It is shown that if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for the entanglement of formation and the distillable entanglement, and their validity naturally extends to other bipartite entanglement measures in between. Robustness of derived criteria is analyzed and their tightness compared. Finally, as a by-product, we prove a bound quantifying how large the gap between the entanglement of formation and distillable entanglement can be for any given finite dimensional bipartite system, thus providing a sufficient condition for distillability in term of the entanglement of formation.

A heavy focus for optical quantum computing is the introduction of error correction, and the minimization of resource requirements. We detail a complete encoding and manipulation scheme designed for circuit-model linear optics quantum computing, incorporating scalable operations and loss-tolerant architecture. We also calculate loss thresholds for the gate systems described, with an efficiency of $83\%$ required for the single-qubit operations, and $90\%$ for the two-qubit controlled-NOT gate.

We present total charge transfer for ${\text{H}}^{+}+\text{Li}$ collisions and total and state-selected cross sections for charge transfer and excitation in ${\text{Li}}^{+}+\text{H}$ collisions in the energy range 25–2500 eV/amu. The calculation employs quantal and semiclassical treatments and a molecular expansion in terms of both ab initio and model potential orbitals. Isotopic dependence of ${\text{Li}}^{+}+\text{H}$ charge-transfer cross section is studied.

We study the Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical expressions for the transition probability. Numerical explorations are made for a wide range of parameters of the general case. Possible applications of our theory to Bose-Einstein condensates (BECs) and solid-state physics are discussed.

We show that one of the key characteristics of interacting one-dimensional electronic quantum systems, the separation of spin and charge, can be observed in a two-component system of bosonic ultracold atoms even close to a competing phase separation regime. To this purpose we determine the real-time evolution of a single particle excitation and the single particle spectral function using density-matrix renormalization group techniques. Due to efficient bosonic cooling and good tunability this setup exhibits very good conditions for observing this strong correlation effect. In anticipation of experimental realizations we calculate the velocities for spin and charge perturbations for a wide range of parameters.

When a stationary reflecting wall acting as a perfect mirror for an atomic beam with well-defined incident velocity is suddenly removed, the density profile develops during the time evolution an oscillatory pattern known as diffraction in time. The interference fringes are suppressed or their visibility is diminished by several effects such as averaging over a distribution of incident velocities, apodization of the aperture function, atom-atom interactions, imperfect reflection, or environmental noise. However, when the mirror moves with finite velocity along the direction of propagation of the beam, the visibility of the fringes is enhanced. For mirror velocities below beam velocity, as used for slowing down the beam, the matter wave splits into three regions separated by space-time points with classical analogs. For mirror velocities above beam velocity a visibility enhancement occurs without a classical counterpart. When the velocity of the beam approaches that of the mirror the density oscillations rise by a factor 1.8 over the stationary value.

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in detail. The obtained formulas are checked on the example of cut disks. A good agreement is found with direct numerical simulations and far-field experiments.

Bound muons (also pions, kaons, etc.) increase the fission barrier and produce some stabilizing effects for highly charged nuclei. If the binding energy of the muon exceeds $m{c}^2$, it becomes stable. The $1s$ state of a muon inside an exotic nucleus with atomic number $A=5Z∕2$ and such large charge $Z$ that the $1s$ energy $E$ is in the range $0\le E<-m{c}^2$ is considered.

We report on the observation of two Feshbach resonances in collisions between ultracold ${}^6\mathrm{Li}$ and ${}^{87}\mathrm{Rb}$ atoms in their respective hyperfine ground states $\mid F,m_F⟩=\mid 1∕2,1∕2⟩$ and ∣1,1⟩. The resonances show up as trap losses for the ${}^6\mathrm{Li}$ cloud induced by inelastic Li-Rb-Rb three-body collisions. The magnetic field values where they occur represent important benchmarks for an accurate determination of the interspecies interaction potentials. A broad Feshbach resonance located at $1066.92\mathrm{G}$ opens interesting prospects for the creation of ultracold heteronuclear molecules. We furthermore observe a strong enhancement of the narrow $p$-wave Feshbach resonance in collisions of ${}^6\mathrm{Li}$ atoms at $158.55\mathrm{G}$ in the presence of a dense ${}^{87}\mathrm{Rb}$ cloud. The effect of the ${}^{87}\mathrm{Rb}$ cloud is to introduce Li-Li-Rb three-body collisions occurring at a higher rate than Li-Li-Li collisions.

We present a number of rapid-purification feedback protocols for optical homodyne detection of a single optical qubit. We derive first a protocol that speeds up the rate of increase of the average purity of the system, and find that as in the equivalent protocol for a nondissipative measurement, this generates a deterministic evolution for the purity in the limit of strong feedback. We also consider two analogs of the Wiseman-Ralph rapid-purification protocol in this setting, and show that as in that protocol they speed up the average time taken to reach a fixed level of purity. We also examine how the performance of these algorithms changes with detection efficiency, being an important practical consideration.

In order to eliminate disturbing effects of decoherence, encoding of quantum information in decoherence-free subspaces has been suggested. We analyze the benefits of this concept for a quantum register that is realized in a spin chain in contact with a common bosonic bath. Within a dissipationless model, we provide explicit analytical results for the average fidelity of plain and encoded quantum registers. For the investigation of dissipative spin-boson couplings, we employ a master equation of Bloch-Redfield type.

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized $\pi /2$ pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.

The double-bound analog of the double-continuum three-body Coulomb (C3) wave function, recently introduced by the authors, allows us to propose two different basis sets of correlated functions which can be used for describing double-bound states. The components of the two basis diagonalize the Coulomb interactions but differ in the definition of the distortion factor which depends only on the interelectronic coordinate. In the first set, this factor includes a nonlinear parameter, while the second set contains parameter-free functions. Through an angular correlated configuration interaction method it is possible to generate highly correlated wave functions for $S$ bound states of heliumlike systems. By construction, these states form an orthogonal set, satisfy all two-body cusp conditions, and retain the C3 double-continuum character. Even when a limited number of configurations is included, rather good energy values for the ground and excited states are obtained. A systematic improvement by inclusion of more configurations can be easily achieved, in particular with the computationally efficient, parameter-free basis.

We have employed conventional ab initio and density-functional-theory (DFT) methods to study the structure, stability and electric polarizability of small gallium arsenide clusters ${\mathrm{Ga}}_n{\mathrm{As}}_n$. We relied on purpose-oriented, carefully optimized basis sets of Gaussian-type functions. We have calculated both the mean dipole polarizability $\left(\overline{\alpha }\right)$ and the anisotropy $\left(\mathrm{\Delta }\alpha \right)$. Our results show that the differential-per-atom polarizability of the most stable isomers decreases rapidly with cluster size. Compared to the ab initio results, the widely used Becke’s three-parameter exchange DFT functional with the Lee, Yang, and Parr correlation functional and Becke’s three-parameter exchange DFT functional with Perdew and Wang’s 1991 gradient-corrected correlation functional density-functional-theory methods follow clearly the trend of the differential-per-atom polarizability ${\overline{\alpha }}_{\mathrm{diff}}∕\mathrm{atom}$ for the most stable isomers and predict values closer to the self-consistent field method but distinctly lower than second-order Møller-Plesset perturbation theory. All methods predict a positive value for the dimer, ${\overline{\alpha }}_{\mathrm{diff}}∕\mathrm{atom}$ $\left({\mathrm{Ga}}_2{\mathrm{As}}_2\right)>0$.

The formation of near-threshold structures in the angle-resolved photoelectron spectrum, the cusp in the transverse electron momentum distribution, and the forward-backward asymmetry is influenced by the residual Coulomb potential of the remaining atomic core acting on the electron detached by strong short-laser pulses. We show that an improvement beyond the strong-field approximation—the Coulomb-Volkov distorted wave approximation—is capable to reproduce these features found in the exact solution of the time-dependent Schrödinger equation in the multiphoton regime and the transition from the multiphoton to the tunneling regime.

We demonstrate an ultrafast transient, ring-shaped population grating induced by an ultrashort hollow Gaussian laser bullet by solving the three-dimensional full-wave Maxwell-Bloch equations. Through adjusting the beam waist and the area of the pulse, we can control the number of lines and the period of the grating. Based on this coherent control scheme, a door to produce gratings with complex transverse structure is opened.

A nonlinear planar waveguide pumped by a beam orthogonal to its surface may serve as a versatile source of photon pairs. By changing the pump-pulse duration, pump-beam transverse width, and angular decomposition of the pump-beam frequency characteristics of a photon pair, including the spectral widths of signal and idler fields, the pair time duration as well as the degree of entanglement of the two fields, can be changed significantly. Using the measured spectral widths of the down-converted fields and the width of a coincidence-count dip in a Hong-Ou-Mandel interferometer, the entropy of entanglement can be determined.

A theoretical method for the calculation of the second-order intensity correlation function for the light transmitted from a weakly driven optical cavity containing an inhomogeneous medium is presented. This method is based on the expectation-value approach [H. Goto and K. Ichimura, Phys. Rev. A 70, 023815 (2004)]. This method allows one to calculate the second-order intensity correlation function in the case where there are many atoms whose transition frequencies and coupling rates have various values. We discuss the effects of the inhomogeneities of the atomic transition frequency and the coupling rate.

Motivated by recent experiments, we address the behavior and evolution of radio-frequency (RF) spectra as temperature and polarization are varied in population-imbalanced Fermi gases from above to below $T_c$. We discuss a series of scenarios for the experimentally observed zero-temperature pseudogap phase and show how present and future RF experiments may help in its elucidation. We conclude that the experiments of Zwierlein and co-workers at the lowest $T$ may well reflect ground-state properties, but take issue with their claim that the pairing gap survives up to temperatures of the order of the degeneracy temperature $T_F$ at unitarity.

We generalize the concept of nonlinear periodic structures to systems that show arbitrary spacetime variations of the refractive index. Nonlinear pulse propagation through these spatiotemporal photonic crystals can be described, for shallow nonstationary gratings, by coupled mode equations which are a generalization of the traditional equations used for stationary photonic crystals. Additional gap soliton solutions are found analytically. They represent a generalization of the gap solitons in static photonic crystals and resonance solitons found in dynamic gratings.