We investigate how the introduction of different types of disorder affects the generation of entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional quantum random walks (QRWs). Disorder is modeled by adding another random feature to QRWs, i.e., the quantum coin that drives the system's evolution is randomly chosen at each position and/or at each time step, giving rise to dynamic, fluctuating, or static disorder. The first one is position independent, with every lattice site having the same coin at a given time; the second has time- and position-dependent randomness; and the third one is time independent. We show for several levels of disorder that dynamic disorder is the most powerful entanglement generator, followed closely by fluctuating disorder. Static disorder is the less efficient entangler, being almost always less efficient than the ordered case. Also, dynamic and fluctuating disorder lead to maximally entangled states asymptotically in time for any initial condition, while static disorder has no asymptotic limit and, similarly to the ordered case, has a long-time behavior highly sensitive to the initial conditions.

We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbor level-spacing distribution $P\left(s\right)$, the level number variance ${\Sigma }^2\left(L\right)$, and the Dyson-Mehta ${\Delta }_3$ statistics for various cluster sizes. For large clusters we find that although the Bohigas-Giannoni-Schmit conjecture seems to be valid, it does not exhibit true signatures of quantum chaos. However, contrasting conjecture of Berry and Tabor is observed with smaller cluster size. For a small number of bosons, we observe the existence of a large number of quasidegenerate states in low-lying excitation which exhibits the Shnirelman peak in $P\left(s\right)$ distribution. We also find a narrow region of intermediate spectrum which can be described by semi-Poisson statistics whereas the higher levels are regular and exhibit Poisson statistics. These observations are further supported by the analysis of the distribution of the ratio of consecutive level spacings $P\left(r\right)$ which is independent of unfolding procedure and thereby provides a tool for more transparent comparison with experimental findings than $P\left(s\right)$. Thus our detail numerical study clearly shows that the van der Waals clusters become more correlated with the increase in cluster size.

The optical response of a one-dimensional string made of dipoles with a periodically varying density excited by a spot of light moving along the string at superluminal (subluminal) velocity is studied theoretically. The Cherenkov radiation in such a system is rather unusual, possessing both transient and resonant character. We show that, under certain conditions, in addition to the resonant Cherenkov peak, another Doppler-like frequency appears in the radiation spectrum. Both linear (small-signal) and nonlinear regimes as well as different string topologies are considered.

We retrieve x-ray phase images from ptychographical data which, according to the conventional coherent diffractive imaging (CDI) criterion, have been grossly undersampled. Ptychographical data are intrinsically oversampled in real space, as the illumination function of subsequent exposures overlap. By exploiting the real-space redundancy in ptychography, we are able to recover the conventional CDI reciprocal sampling, despite an increase in the solid angle of the detector pixels. As a result the current experimental geometrical constraints placed upon probe size, object to detector distance, and pixel size are all relaxed.

We theoretically investigate the influence of losses on the wave-particle duality in a Mach-Zehnder interferometer. Balanced losses (equal loss on the two paths) have no effect on the visibility and predictability (also the duality relation), while unbalanced losses do have influence on them. If the unbalanced losses occur inside the interferometer, the losses have an effect on both the visibility and predictability, while the losses have no effect on the duality relation. If the unbalanced losses occur after the interferometer, the losses have no effect on the visibility, but do have an effect on the predictability (also the wave-particle duality), which can lead to a result that the duality relation exceeds 1, $P^2+V^2>1$. The influence of losses can be eliminated by exchanging the two detectors or the two inputs (one photon and the vacuum) of the interferometer and then averaging the two results. Consequently, we have the visibility, predictability, and duality relation $P^2+V^2\le 1$ independent of the unbalanced losses. The obtained $P$ and $V$ for the unbalanced losses in the two paths do not represent the original predictability and visibility, and the result of $P_D^2+V_D^2>1$ does not mean the “violation” of the original duality.

The nearest-neighbor spins in the one-dimensional spin-1/2 $XX$ model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, $h_c$. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.

We present comparisons between measured isolated line shapes of molecular oxygen in air at various pressures and those calculated, free of any adjusted parameter, using requantized classical molecular dynamics simulations (rCMDS). The measurements have been made for the R1Q2, P9P9, P11P11, P13P13, and P15Q14 transitions in the ${\mathrm{O}}_2$ singlet-Δ band [$a{}^1{\Delta }_g\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$] by the frequency-stabilized cavity ring-down spectroscopy technique. This work extends a previous study made for a single oxygen line [Phys. Rev. A 87, 032510 (2013)] and confirms the quality of this theoretical approach over broad ranges of pressure and rotational quantum number. Indeed, not only the collisional broadening coefficients but also the (small) deviations of observed line shapes with respect to the Voigt profile are accurately predicted. These results illustrate the viability of using the rCMDS method as a benchmark for the development and testing of simpler parametrized line profiles that are suitable for the analysis of underlying physical mechanisms and for atmospheric remote sensing applications.

We measure the power spectrum of density fluctuations emerging in a freely expanding quasi-two-dimensional (2D) degenerate Bose gas, and we investigate the scaling behavior of the spectrum for the expansion time. The power spectrum shows an oscillatory shape for long expansion times, where the spectral peak positions are observed to be shifted to lower spatial frequencies than the theoretical prediction for a noninteracting expansion case. We find the spectral peak positions in good agreement with the recent numerical simulation presented by Mazets [Phys. Rev. A 86, 055603 (2012)], where the atom-atom interactions are taken into account. We present a mean-field description of the interaction effect in the expansion dynamics and quantitatively account for the observed spectral peak shifts. The spectral shift is intrinsic to the free expansion of a quasi-2D Bose gas due to finite axial confinement. Finally, we investigate the defocusing effect in the power spectrum measurement.

It is known that parity measurement, together with single-qubit rotation, is sufficient for implementing scalable quantum computation. In this Brief Report, we propose a scheme for a projective measurement of the parity operator $P_z={\otimes }_{i=1}^N{\sigma }_{i,z}$ of $N$ distant atoms trapped in spatially separated cavities. Instead of direct interaction between the atoms, quantum interference of polarized photons decaying from the optical cavities is used to realize expected measurement without resorting to a sequence of single- and two-qubit operations. It is shown that parity measurement can be implemented repeatedly until success without destroying the qubits at any stage of the operation.

We propose a scheme to realize optical quantum memories in an ensemble of nitrogen-vacancy centers in diamond that are coupled to a microcavity. The scheme is based on off-resonant Raman coupling, which allows one to circumvent optical inhomogeneous broadening and store optical photons in the electronic spin coherence. This approach promises a storage time of order 1 s and a time-bandwidth product of order ${10}^7$. We include all possible optical transitions in a nine-level configuration, numerically evaluate the efficiencies, and discuss the requirements for achieving high efficiency and fidelity.

We compare three different types of optical qubits for information transfer via quantum teleportation and direction transmission under photon losses. The three types of qubits are (1) qubits using the vacuum and the single-photon (VSP) states, (2) single-photon qubits using polarization degrees of freedom, i.e., polarized single-photon (PSP) qubits, and (3) coherent-state qubits that use two coherent states with opposite phases as the qubit basis. Our analysis shows that the teleportation scheme outperforms the direct transmission for most of cases as far as fidelities are concerned. Overall, VSP qubits are found to be the most efficient for both the direct transmission and teleportation under photon loss effects. The coherent-state qubits are more robust than PSP qubits either when their amplitudes are small as $\left|\alpha \right|\lesssim 1.22$ or when photon loss effects are strong. Our results would provide useful and timely information for the development of practical optical quantum information processing particularly in the context of hybrid architectures.

We present a systematic comparison of different methods of fidelity estimation of a linear optical quantum-controlled-$Z$ gate implemented by two-photon interference on a partially polarizing beam splitter. We utilize a linear fidelity estimator based on the Monte Carlo sampling technique as well as a nonlinear estimator based on maximum likelihood reconstruction of a full quantum-process matrix. In addition, we evaluate the lower bound on quantum-gate fidelity determined by average quantum-state fidelities for two mutually unbiased bases. In order to probe various regimes of operation of the gate we introduce a tunable time delay between the two photons. This allows us to move from high-fidelity operation to a regime where the photons become distinguishable and the success probability of the scheme significantly depends on the input state. We discuss in detail possible systematic effects that could influence the gate-fidelity estimation.

Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review several known and new definitions, with the qualifying criterion being that for pure states the measure is a linear or logarithmic function of the maximal fidelity with product states. The entanglement axioms and properties of the measures are studied, and qualitative and quantitative comparisons are made between all definitions. Streltsov et al. [New J. Phys. 12, 123004 (2010)] proved the equivalence of two linear definitions of GM, whereas we show that the corresponding logarithmic definitions are distinct. Certain classes of states such as “maximally correlated states” and isotropic states are particularly valuable for this analysis. A little-known GM definition is found to be the first one to be both normalized and weakly monotonous, thus being a prime candidate for future studies of multipartite entanglement. We also find that a large class of graph states, which includes all cluster states, have a “universal” closest separable state that minimizes the quantum relative entropy, the Bures distance, and the trace distance.

The inelastic Raman scattering of light by hydrogenlike ions has been studied by means of second-order perturbation theory and the relativistic Coulomb Green's-function approach. In particular, we investigate the total and angle-differential Raman cross sections as well as the magnetic sublevel population of the residual (excited) ions. Detailed calculations are performed for the inelastic scattering of photons by neutral hydrogen as well as hydrogenlike xenon and uranium ions, accompanied by the $1s_{1/2}\to 2s_{1/2}$, $1s_{1/2}\to 2p_{1/2}$, and $1s_{1/2}\to 2p_{3/2}$ transitions. Moreover, we discuss how the Raman scattering is affected by relativistic and resonance effects as well as the higher-multipole contributions to the electron-photon interaction.

We present a detailed study of the effect of a strong and circularly polarized coupling beam on a probe beam locked to a hyperfine transition of the rubidium $D_2$ manifold. Experiments were carried out in the co- and counterpropagating configurations. Counterpropagating beams are used to study the effect of the probe beam intensity on absorption and polarization spectra. These data are compared with results of a rate-equation calculation. The absorption spectra show very clear indication of saturation, with different saturation intensities for each atomic line. The slope of the dispersionlike profile of the polarization signal increases with the intensity of the probe beam. These results are in very good agreement with the calculation. Experimental absorption and polarization spectra in the copropagating configuration are also well reproduced by the rate-equation calculation. The dispersion profiles in the polarization signal can be used to lock the coupling laser frequency at well defined frequencies.

An approach is proposed for the generation of virtual spin orbitals required to construct a configuration state function basis set for relativistic configuration interaction calculations. Screened hydrogenic spin orbitals, corresponding to noninteger nuclear numbers determined separately for each orbital employing the so-called condensed-space concept are proposed and used here. To test the method calculations are performed of ionization and transition energies of two- and three-electron systems such as He, He-like Ne and He-like U, Li, Li-like Ne and Li-like U, including Breit interaction and quantum electrodynamic corrections.

We study relativistic effects in the time delay of atomic photoionization using an example of the Xe atom subjected to a circularly polarized electromagnetic pulse. We find that while relativistic effects play only a fairly small role for both the ionization probabilities and the time delay of the corotating electron with the same sign of the angular momentum projection as the circularly polarized light, these effects produce substantial change in the time delay for a counter-rotating electron with the opposite sign of the angular momentum projection.

We propose a method for measuring velocities of atoms or molecules in a gas phase based on time-resolved laser experiments. Two intensity gratings of electromagnetic field with variable time delay $\tau$ are created by interfering of four laser pulses. Using first-order perturbation theory, we show that such arrangement can be used for measuring particle velocities, which have an optical transition to a long-living excited state. It is shown that the optical Ramsey oscillations obtain a characteristic modulation that reflects the distribution of velocities.

An attractive Bose-Einstein condensate in two spatial dimensions is expected to collapse for supercritical values of the interaction strength. Moreover, it is known that for nonzero quanta of angular momentum and infinitesimal attraction the gas prefers to fragment and distribute its angular momentum over different orbitals. In this work we examine the two-dimensional trapped Bose gas for finite values of attraction and describe the ground state in connection to its angular momentum by theoretical methods that go beyond the standard Gross-Pitaevskii theory. By applying the best-mean-field approach over a variational ansatz whose accuracy has been checked numerically, we derive analytical relations for the energy, the fragmentation of the ground states, and the critical (for collapse) value of the attraction strength as a function of the total angular momentum $L$.

We propose a model to realize a fermionic superfluid state in an optical lattice circumventing the cooling problem. Our proposal exploits the idea of tuning the interaction in a characteristically low-entropy state, a band insulator in an optical bilayer system, to obtain a superfluid. By performing a detailed analysis of the model including fluctuations and augmented by a variational quantum Monte Carlo calculation of the ground state, we show that the superfluid state obtained has a high transition temperature of the order of the hopping energy. Our system is designed to suppress other competing orders such as a charge density wave. We suggest a laboratory realization of this model via an orthogonally shaken optical lattice bilayer.