A direct analysis of the task of randomness amplification from Santha-Vazirani sources using the violation of the chained Bell inequality is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. This analysis is used to find the exact threshold value of the initial randomness parameter from which perfect randomness can be extracted in the asymptotic limit of a large number of measurement settings. As a byproduct, we provide a tool for the analysis of randomness amplification protocols, namely a general characterization of the probability distributions of bits generated by Santha-Vazirani sources, which are shown to be mixtures of specific permutations of Bernoulli distributions with a parameter defined by the source.

Entanglement distribution with separable states has recently attracted considerable attention. Recent results suggest that quantum discord, a measure for quantum correlations beyond entanglement, is responsible for this counterintuitive phenomenon. In this work we study this question from a different perspective and find minimal requirements for a separable state to be useful for entanglement distribution. Surprisingly, we find that the presence of quantum discord is not sufficient to ensure entanglement distribution: There exist states with nonzero quantum discord that nevertheless cannot be used for entanglement distribution. As a result, we show that entanglement distribution is not possible with rank-2 separable states. Our work sheds light on the task of entanglement distribution with separable states and reveals a classification of quantum states with respect to their usefulness for this task.

Reflection of electromagnetic waves from a periodic grating can be described in terms of a discrete coupled multichannel scattering problem. By modeling the grating as a space- and frequency-dependent dielectric, it is possible to use a variable phase method, applied to a generalized Helmholtz equation incorporating both transverse and longitudinal modes, to efficiently compute the scattering $S$ matrix. The projection onto transverse modes of this result, evaluated for imaginary wave vector, provides the information necessary for a Casimir energy calculation. This approach is of particular interest for gratings with deep corrugations, which can limit the applicability of techniques based on the Rayleigh expansion. We demonstrate the method by calculating the Casimir interaction energy between sinusoidal grating profiles as a function of separation and lateral displacement.

The electric and magnetic dipole radiations due to a double-electron jump from the ${}^1{S}_0$ state of He-like ions with an empty $K$ shell are evaluated for 21 ions with $10\le Z\le 92$ using fully relativistic multiconfiguration Dirac-Fock wave functions in the active space approximation with the inclusion of a finite nuclear size, the Breit interaction, self-energy, and vacuum polarization. The contributions from correlation and higher-order corrections to the x-ray energies and rates are discussed in detail. The effects of biorthogonal and partially orthogonal spin orbitals of the initial and final states on the correlation sensitive radiative rates are analyzed. The accuracy of our computed data is judged by the uncertainties in the fine structure energy levels along with the agreement in the length and velocity forms of transition rates. The present results are compared with other available theoretical data.

The ${\mathrm{He}}_2\text{−}\mathrm{Ne}$ system with the combination of the isotopes of helium (${}^3\mathrm{He}$ and ${}^4\mathrm{He}$) is used in structure calculations. Three-body channel functions and adiabatic potential functions have been calculated using the $B$-spline method. We use these channel functions in the slow variable discretization method to calculate the three-body bound states of the ${\mathrm{He}}_2\text{−}\mathrm{Ne}$ system. Using this method, two bound states for the ${}^4{\mathrm{He}}_2\text{−}{}^{20}\mathrm{Ne}$ system and one bound state for each of the ${}^4\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^{20}\mathrm{Ne}$ and ${}^3\mathrm{He}{}_2\text{−}{}^{20}\mathrm{Ne}$ systems have been found. The geometry of the trimer is also analyzed using the probability densities and expectation values.

Using the classical ensemble model, we investigate the sensitivity of double ionization in circularly polarized laser fields to the initial ensembles that are generated for an Ar atom with a definite total angular momentum. The numerical results show that the double-ionization probability in the counter-rotating case, where the electrons initially rotate against the laser field, can be much higher than that in the corotating case, where the electrons rotate with the laser field. By analyzing the energy distributions of double-ionized electrons versus time, we find that, for the counter-rotating case, the ionization of the second electron occurs much earlier than in the corotating case, and the first ionization can leave the $\mathrm{Ar}{}^{+}$ ion in a higher energy state, which can increase the second ionization probability. These results indicate that nonadiabatic effects can play an important role in double-ionization dynamics.

We use the mean-field method, the quantum Monte Carlo method and the density-matrix-renormalization-group method to study the trimer superfluid phase and the quantum phase diagram of the Bose-Hubbard model in a one-dimensional optical lattice, with an explicit trimer-tunneling term. Theoretically, we derive the explicit trimer hopping terms, such as $a_i^{3†}{a}_j^3$, by the Schrieffer-Wolf transformation. In practice, the trimer superfluid described by these terms is driven by photoassociation. The phase transition between the trimer superfluid phase and other phases are also studied. Without the on-site interaction, the phase transition between the trimer superfluid phase and the Mott insulator phase is continuous. Turning on the on-site interaction, the phase transitions are first order with Mott insulators of atoms filling 1 and 2. With nonzero atom tunneling, the phase transition is first order from the atom superfluid to the trimer superfluid. In the trimer superfluid phase, the winding numbers can be divided by three without any remainder. The power-law decay exponent is $1/2$ for the nondiagonal correlation $a_i^{†3}{a}_j^3$, i.e., the same as the exponent of the correlation $a_i^{†}{a}_j$ in hardcore bosons. The density-dependent atom-tunneling term $n_i^2{a}_i^{†}{a}_j$ and pair-tunneling term $n_i{a}_i^{†2}{a}_j^2$ are also studied. With these terms, the phase transition from the empty phase to atom superfluid is first order and different from the cases without the density-dependent terms. The effects of finite three-body interactions and finite temperatures are also studied. Our results will be helpful in realizing the trimer superfluid by a cold-atom experiment.

We study isolated finite interacting quantum systems after an instantaneous perturbation and show three scenarios in which the probability for finding the initial state later in time (fidelity) decays nonexponentially, often all the way to saturation. The decays analyzed involve Gaussian, Bessel of the first kind, and cosine squared functions. The Gaussian behavior emerges in systems with two-body interactions in the limit of strong perturbation. The Bessel function, associated with the evolution under full random matrices, is obtained with surprisingly sparse random matrices. The cosine squared behavior, established by the energy-time uncertainty relation, is approached after a local perturbation in space.

We study light-induced spatial crystallization of ultracold quantum particles confined along the axis of a high-$Q$ linear cavity via a transverse multicolor pump using numerical simulations. Whenever a pump frequency is tuned close to resonance with a longitudinal cavity mode, the dynamics favors bistable spatial particle ordering into a Bragg grating at a wavelength distance. Simultaneous pumping at several resonant frequencies fosters competition between the different spatial lattice orders, exhibiting complex nonlinear field dynamics involving several metastable atom-field states. For few particles, even superpositions of different spatial orders entangled with different light-mode amplitudes appear. By a proper choice of trap geometry and pump frequencies, a broad variety of many-particle Hamiltonians with a nontrivial long-range coupling can be emulated in such a setup. When applying quantum Monte Carlo wave-function simulations to study time evolution, we find simultaneous superradiant scattering into several light modes and the buildup of strong nonclassical atom-field correlations.

Interferometry with massive particles may have the potential to explore the limitations of standard quantum mechanics, in particular where it concerns its boundary with general relativity and the yet to be developed theory of quantum gravity. This development is hindered considerably by the lack of experimental evidence and testable predictions. Analyzing effects that appear to be common to many of such theories, such as a modification of the energy dispersion and of the canonical commutation relation within the standard framework of quantum mechanics, has been proposed as a possible way forward. Here we analyze in some detail the impact of a modified energy-momentum dispersion in a Ramsey-Bordé setup and provide achievable bounds of these correcting terms when operating such an interferometer with nanodiamonds. Thus, taking thermal and gravitational disturbances into account will show that without specific prerequisites, quantum gravity modifications may in general be suppressed requiring a revision of previously estimated bounds. As a possible solution we propose a stable setup which is rather insensitive to these effects. Finally, we address the problems of decoherence and pulse errors in such setups and discuss the scalings and advantages with increasing particle mass.

Experimental setups for the optical implementation of projective measurements in the Laguerre-Gaussian basis are discussed. Special attention is given to the case where the measurements are made with the aid of single-mode fibers that are used to extract the Gaussian component from an optical distribution. Although this setup can, under some conditions, implement the inner product operation accurately, the overlap with the Gaussian mode in the single-mode fiber often produces cross-talk among Laguerre-Gaussian modes with different radial indices. The extent of the cross-talk is analyzed quantitatively.

We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton “tail” are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee generation of entanglement in the relevant qubit subspaces and compare it with classicality criteria. We also quantify the amount of entanglement that can be produced with imperfect single-photon sources, optimized over setup parameters, using as a measure entanglement of formation. Finally, we discuss verification of the generated entanglement by testing Bell's inequalities. The analysis is carried out for two schemes. The first one is the well-established one-photon scheme, which produces a photon in a delocalized superposition state between two nodes, each of them fed with one single photon at the input. As the second scheme, we introduce and analyze a linear optics analog of the robust scheme based on interfering two Stokes photons emitted by atomic ensembles, which does not require phase stability between the nodes.

We study secondary instabilities in a coherently driven passive optical fiber cavity. We show that time-modulated solutions which are generated at the onset of instability experience convective and absolute Eckhaus instabilities. The splitting of the secondary instabilities into convective and absolute instabilities drastically impacts the instability boundaries. As a consequence, the stability range of time-modulated waves is enlarged. More importantly, the threshold of absolute instability determines the transition from time-periodic wave trains to a chaotic regime. In the latter the wave trains are composed of irregular oscillations embedded in regular ones. The predictions are in excellent agreement with numerical simulations.

We investigate a hybrid quantum system consisting of a cavity optomechanical device optically coupled to an ultracold quantum gas. We show that the dispersive properties of the ultracold gas can be used to dramatically modify the optomechanical response of the mechanical resonator. We examine hybrid schemes wherein the mechanical resonator is coupled either to the motional or the spin degrees of freedom of the ultracold gas. In either case, we find an enhancement of more than two orders of magnitude in optomechanical cooling due to this hybrid interaction. Significantly, based on demonstrated parameters for the cavity optomechanical device, we identify regimes that enable the ground-state cooling of the resonator from room temperature. In addition, the hybrid system considered here represents a powerful interface for the use of an ultracold quantum gas for state preparation, sensing, and quantum manipulation of a mesoscopic mechanical resonator.

We identify that both the dynamic core polarization and dynamic orbital deformation are important in the orientation-dependent high-order harmonic generation of CO molecules subjected to intense few cycle laser fields. These polarization dynamics allow for the observation of strong orientation effects and dynamic minimum in the harmonic spectra. The generated attosecond pulses can be greatly affected by these multielectron effects. This work sheds light on future development of dynamic orbital imaging on attosecond time scale.

Electron scattering on a nucleus in a field of two unidirectional pulsed laser waves is considered. The parametric interference effect is studied, which manifests in electron scattering within the plane formed by both the direction of laser-wave propagation and the initial electron momentum (the interference region). In this kinematics the electron emits and absorbs photons of both waves in a correlated manner. The distribution of the differential cross section of the final-electron energy for the process of electron-nucleus scattering in the field of two pulsed waves is considered. This distribution in the interference region differs qualitatively and quantitatively from the corresponding distribution in any other geometry. The appearance of the parametric interference effect may be experimentally verified by measuring the energy spectrum of final electrons in the framework of modern research projects, which use sources of pulsed laser radiation (XFEL, ELI, PHELIX).

The physics of one-dimensional optical superlattices with resonant $s\text{−}p$ orbitals is reexamined in the language of appropriate Wannier functions. It is shown that details of the tight-binding model realized in different optical potentials crucially depend on the proper determination of Wannier functions. We discuss the properties of a superlattice model which quasiresonantly couples $s$ and $p$ orbitals and show its relation with different tight-binding models used in other works.

Optical-frequency combs consisting of equally spaced sharp lines in frequency space have triggered substantial advances in optical-frequency metrology and precision measurements and in applications such as laser-based gas sensing and molecular fingerprinting. Here, we propose a scheme to generate a type of optical-frequency combs and convert them from one cavity to the other in a hybrid optical system composed of a pair of coupled photonic crystal cavities called a photonic molecule (PM) and a single semiconductor quantum dot (QD) embedded in one cavity of the molecule. Optical-frequency combs are formed by the interaction between a cavity mode and a continuous-wave (CW) two-tone driving laser consisting of a pump field and a seed field via QD-induced strong nonlinearity. In this situation, the initial input pump and seed CW lasers can interact among each other and produce optical higher-order sidebands with equal spacing via parametric frequency conversion provided by QD-induced nonlinear optical effects. Using numerical simulations, it is clearly shown that the beat frequency of the two-tone components plays an important role in determining the comb spacing and matched frequency combs can be formed in the PM. We also demonstrate that the present interacting QD-PM system can serve as a platform to generate large-scale quantum entanglement between two comb modes. The results obtained here may be useful for real experiments in a photonic crystal platform.