Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent quantum error correction can combat ESD. We find that in some cases quantum error correction can delay entanglement sudden death but in other cases quantum error correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different error correction codes since the fidelity is not directly coupled to a state’s remaining entanglement.

A linear optical probabilistic scheme for the optimal cloning of a pair of orthogonally polarized photons is devised, based on single- and two-photon interferences. It consists in a partial symmetrization device realized with a modified unbalanced Mach-Zehnder interferometer, followed by two balanced beam splitters where the Hong-Ou-Mandel photon bunching occurs. This scheme has the advantage that it enables quantum cloning without the need for stimulated amplification in a nonlinear medium. It can also be modified so to make an optical two-qubit partial SWAP gate, thereby providing a potentially useful tool to linear optics quantum computing.

We make a detailed analysis of error mechanisms, gate fidelity, and scalability of proposals for quantum computation with neutral atoms in addressable (large lattice constant) optical lattices. We have identified possible limits to the size of quantum computations, arising in three-dimensional (3D) optical lattices from current limitations on the ability to perform single-qubit gates in parallel and in 2D lattices from constraints on laser power. Our results suggest that 3D arrays as large as $100\times 100\times 100$ sites (i.e., $\sim {10}^6$ qubits) may be achievable, provided two-qubit gates can be performed with sufficiently high precision and degree of parallelizability. The parallelizability of long-range interaction-based two-qubit gates is qualitatively compared to that of collisional gates. Different methods of performing single-qubit gates are compared, and a lower bound of $1\times {10}^{-5}$ is determined on the error rate for the error mechanisms affecting ${}^{133}\text{C}\text{s}$ in a blue-detuned lattice with Raman-transition-based single-qubit gates, given reasonable limits on experimental parameters.

We investigate magnetic Feshbach resonances in two different ultracold K-Rb mixtures. Information on the ${}^{39}\text{K}\text{−}{}^{87}\text{R}\text{b}$ isotopic pair is combined with preexisting observations of resonance patterns for ${}^{40}\text{K}\text{−}{}^{87}\text{R}\text{b}$. Interisotope resonance spectroscopy improves significantly our near-threshold model for scattering and bound-state calculations. Our analysis determines the number of bound states in singlet and triplet potentials and establishes precisely near-threshold parameters for all K-Rb pairs of interest for experiments with both atoms and molecules. In addition, the model verifies the validity of the Born-Oppenheimer approximation at the present level of accuracy.

In this paper we study the density noise correlations of the two component Fermi gas in optical lattices. Three different types of phases, the BCS state (Bardeen, Cooper, and Schieffer), the FFLO state (Fulde, Ferrel, Larkin, and Ovchinnikov), and the BP (breach pair) state are considered. We show how these states differ in their noise correlations. The noise correlations are calculated not only at zero temperature, but also at nonzero temperatures paying particular attention to how much the finite temperature effects might complicate the detection of different phases. Since one-dimensional systems have been shown to be very promising candidates to observe FFLO states, we apply our results also to the computation of correlation signals in a one-dimensional lattice. We find that the density noise correlations reveal important information about the structure of the underlying order parameter as well as about the quasiparticle dispersions.

A theoretical and experimental study of multimode operation regimes in quantum cascade lasers (QCLs) is presented. It is shown that the fast gain recovery of QCLs promotes two multimode regimes: One is spatial hole burning (SHB) and the other one is related to the Risken-Nummedal-Graham-Haken instability predicted in the 1960s. A model that can account for coherent phenomena, a saturable absorber, and SHB is developed and studied in detail both analytically and numerically. A wide variety of experimental data on multimode regimes is presented. Lasers with a narrow active region and/or with metal coating on the sides tend to develop a splitting in the spectrum, approximately equal to twice the Rabi frequency. It is proposed that this behavior stems from the presence of a saturable absorber, which can result from a Kerr lensing effect in the cavity. Lasers with a wide active region, which have a weaker saturable absorber, do not exhibit a Rabi splitting and their multimode regime is governed by SHB. This experimental phenomenology is well-explained by our theoretical model. The temperature dependence of the multimode regime is also presented.

We present a general quasimode formalism for the quantum treatment of quantum-dot–photon dynamics in coupled-cavity systems in photonic-crystal slabs. The coupled-cavity systems are characterized by a large number of discrete lossy nonorthogonal quasimodes that can be obtained using a combination of the finite-difference time-domain method and the tight-binding approach. We project the electric field Green tensor onto the quasimodes using a non-Hermitian projector and thereby avoid the prohibitive finite-difference time-domain calculation of the Green tensor in large systems. We extend our projection approach to show that the quantum dynamics can be derived from an effective non-Hermitian Hamiltonian that is the full Hamiltonian projected onto the quasimode basis. We demonstrate the equivalence of the effective Hamiltonian approach with the Green tensor approach for the case of spontaneous emission and show how it can be used to treat multiple-photon, multiple-dot dynamics. The effective Hamiltonian provides a systematic approach to treating interacting quantum-dot–photon dynamics in coupled-cavity systems with a moderate number of quantum dots and photons and can be easily generalized to include nonradiative decay and decoherence of the quantum dots. Finally, we use our approach to model spontaneous emission in an asymmetric two-cavity system in a photonic crystal slab. We show that results obtained using our approach are essentially identical to results using the full Green tensor in the weak-coupling regime. In the strong-coupling regime, we show that the spontaneous emission dynamics are strongly affected by the nonorthogonality of the quasimodes and the results can be easily understood in terms of the quasimode dressed states.

We report an uncertainty evaluation of an optical lattice clock based on the ${}^1{S}_0\leftrightarrow {}^3{P}_0$ transition in the bosonic isotope ${}^{174}\mathrm{Yb}$ by use of magnetically induced spectroscopy. The absolute frequency of the ${}^1{S}_0\leftrightarrow {}^3{P}_0$ transition has been determined through comparisons with optical and microwave standards at NIST. The weighted mean of the evaluations is $\nu \left({}^{174}\mathrm{Yb}\right)=518294025309217.8\left(0.9\right)\mathrm{Hz}$. The uncertainty due to systematic effects has been reduced to less than $0.8\mathrm{Hz}$, which represents $1.5\times {10}^{-15}$ in fractional frequency.

What will happen if two identical microspheres, with fundamental whispering-gallery modes excited in each of them, become optically coupled? Conventional wisdom based on coupled-mode arguments says that two new modes, bonding and antibonding, with two split frequencies would be formed. In this Rapid Communication, we demonstrate, using exact multisphere Mie theory, that in reality an attempt to couple two fundamental modes of microspheres would result in a complex multiresonance optical response with the field distribution significantly deviating from predictions of coupled-mode-type theories.

Generalized quantum measurements (positive operator valued measures or probability operator measures) are important for optimally extracting information for quantum communication and computation. The standard realization via the Neumark extension requires extensive resources in the form of operations in an extended Hilbert space. For an arbitrary measurement, we show how to construct a binary search tree with a depth logarithmic in the number of possible outcomes. This could be implemented experimentally by coupling the measured quantum system to a probe qubit which is measured, and then iterating.

The multiparticle entanglement in the Lipkin-Meshkov-Glick model has been discussed extensively in this paper. Measured by the global entanglement and its generalization, our calculation shows that the multiparticle entanglement can faithfully detect quantum phase transitions. For an antiferromagnetic case the multiparticle entanglement reaches the maximum at the transition point, whereas for ferromagnetic coupling, two different behaviors of multiparticle entanglement can be identified, dependent on the anisotropic parameter in the coupling.

We investigate the quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasienergies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasienergy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second-quantized model, we find also a triangular structure in the quantum quasienergy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasienergies is further explored by a semiclassical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasienergies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.

We generalize the concept of an optical cavity mode to the case of an astigmatic cavity that rotates about its optical axis. We show that the modes of such a cavity are both spatially and spectrally confined and use an algebraic method to study their spatial and spectral structure. Our method involves ladder operators in the spirit of the quantum-mechanical harmonic oscillator. It hinges upon their algebraic properties as well as on the group-theoretical properties of the ray $\left(ABCD\right)$ matrix that describes the time-dependent ray dynamics of the rotating cavity.

In a recent paper [D. Li, X. Li, H. Huang, and X. Li, Phys. Rev. A 76, 032304 (2007)], Li et al. proposed the definition of the residual entanglement for general $n$ qubits by means of the stochastic local operations and classical communication. Here we argue that their definition is not suitable for the case of odd-$n$ qubits.

In D. Li, X. Li, H. Huang, and X. Li [Phys. Rev. A 76, 032304 (2007)], we defined the residual entanglement for odd $n$ qubits. In this reply, we improve the definition by averaging the original residual entanglement with respect to each qubit, which makes the defined quantity invariant under any permutation of all the qubits.

Gravitating bodies in motion, regardless of their constitution, always produce electromagnetic radiation in the form of photon pairs. This phenomenon is an analog of the radiation caused by the motion of dielectric (or magnetic) bodies. It is a member of a wide class of phenomena named dynamical Casimir effects, and it may be viewed as the squeezing of the electromagnetic vacuum. Production of photon pairs is a purely quantum-mechanical effect. Unfortunately, as we show, the emitted radiation is extremely weak as compared to radiation produced by other mechanisms.

We discuss a method to achieve decoherence resistant entanglement generation in strongly interacting ensembles of two-level spin systems. Our method uses designed gapped Hamiltonians to create a protected manifold of multidegenerate levels which is robust against local decoherence processes. We apply the protected evolution to achieve decoherence resistant generation of many-particle Greenberger-Horne-Zeilinger (GHZ) states in two specific physical systems, trapped ions and neutral atoms in optical lattices, and discuss how to engineer the desired many-body protected manifold with them. We analyze the fidelity of GHZ generation and show our method can significantly increase the sensitivity in frequency spectroscopy.

We construct simple analytic models of the $S$ matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the $s$-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of ${}^{133}\text{C}\text{s}$ atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the $s$-wave threshold, they cannot be studied easily using direct numerical solutions of the Schrödinger equation. Using our analytic model, we extend previous studies of negative-energy scattering to the multichannel case, accounting for the interplay of Feshbach resonances, large background scattering lengths, and inelastic processes.

The synchrotron-radiation-excited $4d$ photoelectron and subsequent Auger spectra of atomic Eu have been recorded with high resolution. The lifetime widths, intensity ratios, and binding energies of the most prominent ${}^{9}D$ states of the $4d^{-1}$ configuration have been determined with high accuracy from the measured spectrum. Experimental spectra have been compared with the results of relativistic multiconfiguration Dirac-Fock calculations. The features seen in the Auger spectrum have been found to be predominantly due to Coster-Kronig and super-Coster-Kronig transitions.

Measurements of positron-on-molecule annihilation have established that positrons attach to a variety of molecules via vibrational Feshbach resonances (VFRs). These resonances, in turn, result in greatly enhanced positron annihilation rates beyond those expected in simple collisions. A recent paper [J. A. Young and C. M. Surko, Phys. Rev. Lett. 99, 133201 (2007)] described experimental studies and analysis of positron annihilation in large molecules. Presented here is a more complete description of those results as well as data and analysis. Positron-molecule binding energy data are presented for twenty-five molecules, including the relatively deeply bound species 1-chlorohexane, benzene, and naphthelene. When a relatively weak dependence of resonant annihilation rate on incident positron energy and binding energy is removed, the resulting rates for hydrocarbons are shown to obey a universal scaling as a function of the number of vibrational degrees of freedom. Previously measured annihilation rates for alkanes using thermal positrons at 300 K are shown to be in quantitative agreement with measurements at higher energies. Results are presented for partially fluorinated hydrocarbons, providing evidence that the unusual suppression of resonant annihilation observed in these molecules occurs via a vibrational deexcitation process. The role of molecular temperature and inelastic escape channels in VFR-mediated positron annihilation in molecules is discussed. The implications of these results for theories of the annihilation process are also discussed.