominated by single-particle tunneling. The many-body system can be effectively described in a truncated Fock space. It exhibits coherence-decoherence oscillations in the temporal evolution. We predict an interesting phenomenon of dynamical revival and collapse of matter wave fields in optical lattices in regimes near the superfluid–Mott-insulator phase boundary.

A sample of cryogenically cooled atomic ytterbium is used to create a memory for a classical pulse of light. The information of the light pulse is stored in the nuclear spin of ground-state (${}^1{S}_0$) ${}^{173}\mathrm{Yb}$ ($I=5/2$). Because nuclear spin states interact very weakly with their environment, the atomic ensemble is resistant to decoherence due to inelastic collisions and inhomogeneous fields, and storage times of hundreds of milliseconds are observed.

We analyze the statistics of observables in continuous-variable (CV) quantum teleportation in the formalism of the characteristic function. We derive expressions for average values of output-state observables, in particular, cumulants which are additive in terms of the input state and the resource of teleportation. Working with a general class of teleportation resources, the squeezed-bell-like states, which may be optimized in a free parameter for better teleportation performance, we discuss the relation between resources optimal for fidelity and those optimal for different observable averages. We obtain the values of the free parameter of the squeezed-bell-like states which optimize the central momenta and cumulants up to fourth order. For the cumulants the distortion between in and out states due to teleportation depends only on the resource. We obtain optimal parameters ${\Delta }_{(2)}^{\mathrm{opt}}$ and ${\Delta }_{(4)}^{\mathrm{opt}}$ for the second- and fourth-order cumulants, which do not depend on the squeezing of the resource. The second-order central momenta, which are equal to the second-order cumulants, and the photon number average are also optimized by the resource with ${\Delta }_{(2)}^{\mathrm{opt}}$. We show that the optimal fidelity resource, which has been found previously to depend on the characteristics of input, approaches for high squeezing to the resource that optimizes the second-order momenta. A similar behavior is obtained for the resource that optimizes the photon statistics, which is treated here using the sum of the squared differences in photon probabilities of input versus output states as the distortion measure. This is interpreted naturally to mean that the distortions associated with second-order momenta dominate the behavior of the output state for large squeezing of the resource. Optimal fidelity resources and optimal photon statistics resources are compared, and it is shown that for mixtures of Fock states both resources are equivalent.

We numerically investigate the possibilities of driving quantum algorithms with laser pulses in a register of ultracold NaCs polar molecules in a static electric field. We focus on the possibilities of performing scalable logical operations by considering circuits that involve intermolecular gates (implemented on adjacent interacting molecules) to enable the transfer of information from one molecule to another during conditional laser-driven population inversions. We study the implementation of an arithmetic operation (the addition of 0 or 1 on a binary digit and a carry in) which requires population inversions only and the Deutsch-Jozsa algorithm which requires a control of the phases. Under typical experimental conditions, our simulations show that high-fidelity logical operations involving several qubits can be performed in a time scale of a few hundreds of microseconds, opening promising perspectives for the manipulation of a large number of qubits in these systems.

Relativistic configuration interaction results on the weighted oscillator strengths are presented for the K$\beta$ satellite x rays from $1s2s3p-1s^{2}2s$ transitions in Li-like ions with $14⩽Z⩽54$. The calculations are carried out in the active space approximation using multiconfiguration Dirac-Fock wave functions with the inclusion of the finite nuclear size effect, the Breit interaction, and quantum electrodynamic corrections. The resulting x-ray wavelengths and rates are compared with other available data. An attempt is also made to analyze the irregularities in the fine-structure energy levels and x-ray rates due to configuration mixing together with the Breit interaction.

Large-scale level-by-level calculations were carried out to obtain as accurate autoionization and dielectronic capture (DC) rates of Ni-like Au${}^{51+}$ and Cu-like Au${}^{50+}$ as possible by including adequate electron correlations. The accuracy is estimated to be better than $20\%$ for strong autoionized levels. Our results of the dielectronic recombination (DR) process through $3d^{9}4{\mathit{lnl}}^{\prime }$ ($n=4,5$) agree excellently (within $10\%$) with other theoretical results also obtained by detailed level-by-level calculations reported in the literature. The level-by-level results were transformed to configuration-by-configuration autoionization and DC rates (which are estimated to be better than $30\%$ in accuracy) and used to check the validity of the rate coefficients in collisonal-radiative (CR) models by using an analytical formula. Large discrepancies were found between the detailed calculated rates and those predicted by the analytical formula. The autoionization and DC rates predicted by the analytical formula can be more than two orders of magnitude larger than the detailed calculated rates, in particular for the autoionized configurations whose energy is near the ionization potential (IP). However, for those autoionized configurations whose energy is far above the IP, the autoionization and DC rates predicted by the analytical formula can be nearly one order of magnitude smaller. Differences between different theoretical methods found in this work, when approximate methods are used to calculate the autoionization and DC rates, would result in differences when non–local-thermodynamic-equilibrium (NLTE) models used the less accurate methods to obtain these atomic data.

Differential, integral, and momentum-transfer cross sections for the rotationally elastic and inelastic scattering of electron by the BH${}_2$ radical at low collision energies ($0$–$8$ eV) are reported in a $22$-state molecular $R$-matrix method. The excitation cross sections from the ground $X\hspace{0.5em}{}^2{A}_1$ state to the first two excited states ${}^2{B}_1$ and ${}^4{A}_2$ are calculated as well, for incident electron energies from the respective thresholds up to 8 eV. Configuration-interaction wave functions are used to represent the target states which account for the correlation effects. Four shape and three Feshbach resonances are detected. The Born-closure approximation is applied for the elastic and dipole-allowed transitions to account for the $l>4$ partial waves excluded from the $R$-matrix calculations.

We present a theoretical scheme used for investigating the formation of ultracold molecules via photoassociation with a slowly-turned-on and rapidly-turned-off (STRT) laser pulse, with Cs${}_2$ as an example. As compared with an unshaped laser pulse, this kind of shaped laser pulse has a prominent advantage by which we can prevent the associated molecules from returning to the initial scattering state. Numerical calculations show that an efficient photoassociation can be realized with the STRT laser pulse, which is available in the current experiment as an optical tool.

A scheme is presented for generation of powerful coherent terahertz radiation by multiphoton resonant excitation of three-level hydrogenlike atoms and homonuclear diatomic molecules or molecular ions with strong laser pulses. The results of analytical and numerical investigations of the problem show that with the proposed mechanism one can achieve the implementation of widely tunable powerful terahertz sources, which may open new perspectives for terahertz science and its applications.

We examine the dynamics of a Bose-Einstein condensate in a symmetric double-well potential for a broad range of nonlinear couplings. We demonstrate the existence of a region, beyond those of Josephson oscillations and self-trapping, which involves the dynamical excitation of the third mode of the double-well potential. We develop a simple semiclassical model for the coupling between the second and third modes that describes very satisfactorily the full time-dependent dynamics. Experimental conditions are proposed to probe this phenomenon.

We propose an interaction-free scheme for all-optical switching which does not rely on the physical coupling between signal and control waves. The interaction-free nature of the scheme allows it to overcome the fundamental photon-loss limit imposed by the signal-pump coupling. The same phenomenon protects photonic-signal states from decoherence, making devices based on this scheme suitable for quantum applications. Focusing on $\chi {}^{(2)}$ waveguides, we provide device designs for traveling-wave and Fabry-Perot switches. In both designs, the performance is optimal when the signal switching is induced by coherent dynamical evolution. In contrast, when the switching is induced by a rapid dissipation channel, it is less efficient.

We examine a two-level system coupled to a quantum oscillator, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and oscillator frequency approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the qubit tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including, in particular, also the finite-bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the qubit for an oscillator at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many frequencies contribute to the dynamics. They are gathered into groups whose spacing depends on the qubit-oscillator detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a nontrivial dressing of the tunneling matrix element, which can be used to suppress specific frequencies through a variation of the coupling.

In this work we study the entangled states that can be created in bipartite two-dimensional optical lattices loaded with ultracold atoms. We show that, by using only two sets of measurements, it is possible to compute a set of entanglement witness operators distributed over arbitrarily large regions of the lattice, and use these witnesses to produce two-dimensional plots of the entanglement content of these states. We also discuss the influence of noise on the states and on the witnesses, as well as the relation to ongoing experiments.

We improve the steady-state ab initio laser theory (SALT) of Türeci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities with nonuniform index and/or nonuniform gain, the new basis set allows the steady-state lasing properties to be computed with much greater efficiency. This formulation of the SALT can be solved in the single-pole approximation, which gives the intensities and thresholds, including the effects of nonlinear hole-burning interactions to all orders, with negligible computational effort. The approximation yields a number of analytic predictions, including a “gain-clamping” transition at which strong modal interactions suppress all higher modes. We show that the single-pole approximation agrees well with exact SALT calculations, particularly for high-$Q$ cavities. Within this range of validity, it provides an extraordinarily efficient technique for modeling realistic and complex lasers.

We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.