This paper reports $1.5\text{−}\mu \mathrm{m}$ band time-bin entanglement generation. We employed a spontaneous four-wave mixing process in a dispersion shifted fiber, with which correlated photon pairs with very narrow bandwidths were generated efficiently. To observe two-photon interference, we used planar lightwave circuit based interferometers that were operated stably without feedback control. As a result, we obtained coincidence fringes with 99% visibilities after subtracting accidental coincidences, and successfully distributed entangled photons over 20-km standard single-mode fiber without any deterioration in the quantum correlation.

We consider the maximum bipartite entanglement that can be distilled from a single copy of a multipartite mixed entangled state, where we focus mostly on $(d\times d\times n)$-dimensional tripartite mixed states. We show that this assisted entanglement, when measured in terms of the generalized concurrence (called the $G$ concurrence), is (tightly) bounded by an entanglement monotone, which we call the $G$ concurrence of assistance. The $G$ concurrence is one of the possible generalizations of the concurrence to higher dimensions, and for pure bipartite states it measures the geometric mean of the Schmidt numbers. For a large (nontrivial) class of $(d\times d)$-dimensional mixed states, we are able to generalize Wootters’ formula for the concurrence into lower and upper bounds on the $G$ concurrence. Moreover, we have found an explicit formula for the $G$ concurrence of assistance that generalizes the expression for the concurrence of assistance for a large class of $(d\times d\times n)$-dimensional tripartite pure states.

A spin-$1∕2$ chain model that includes three-spin interactions can effectively describe the dynamics of two species of bosons trapped in an optical lattice with a triangular-ladder configuration. A perturbative theoretical approach and numerical study of its ground state is performed that reveals a rich variety of phases and criticalities. We identify phases with periodicity one, two, or three, as well as critical points that belong in the same universality class as the Ising or the three-state Potts model. We establish a range of parameters, corresponding to a large degeneracy present between phases with period 2 and 3, that nests a gapless incommensurate chiral phase.

We have recently derived a gapless theory of the linear response of a Bose-condensed gas to external perturbations at finite temperature and used it to explain quantitatively the measurements of condensate excitations and decay rates made at the Joint Institute for Laboratory Astrophysics [D. S. Jin et al., Phys. Rev. Lett. 78, 764 (1997)]. The theory describes the dynamic coupling between the condensate and noncondensate via a full quasiparticle description of the time-dependent normal and anomalous averages and includes all Beliaev and Landau processes. In this paper, we provide a full discussion of the numerical calculations and a detailed analysis of the theoretical results in the context of the JILA experiment. We provide unambiguous proof that the dipole modes are obtained accurately within our calculations and present quantitative results for the relative phase of the oscillations of the condensed and uncondensed atom clouds. One of the main difficulties in the implementation of the theory is obtaining results which are not sensitive to basis cutoff effects, and we have therefore developed a novel asymmetric summation method which solves this problem and dramatically improves the numerical convergence. This technique should make the implementation of the theory and its possible future extensions feasible for a wide range of condensate populations and trap geometries.

By solving the self-consistent system of Maxwell and density-matrix equations in the case where the time of relaxations to the ground state is much shorter than the pulse duration we derive an analytical solution for the probe pulse propagation. We obtain an excellent consistency of our analytical solution with direct numerical integration. We investigate the asymptotic behavior of analytical solution and show that under certain conditions it passes to the well-known dark-state polariton propagation regime. We analyzed the dynamics of propagation and, in particular, explain the fact that in the well-known experiments only fractions of pulses were stored.

We present an ab initio method of calculation of the isotope and relativistic shifts in atoms with a few valence electrons. It is based on an energy calculation involving the combination of the configuration-interaction method and many-body perturbation theory. This work is motivated by analyses of quasar absorption spectra that suggest that the fine-structure constant $\alpha$ was smaller at an early epoch. Relativistic shifts are needed to measure this variation of $\alpha$, while isotope shifts are needed to resolve systematic effects in this study. The isotope shifts can also be used to measure isotopic abundances in gas clouds in the early universe, which are needed to study nuclear reactions in stars and supernovae and test models of chemical evolution. This paper shows that the isotope shift in magnesium can be calculated to very high precision using our method.

We determine the third Zemach moment of hydrogen $\left({⟨r^3⟩}_{\left(2\right)}\right)$ using only the world data on elastic electron-proton scattering. This moment dominates the $\mathcal{O}{\left(Z\alpha \right)}^5$ hadronic correction to the Lamb shift in muonic atoms. The resulting moment, ${⟨r^3⟩}_{\left(2\right)}=2.71\left(13\right){\mathrm{fm}}^3$, is larger than some previously inferred values based on simple models. The contribution of that moment to the muonic hydrogen 2S level is $-0.0247\left(12\right)\mathrm{meV}$.

We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time-of-arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time-of-arrival eigenfunctions is also numerically investigated and demonstrated that the eigenfunctions evolve to have point supports at the arrival point at their respective eigenvalues in the limit of arbitrarily large confining lengths, giving insight into the ideal physical content of the Kijowsky distribution.

Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data processing of the measurement outcomes. In particular, an informationally complete measurement can be used to perform quantum tomography, namely to estimate the density matrix of the quantum state. The data processing is generally nonunique, and can be optimized according to a given criterion. In this paper we provide the solution of the optimization problem which minimizes the variance in the estimation. We then consider informationally complete measurements performed over bipartite quantum systems focusing attention on universally covariant measurements, and compare their statistical efficiency when performed either locally or globally on the two systems. Among global measurements we consider the special case of Bell measurements, which allow us to estimate the expectation of a restricted class of operators. We compare the variance in the three cases: local, Bell, and unrestricted global—and derive conditions for the operators to be estimated such that one type of measurement is more efficient than the other. In particular, we find that for factorized operators and Bell projectors the Bell measurement always performs better than the unrestricted global measurement, which in turn outperforms the local one. For estimation of the matrix elements of the density operator, the relative performances depend on the basis on which the state is represented, and on the matrix element being diagonal or off-diagonal, however, with the global unrestricted measurement generally performing better than the local one.

The “power of one qubit” refers to a computational model that has access to only one pure bit of quantum information, along with $n$ qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of $n$, for all bipartite divisions of the $n+1$ qubits, and so becomes, when $n$ is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.

In Phys. Rev. A 71, 060312(R) (2005), the robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian was examined. We expand this analysis to include the case of the global adiabatic quantum search. As in the case of the local search the asymptotic time complexity for the global search is the same as for the ideal closed case, as long as the Hamiltonian dynamics is present. In the case of pure decoherence, where the environment monitors the search Hamiltonian, we find that the time complexity of the global quantum adiabatic search scales like $N^{3∕2}$, where $N$ is the list length. We moreover extend the analysis to include success probabilities $p<1$ and prove bounds on the run time with the same scaling as in the conditions for the $p\to 1$ limit. We supplement the analytical results by numerical simulations of the global and local search.

The ground-state electron density $\rho \left(r\right)$ in a model of the He-like sequence of atomic ions, in which the Coulomb repulsion is replaced by the $s$-wave component, has recently been obtained by Howard and March [Phys. Rev. A 71, 042501 (2005)]. Their result is here generalized to derive the one-particle density matrix yielding the Howard and March $\rho \left(r\right)$ on the diagonal. Its momentum space counterpart is also presented and the momentum density is studied in detail, with particular emphasis on the asymptotic behavior of momentum distribution. Attention is then focussed on the kinetic energy density and on the spectral decomposition of the ground-state wave function. A natural orbital analysis in both direct and momentum space is also presented. Finally, the relevance for density functional theory of this exactly solvable model is briefly considered.

“Complete” two-dimensional photoelectron spectra of Ar in the vicinity of the $2p$ ionization thresholds have been measured allowing several features in the spectra to be explained. Nine reemission series are observed and their initial and final states are determined based on the kinetic energies of these electrons. The photoelectron recapture yield above the $L_2$ threshold has been studied by measuring directly the reemitted electrons as a function of the photon energy. Our experimental results are found to be in reasonable agreement with our semiclassical calculations which in turn are in good agreement with the quantum-mechanical calculation of Tulkki et al. [Phys. Rev. A 41, 181 (1990)].

In this paper, we study the three-body recombination rate of a homogeneous dilute Bose gas with a Feshbach resonance at zero temperature. The ground state and excitations of this system are obtained. The three-body recombination in the ground state is due to the breakup of an atom pair in the quantum depletion and the formation of a molecule by an atom from the broken pair and an atom from the condensate. The rate of this process is in good agreement with the experiment on ${}^{23}\mathrm{Na}$ in a wide range of magnetic fields.

The absolute time of emission of the x-ray laser output with respect to the arrival of a $100\text{−}\mathrm{ps}$ pump pulse has been measured with the aid of a calibrated timing fiducial. The results show the x-ray laser to appear up to $60\mathrm{ps}\left(80\mathrm{ps}\right)$ before the peak of the pump pulse in the case of the Sn (Pd) x-ray laser, which is in good agreement with simulations obtained from the LASNEX and CRETIN codes. The pulse duration was found to be $\sim 45\mathrm{ps}$ for both the Sn and the Pd x-ray lasers.

We analyzed the security of the multiparty quantum secret sharing (MQSS) protocol recently proposed by Zhang, Li, and Man [Phys. Rev. A 71, 044301 (2005)] and found that this protocol is secure for any other eavesdropper except for the agent Bob who prepares the quantum signals as he can attack the quantum communication with a Trojan horse. That is, Bob replaces the single-photon signal with a multiphoton one and the other agent Charlie cannot find this cheating as she does not measure the photons before they run back from the boss Alice, which reveals that this MQSS protocol is not secure for Bob. Finally, we present a possible improvement of the MQSS protocol security with two single-photon measurements and four unitary operations.

The cesium $D_2$ line closed hyperfine transition $F=4\to F^{\prime }=5$ was simultaneously coupled and probed in a hot atomic beam. We experimentally showed that, when the probe laser frequency approached that of the two-photon-resonance corresponding to electromagnetically induced absorption conditions, an enhanced transparency of the coupling laser appeared, combined with a further central absorption peak at zero probe laser detuning. Simultaneously, the coupling laser parametric dispersion showed a broad negative pattern together with a narrower steep positive phase shift in correspondence with the two-photon resonance, with sub-Doppler half-widths down to about $10\mathrm{kHz}$.