We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement record is averaged over and the case wherein it is retained. We find, in particular, that there is interesting dynamics in the latter situation, which cannot be revealed by considering the average case. We then consider in detail how a sequence of rotationally invariant unitary interactions affects the reference frame, a situation, which leads to quite different dynamics than the case of repeated measurements. We then consider strategies for correcting reference frame drift if we are given a set of particles with polarization opposite to the direction of drift. In particular, we find that, by implementing a suitably chosen unitary interaction after every two measurements, we can eliminate the rotational drift of the reference frame.

We study the dynamics of two lower bounds of concurrence in bipartite quantum systems when one party goes through an arbitrary channel. We show that these lower bounds obey the factorization law similar to that of [Konrad et al., Nat. Phys. 4, 99 (2008)]. We also discuss the application of this property in an example.

In this paper, we investigate the generation of polychromatic quadripartite entanglement of continuous variables from a three-level $\Lambda$-type atomic system inside an optical quadruply resonant cavity. The atoms are driven by external lasers and simultaneously coupled to four cavity modes by means of multiply concurrent four-wave mixing interactions. The general master equation of the cavity field is derived explicitly. By solving the Gaussian-type master equation and using the negative-partial-transpose criterion for bipartite entanglement, we show that the genuine quadripartite entanglement of the field can be generated over a wide range of parameters. The entanglement properties of the four-mode field are discussed in detail. We find that the optimal quadripartite entanglement can be obtained when the cavity modes are tuned to be resonant with the Rabi sidebands of the driven atoms.

Auger spectra of resonantly excited $2p_{3/2}^{-1}4s$ and $2p_{3/2}^{-1}4p$ states in argon were measured by $(e,2e)$ technique. The 99.2-eV scattered electrons were detected in coincidence with $L_3–M_{23}{M}_{23}$ Auger electrons, and the experiment was performed at 343.6- and 344.9-eV electron impact to tune the energy loss to the energy of the dipole-allowed and the dipole-forbidden excitations, respectively. The resonant Auger spectra are obtained upon subtraction of the overlapping signal due to the outer-shell ionization, which was recorded at 340-eV electron-impact energy. The most intense groups of Auger transitions from $2p_{3/2}^{-1}4s\hspace{0.5em}(J=1,2)$ and $2p_{3/2}^{-1}4p\hspace{0.5em}(J=0,1,2,3)$ states are identified by comparison with the results of the two-step model, based on distorted-wave Born approximation with exchange and multiconfiguration descriptions of the relaxed states. The $4\hspace{0.5em}s$ spectrum displays a substantially larger shake-up contribution than the one observed in photoexcitation experiments, which may be explained by the interference of the resonant decay path with the direct ionization excitation of the Ar $3p$ subshell. The majority of the observed $4p$ signal is assigned to the monopole and quadrupole excitations of the ground state.

We have performed relativistic distorted-wave calculations to study the excitation of Kr from its ground $4p^6$ configuration to the higher lying fine-structure levels of the $4p^5$$4d$, $4p^5$$5p$, and $4p^{5}6s$ manifolds. We have obtained relativistic Dirac-Fock multiconfiguration wave functions for the ground and the excited states. We present results for differential cross section and compare these with the available experimental measurements for energies up to 100 eV. We also report integrated cross sections for incident electron energies up to 300 eV and provide analytic fits for plasma modeling applications.

We demonstrate lasing based on a random distributed feedback due to the Raman amplified Rayleigh backscattering in different types of cavities with and without conventional point-action reflectors. Quasistationary generation of a narrowband spectrum is achieved despite the random nature of the feedback. The generated spectrum is localized at the reflection or gain spectral maxima in schemes with and without point reflectors, respectively. The length limit for a conventional cavity and the minimal pump power required for the lasing based purely on a random distributed feedback are determined.

A quantum search algorithm based on the partial adiabatic evolution [Phys. Rev. A 80, 052328 (2009)] is provided. We calculate its time complexity and find that the algorithm improves the time complexity, which is $O(\sqrt{N/M})$, of the local adiabatic search algorithm [Phys. Rev. A 65, 042308 (2002)] to $O(\sqrt{N}/M)$.

We find an analytical lower bound of concurrence for both bipartite and multipartite quantum states. It is shown that our bound can be used as a strong entanglement criterion.

Following the idea of Gill and Pople [Phys. Rev. A 47, 2383 (1993)] in three dimensions, we have constructed a gradient-corrected functional for the hydrogen atom for the two-dimensional case. The corresponding potential is constrained by the requirement that it cancel precisely the Coulomb potential of the normalized ground-state electronic charge density distribution which characterizes the localized single-electron state around a proton. Within this condition for a gradient-corrected functional, the dimensionality dependence is quantified and found to be relatively small.

Recently a study [J. K. Saha and T. K. Mukherjee, Phys. Rev. A 80, 022513 (2009)] on the doubly excited ${}^3{P}^e$ states of helium reports some resonance states that are not in conformity with previously published works [Y. K. Ho and A. K. Bhatia, Phys. Rev. A 47, 2628 (1993)]. Owing to discrepancies between the works, we investigate the resonance parameters (positions and widths) of the doubly excited Feshbach resonances of the ${}^3{P}^e$ symmetries associated with $N$ $=$ $3$, $4$, and $5$ He${}^{+}$ thresholds using a different choice of correlated wave functions in the framework of the complex-coordinate rotation method and the stabilization method. Resonance parameters below the $N=4$ and $N=5$ He${}^{+}$ thresholds obtained from the present calculations are not consistent with the results and discussions made in the recent work. Here we point out an error in assessment made by Saha and Mukherjee in an earlier work as well as the lack of numerical accuracy of the results for some high-lying doubly excited states reported by Saha and Mukherjee. The bound $2p^2\hspace{0.5em}{}^3{P}^e$ and $2p3p\hspace{0.5em}{}^3{P}^e$ state energies obtained from this calculation are consistent with the best reported results but not with the reported values of Saha and Mukherjee.

In response to the comment by Kar and Ho [Phys. Rev. A 82, 036501 (2010)], we have clarified the reason for anomaly between our and their results for the resonance states below the $N=5$ ionization threshold of He${}^{+}$.

In a recent article by Chen et al. [Phys. Rev. A 79, 062715 (2009)], reference is made to magnetic sublevel collision strengths in an earlier relativistic distorted-wave (RDW) article by Zhang et al. [Phys. Rev. A 41, 198 (1990)]. In the former reference, Chen et al. carried out Dirac $R$-matrix calculations that suggest the polarization of the $3C$ and $3D$ lines of Fe xvii, which can be computed from the magnetic sublevel collision strengths, differ from RDW results by as much as $20\%$. We have recently carried out a variety of RDW and Dirac $R$-matrix calculations of the $3C$ and $3D$ polarizations that demonstrate this quantity to be relatively insensitive to the size and details of the atomic model. Moreover, the polarizations obtained from these recent RDW and Dirac $R$-matrix calculations agree well, and they also agree well with the polarizations that can be obtained from the fundamental collision data published by Zhang et al. This good agreement between RDW and Dirac $R$-matrix polarizations contradicts the behavior reported by Chen et al.

In response to the Comment written by Zhang et al. [Phys. Rev. A 82, 036701 (2010)] we show that the main ideas and results (about the physics and method) reported in our paper [Phys. Rev. A 79, 062715 (2009)] still appear to be correct. Although none of the conjectures given in the Comment about the potential problems in our code are correct, there was a small error in our code, so the part of our paper with numerical data, presented to support our method, appears to be incorrect. The wealth of resonance features in the x-ray line $3D$ demonstrated in our paper still appears to be real and is reconfirmed by a revised calculation with the error fixed.

We demonstrate that intensity correlations of second order in the fluorescence light of $N>2$ single-photon emitters may violate locality while the visibility of the signal remains below $1/\sqrt{2}\approx 71\%$. For this, we derive a homogeneous Bell-Wigner–type inequality, which can be applied to a broad class of experimental setups. We trace the violation of this inequality back to path entanglement created by the process of detection.

A general method for the study of the entanglement evolution of graph states under the action of Pauli maps was recently proposed in Cavalcanti et al. [Phys. Rev. Lett. 103, 030502 (2009)]. This method is based on lower and upper bounds to the entanglement of the entire state as a function only of the state of a (typically) considerably smaller subsystem undergoing an effective noise process related to the original map. This provides a huge decrease in the size of the matrices involved in the calculation of entanglement in these systems. In the present paper we elaborate on this method in detail and generalize it to other natural situations not described by Pauli maps. Specifically, for Pauli maps we introduce an explicit formula for the characterization of the resulting effective noise. Beyond Pauli maps, we show that the same ideas can be applied to the case of thermal reservoirs at arbitrary temperature. In the latter case, we discuss how to optimize the bounds as a function of the noise strength. We illustrate our ideas with explicit exemplary results for several different graphs and particular decoherence processes. The limitations of the method are also discussed.

It is impossible to unambiguously distinguish the four Bell states in polarization, resorting to linear optical elements only. Recently, the hyperentangled Bell state, the simultaneous entanglement in more than one degree of freedom, has been used to assist in the complete Bell-state analysis of the four Bell states. However, if the additional degree of freedom is qubitlike, one can only distinguish 7 from the group of 16 states. Here we present a way to distinguish the hyperentangled Bell states completely with the help of cross-Kerr nonlinearity. Also, we discuss its application in the quantum teleportation of a particle in an unknown state in two different degrees of freedom and in the entanglement swapping of hyperentangled states. These applications will increase the channel capacity of long-distance quantum communication.

In this article, the scheme of quantum computing based on the Stark-chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei, J. R. Johansson, L. X. Cen, S. Ashhab, and F. Nori, Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement quantum state manipulations in flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark shifts. Then, assisted by various transition pulses, universal quantum logic gates as well as arbitrary quantum state preparations can be implemented. Compared with the usual $\pi$-pulse operations widely used in experiments, the adiabatic population passages proposed here are insensitive to the details of the applied pulses and thus the desirable population transfers can be satisfyingly implemented. The experimental feasibility of the proposal is also discussed.

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with nonequal scattering lengths and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified, resulting in highly directional, oppositely propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet’s theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov–de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable helium atom laser experiment by Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show that it explains the anomalous beam profiles they observed. Finally, we demonstrate that the paired particle beams will be Einstein-Podolsky-Rosen entangled on formation.

We report on the creation of three-vortex clusters in a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate by oscillatory excitation of the condensate. This procedure can create vortices of both circulations, so that we are able to create several types of vortex clusters using the same mechanism. The three-vortex configurations are dominated by two types, namely, an equilateral-triangle arrangement and a linear arrangement. We interpret these most stable configurations respectively as three vortices with the same circulation and as a vortex-antivortex-vortex cluster. The linear configurations are very likely experimental signatures of predicted stationary vortex clusters.