In this paper, a photon-number-resolving decoy-state quantum key distribution (QKD) scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given, which seems inherent as long as weak coherent sources and high lossy channel are used. This implies that our scheme is optimal in long-distance QKD with weak coherent sources. We show that Eve’s coherent multiphoton pulse (CMP) attack is more efficient than a symmetric individual attack when the quantum bit error rate is small, so that the CMP attack should be considered to ensure the security of the final key. Our results show that a not-so-weak pulse can be used to transmit the key. Optimal intensity of the laser source is presented which provides a $23.9\mathrm{km}$ increase in the transmission distance.

In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an inverse eigenvalue problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.

Chiaverini et al. [Quantum Inf. Comput. 5, 419 (2005)] recently suggested a linear Paul trap geometry for ion-trap quantum computation that places all of the electrodes in a plane. Such planar ion traps are compatible with modern semiconductor fabrication techniques and can be scaled to make compact, many-zone traps. In this paper we present an experimental realization of planar ion traps using electrodes on a printed circuit board to trap linear chains of tens of charged particles of $0.44\mathrm{\mu }\mathrm{m}$ diameter in a vacuum of $15\mathrm{Pa}\left({10}^{-1}\mathrm{torr}\right)$. With these traps we address concerns about the low trap depth of planar ion traps and develop control electrode layouts for moving ions between trap zones without facing some of the technical difficulties involved in an atomic ion-trap experiment. Specifically, we use a trap with 36 zones (77 electrodes) arranged in a cross to demonstrate loading from a traditional four-rod linear Paul trap, linear ion movement, splitting and joining of ion chains, and movement of ions through intersections. We further propose an additional dc-biased electrode above the trap which increases the trap depth dramatically, and a planar ion-trap geometry that generates a two-dimensional lattice of point Paul traps.

Exact solutions for three identical bosons interacting via zero-range $s$-wave potentials are derived. The solutions are contour integrals over a product of hyperradial Bessel functions times angular functions weighted by a coefficient. The product function is a solution of the free-particle Schrödigner equation and the weight function is chosen to satisfy the zero-range boundary conditions. Scattering matrix elements for boson-dimer elastic scattering, breakup of a dimer into three particles and the time-reversed recombination process are derived. For vanishing total energy $E$, these quantities are given as closed-form functions of the two-body $s$-wave scattering length $a$ and a three-body renormalization constant $R_0$. The exact results obtained by this method are compared with those obtained using other methods. Differences in the functional dependence on $R_0$ of the order of 2% are noted. Comparison with the hidden-crossing theory finds similar agreement with the functional dependence upon $a$ and $R_0$.

We present a technique for measuring the radiative lifetimes of metastable states of negative ions that involves the use of a heavy-ion storage ring. The method has been applied to investigate the radiative decay of the $n{p}^3{}^{2}P_{1∕2}$ levels of ${\mathrm{Te}}^{-}(n=5)$ and ${\mathrm{Se}}^{-}(n=4)$ and the $3p^3{}^{2}D$ state of ${\mathrm{Si}}^{-}$ for which the $J=3∕2$ and $5∕2$ levels were unresolved. All of these states are metastable and decay primarily by emission of $E2$ and $M1$ radiation. Multi Configuration Dirac-Hartree-Fock calculations of rates for the transitions in ${\mathrm{Te}}^{-}$ and ${\mathrm{Se}}^{-}$ yielded lifetimes of $0.45\mathrm{s}$ and $4.7\mathrm{s}$, respectively. The measured values agree well with these predicted values. In the case of the ${}^{2}D$ state of ${\mathrm{Si}}^{-}$, however, our measurement was only able to set a lower limit on the lifetime. The upper limit of the lifetime that can be measured with our apparatus is set by how long the ions can be stored in the ring, a limit determined by the rate of collisional detachment. Our lower limit of $1\min$ for the lifetime of the ${}^{2}D$ state is consistent with both the calculated lifetimes of $162\mathrm{s}$ for the ${}^{2}D_{3∕2}$ level and $27.3\mathrm{h}$ for the ${}^{2}D_{5∕2}$ level reported by O’Malley and Beck and $14.5\mathrm{h}$ and $12.5\mathrm{h}$, respectively, from our Breit-Pauli calculations.

Starting from a set of coupled Boltzmann equations, we investigate the thermalization of a two-species cold atomic gas confined either in a box or in an isotropic harmonic trap. We show that the thermalization times, by contrast to the collision rate, depend on the interferences between scattering partial waves. The dynamics of thermalization in a harmonic trap is also strongly dependent upon the ratio between the collision rate and the trap frequencies.

Electron emission from metal surfaces produced by short laser pulses is studied within the framework of the distorted-wave formulation. The proposed approach, named surface-Volkov (SV) approximation, makes use of the band-structure based (BSB) model and the Volkov phase to describe the interaction of the emitted electron with the surface and the external electric field, respectively. The BSB model provides a realistic representation of the surface, based on a model potential that includes the main features of the surface band structure. The SV method is applied to evaluate the photoelectron emission from the valence band of Al(111). Angular and energy distributions are investigated for different parameters of the laser pulse, keeping in all cases the carrier frequency larger than the plasmon one.

Inelastic vibronic ionization (IVI) in the presence of an intense laser field refers to the process of ionization of a target molecule accompanied by vibrational excitation of the residual molecular ion. The recently proposed intense-field many-body $S$-matrix theory of IVI is presented and applied to investigate the distributions of the vibrational states of the residual ${\mathrm{H}}_2^{+}$ ion from ionization of ${\mathrm{H}}_2$ molecule, and the results are compared with the experimental data. The characteristic features of the calculated distributions are found to agree well with those observed. The shift of the IVI distributions toward the lower vibrational states compared to the Frank-Condon distributions, the positions of the maxima of the distributions, as well as the reversal of the maximum from a lower vibrational state to a higher vibrational state (peak-reversal) are analyzed. The results of the “adiabatic nuclei” theory and the “frozen nuclei” approximation are compared to assess the latter. Influences of the choice of the vibrational wave functions on the calculated distributions, the dependence of the distributions on the alignments of the molecular axis with respect to the linear polarization direction of the laser, and the effect of circular polarization of the laser on the IVI distribution are discussed. Possible origins of the remaining discrepancy in the individual heights of the calculated vs. measured yields are pointed out. Finally, an isotopic shift of the IVI distributions toward the higher vibrational states, for the heavier isotopes, is predicted and the corresponding distributions for the two isotopes $\mathrm{HD}$ and ${\mathrm{D}}_2$ are given.

Recent experiments on lasers with large Fresnel numbers have demonstrated a close correspondence between the transverse degrees of freedom (transverse modes) and the two-dimensional harmonic oscillator. Mode patterns that correspond to classical trajectories have been observed. These experiments suggest that such systems may serve as convenient platforms for studying quantum-classical correspondence. But why the paraxial wave equation for the laser leads to two-dimensional harmonic oscillation for the transverse degrees of freedom is yet to be clarified. We use two methods to show that such a correspondence is not a mathematical coincidence: the focusing mirror that stabilizes the laser gives rise to the transverse oscillation, and the reduced equation that governs the transverse degrees of freedom is the Schrödinger equation for the harmonic oscillator. For the fundamental Gaussian mode, the theory remains valid in the weakly nonlinear limit.

This paper deals with the concept of adiabaticity for fully quantum mechanical cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time-dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time-dependent two-level systems.

We report experimental evidence that light storage, understood as the controlled release of a light pulse by an atomic sample dependent on the past presence of a writing pulse, is not restricted to small-group-velocity media but can also occur in a negative-group-velocity medium. We present a numerical modeling in close agreement with our observations and a simple physical picture applicable to light storage experiments in both “slow” and “fast” light media.

We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number $N$ of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where these states are known to lie on the equatorial plane. For the former case we obtain that the optimal measurement does not depend on the prior probability distribution provided it is isotropic. Although the equatorial-plane case does not have this property for arbitrary $N$, we give a prior-independent scheme which becomes optimal in the asymptotic limit of large $N$. We compute the maximum mean fidelity in this asymptotic regime for the two cases. We show that within the pointwise estimation approach these limits can be obtained in a rather easy and rapid way. This derivation is based on heuristic arguments that are made rigorous by using van Trees inequalities. The interrelation between the estimation of the purity and the direction of the state is also discussed. In the general case we show that they correspond to independent estimations whereas for the equatorial-plane states this is only true asymptotically.

We investigate the security of continuous-variable quantum key distribution using coherent states and reverse reconciliation against Gaussian individual attacks based on an optimal Gaussian $1\to 2$ cloning machine. We provide an implementation of the optimal Gaussian individual attack. We also find a Bell-measurement attack which works without delayed choice of measurements and has better performance than the cloning attack.

We study entanglement dynamics of a couple of two-level atoms resonantly interacting with a cavity mode and embedded in a dispersive atomic environment. We show that in the absence of the environment the entanglement reaches its maximum value when only one excitation is involved. Then, we find that the atomic environment modifies that entanglement dynamics and induces a typical collapse-revival structure even for an initial one photon Fock state of the field.

We consider the cloning of sequences of qubits prepared in the states used in the BB84 or six-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is only valid provided that the sequences are much shorter than the total key. It is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size cloning attacks.

We report on cold atom photoassociation of ${}^{87}\mathrm{Rb}$ giving spectroscopy data of the $(5s_{1∕2}+5p_{1∕2})0_g^{-}$ long-range molecular states in the asymptotic range of [$-12.5{\mathrm{cm}}^{-1}$, $-1.5{\mathrm{cm}}^{-1}$] below the dissociation limit. Using a Lu-Fano approach to analyze the data, we show that an improved LeRoy-Bernstein model has to be applied. This approach lets us determine the phase shift of the wave function at the dissociation limit of the $0_g^{-}$ series.

The ${}^{1,3}P^o$ resonance states of positronium negative ions embedded in dense plasma environments are determined by calculating the density of resonance states using the stabilization method. A screened Coulomb potential obtained from the Debye model is used to represent the interaction between the charge particles, together with employing highly correlated wave functions to represent the correlation effect between them. We have calculated one ${}^{1}P^o$ and two ${}^{3}P^o$ resonances associated with and below the $n=2$ threshold of the positronium atom. The resonance energies and widths for various Debye lengths ranging from infinity to a small value are reported.

We use the configuration-interaction method and many-body perturbation theory to perform accurate calculations of energy levels, transition amplitudes, and lifetimes of low-lying states of barium and radium. Calculations for radium are needed for the planning of measurements of parity- and time-invariance-violating effects which are strongly enhanced in this atom. Calculations for barium are used to control the accuracy of the calculations.

We consider the feasibility of observing a trap-induced resonance [Stock et al., Phys. Rev. Lett. 91, 183201 (2003)] for the case of two ${}^{133}\mathrm{Cs}$ atoms, trapped in separated wells of a polarization-gradient optical lattice, and interacting through a multichannel scattering process. Due to the anomalously large scattering length of cesium dimers, a strong coupling can occur between vibrational states of the trap and a weakly bound molecular state that is made resonant by the ac Stark shift of the lattice. We calculate the energy spectrum of the two-atom system as a function of the distance between two potential wells by connecting the solutions of the Schrödinger equation for the short-range molecular potential to that of the long-range trap in a self-consistent manner. The short-range potential is treated through a multichannel pseudopotential, parametrized by the $K$ matrix, calculated numerically for atoms in free space in a close-coupling approximation. This captures both the bound molecular spectrum as well as the energy-dependent scattering for all partial waves. We establish realistic operating conditions under which the trap-induced resonance could be observed and show that this strong and coherent interaction could be used as a basis for high-fidelity two-qubit quantum logic operations.

An accurate ab initio potential energy surface has been employed for the treatment of the full quantum dynamics for isotopic exchange reaction ${}^4\mathrm{He}{}^3\mathrm{He}_2^{+}+{}^4\mathrm{He}$. State-to-state reactive probabilities have been obtained using a time-independent approach at ultralow collision energies. More than one total angular momentum has been calculated in order to provide a converged rate constant for the title reaction within the ultralow temperature regime. The reaction is found to become faster than the Langevin value when $T\to 0$, thus providing connection with experiments with sympathetically cooled molecular ions or superfluid helium nanodroplets.