A calculation of the ground-state energy and average distance between particles in the nonsymmetric muonic ${}^3\mathrm{He}$ atom is given. We have used a wave function with one free parameter, which satisfies boundary conditions such as the behavior of the wave function when two particles are close to each other or far away. In the proposed wave function, the electron-muon correlation function is also considered. It has a correct behavior for $r_{12}$ tending to zero and infinity. The calculated values for the energy and expectation values of $r^{2n}$ are compared with the multibox variational approach and the correlation function hyperspherical harmonic method. In addition, to show the importance and accuracy of approach used, the method is applied to evaluate the ground-state energy and average distance between the particles of nonsymmetric muonic ${}^4\mathrm{He}$ atom. Our obtained results are very close to the values calculated by the mentioned methods and giving strong indications that the proposed wave functions, in addition to being very simple, provide relatively accurate values for the energy and expectation values of $r^{2n}$, emphasizing the importance of the local properties of the wave function.

Magnetic fields from statistical fluctuations in currents in conducting materials broaden atomic linewidths by the Zeeman effect. The constraints imposed by this broadening on the design of experiments that measure the electric dipole moment of the electron are analyzed. Contrary to the predictions of Lamoreaux [S. K. Lamoreaux, Phys. Rev. A 60, 1717 (1999)], the standard material for high-permeability magnetic shields proves to be as significant a source of broadening as is an ordinary metal. A scheme that would replace this standard material with ferrite is proposed.

The influence of relativistic, relaxation, and correlation effects on the low-lying energy levels of the $3d^{10},3d^{9}4s$, and $3d^{9}4p$ configurations of Cu II have been investigated. Large-scale multiconfiguration Dirac-Fock wave functions were applied to calculate the excitation energies and the electric-dipole-allowed transition probabilities and to allow for a systematic improvement of the computations. From these calculations, the theoretical lifetimes of the $3d^{9}4p$ levels are derived and compared with previous experiments and computations. Our results show that we provide not only an improved data basis for the low-lying levels of Cu II but also a useful computational model for studying other ions along the nickel isoelectronic sequence.

We present results of a joint theoretical and experimental investigation of electron scattering from the $4s^2{}^{1}S$ ground state of zinc. The $4s4p{}^{1}P^o$ and $4s5p{}^{1}P^o$ differential cross sections were measured at scattering angles between 10° and 150° and electron-energies of 15, 20, 25, 40, and 60 eV. Corresponding convergent close-coupling calculations have been performed and are compared with experiment.

An alternative design for a planar Penning ion trap is presented. Although the analytical trapping potential is not exactly quadratic, approximate values for the characteristic frequencies around the equilibrium point can be found. An array of traps can be formed simply using long straight wires, and the open geometry of this design means that the structure can be miniaturized using well-known techniques. Consequently, these traps should be considered as excellent candidates for applications in quantum computation.

We derive the low-energy effective action for three-dimensional superfluid Fermi systems in the strong-coupling limit, where superfluidity originates from Bose-Einstein condensation of composite bosons. Taking into account density and pairing fluctuations on the same footing, we show that the effective action involves only the fermion density ${\rho }_{\mathbf{r}}$ and its conjugate variable, the phase ${\theta }_{\mathbf{r}}$ of the pairing order parameter ${\Delta }_{\mathbf{r}}$. We recover the standard action of a Bose superfluid of density ${\rho }_{\mathbf{r}}∕2$, where the bosons have a mass $m_B=2m$ and interact via a repulsive contact potential with amplitude $g_B=4\pi a_B∕m_B,a_B=2a$ ($a$ the $s$-wave scattering length associated to the fermion-fermion interaction in vacuum). For lattice models, the derivation of the effective action is based on the mapping of the attractive Hubbard model onto the Heisenberg model in a uniform magnetic field, and a coherent state path integral representation of the partition function. The effective description of the Fermi superfluid in the strong-coupling limit is a Bose-Hubbard model with an intersite hopping amplitude $t_B=J∕2$ and an on-site repulsive interaction $U_B=2Jz$, where $J=4t^2∕U$ ($t$ and $-U$ are the intersite hopping amplitude and the on-site attraction in the (fermionic) Hubbard model, $z$ the number of nearest-neighbor sites).

We investigate the phase fluctuations of a Bose-Einstein condensate in one- (1D) and three-dimensional (3D) elongated harmonic traps with the help of the numerical simulation using classical field approximation. By calculating the eigenvalues of the one-dimensional single-particle density matrix we show that the phase fluctuations of a Bose-Einstein Condensate in a 1D system are due to the thermal low-energy excitations. We find that the phase fluctuations depend on the temperature as has been predicted [Phys. Rev. Lett. 85, 3745 (2000), Phys. Rev. Lett. 87, 050404 (2001)]. Finally we show that the phase coherence length of a condensate in a harmonic trap depends on the aspect ratio of anisotropy (geometry) of the trap. We determine the border between the 3D and quasi-one-dimensional systems by calculating the phase coherence length of the condensate.

We delineate critical issues for “controlling light with light” in photonic crystal (PC) waveguides coupled to Kerr-nonlinear microresonators. These arise from (a) fundamental trade-off between switching speed and switching intensity threshold inherent in high-quality $Q$-factor cavities and (b) the dynamical nonlinear oscillation of such cavities in response to incident light pulses. Using finite-difference time-domain simulations of electromagnetic pulse propagation, we consider both (i) a nonlinear Fabry-Perot microresonator (embedded within a PC waveguide) exhibiting a narrow transmission resonance and (ii) a nonlinear point defect (side-coupled to a PC waveguide) exhibiting a narrow reflection spectrum. We describe self-induced switching from transmission to reflection induced by pulse intensity tuning as well as control of pulse transmission induced by the secondary, continuous (cw) laser field propagating through the same PC waveguide. For the Fabry-Perot microresonator, a well-defined self-switching threshold is obtained. However, this is accompanied by considerable temporal and spectral distortion of the pulse caused by the oscillatory nonlinear response of the microresonator. When the quality factor of the microresonator is increased, the switching intensity threshold can be lowered but the pulse transit (switching) time and the pulse distortion are increased. For the side-coupled microresonator, a gradual (not sharp) self-switching behavior as a function of incident intensity is obtained. For both the Fabry-Perot and side-coupled nonlinear microresonators, control of pulse transmission can be achieved by means of a secondary cw laser field. The cw power required for switching with realistic Kerr nonlinearities is in excess of $1\mathrm{W}∕\mu {\mathrm{m}}^2$ and may cause optical damage to the semiconducting PC backbone. Both instantaneous and noninstantaneous Kerr-response models are considered. Our results underscore the limitations and trade-offs inherent in the possible control of light with light using Kerr-nonlinear microresonators.

Quite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed [A. Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)]. In this paper we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative superoperators.

The $(e^{-},e^{+})$-pair annihilation in the bipositronium ${\mathrm{Ps}}_2$ (or $e^{-}{e}^{+}{e}^{-}{e}^{+}$) is considered. In particular, the two-, three-, one-, and zero-photon annihilation rates are determined to high accuracy. The corresponding analytical expressions for these annihilation rates are also presented. By using our most recent and accurate variational wave functions produced for the ground $S(L=0)$ state of the bipositronium ${\mathrm{Ps}}_2$ $(E=-0.5160037754\mathrm{a.u.})$ we have found for the two-photon annihilation rate ${\Gamma }_{2\gamma }\approx 4.66424\times {10}^9{\mathrm{s}}^{-1}$, while ${\Gamma }_{3\gamma }\left({\mathrm{Ps}}_2\right)\approx 1.2022\times {10}^6{\mathrm{s}}^{-1}$, ${\Gamma }_{1\gamma }\approx 1.954\times {10}^{-1}{\mathrm{s}}^{-1}$, and ${\Gamma }_{0\gamma }\approx 2.34\times {10}^{-9}{\mathrm{s}}^{-1}$. Also, a large number of bound state properties have been determined for this system.

A recent experimental proposal [S.E. Ahnert and M.C. Payne, Phys. Rev. A 70, 042102 (2004)] outlines a method to measure the weak value predictions of Aharonov in Hardy’s paradox. This proposal contains flaws in the state preparation method and the procedure for carrying out the requisite weak measurements. We identify previously published solutions to some of the flaws.

The comment by Lundeen et al. contains two criticisms of our proposal. While we agree that the state-preparation procedure could be replaced by a simpler setup as proposed by the authors of the comment, we do not agree with the authors on their second, and more important point regarding two-particle weak measurements. We believe this to be the result of a misunderstanding of our original paper [S. E. Ahnert and M. C. Payne, Phys. Rev. A 70, 042102 (2004)].

In the paper [], a quantum direct communication protocol is proposed which is claimed to be unconditionally secure even for the case of a noisy channel. We show that this is not the case by giving an undetectable attack scheme.

We reply to the preceding comment which focused on whether there exists a quantum privacy amplification technique for purifying the unknown single-photon states transmitted. In this Reply, we will show that quantum privacy amplification is principally possible, and a specific scheme for direct communication protocol based on single photons has been constructed and will be published elsewhere. Then the secure direct quantum communication is secure against the attack strategy in the preceeding comment by using quantum privacy amplification directly.

Since there are many examples in which no decoherence-free subsystems exist (among them all cases where the error generators act irreducibly on the system Hilbert space), it is of interest to search for novel mechanisms which suppress decoherence in these more general cases. Drawing on recent work (quant-ph/0502153) we present three results which indicate decoherence suppression without the need for noiseless subsystems. There is a certain trade-off; our results do not necessarily apply to an arbitrary initial density matrix or for completely generic noise parameters. On the other hand, our computational methods are novel and the result—suppression of decoherence in the error-algebra approach without noiseless subsystems—is an interesting new direction.

We describe an implementation of quantum error correction that operates continuously in time and requires no active interventions such as measurements or gates. The mechanism for carrying away the entropy introduced by errors is a cooling procedure. We evaluate the effectiveness of the scheme by simulation, and remark on its connections to some recently proposed error prevention procedures.

The laser induced selective preparation of electronically excited molecules is investigated. Therefore, the control fields are determined from the dynamics of the system. By construction, the obtained pulses carry the signature of the electronic and nuclear motion. It is shown that an effective population transfer to different target states is possible. Time-dependent photoelectron spectra are calculated to illustrate that the achieved control yields can be measured directly.

The quantum-jump approach, where pairs of state vectors follow the stochastic Schroedinger equation (SSE) in order to treat the exact quantum dynamics of two interacting systems, is described. In this work the nonuniqueness of such stochastic Schroedinger equations is investigated to propose strategies to optimize the stochastic paths and reduce statistical fluctuations. In the proposed method, called the “adaptative noise method,” a specific SSE is obtained for which the noise depends explicitly on both the initial state and on the properties of the interaction Hamiltonian. It is also shown that this method can be further improved by introduction of a mean-field dynamics. The different optimization procedures are illustrated quantitatively in the case of interacting spins. A significant reduction of the statistical fluctuations is obtained. Consequently a much smaller number of trajectories is needed to accurately reproduce the exact dynamics as compared to the SSE without optimization.

Up to now, transverse quantum effects (usually labeled as “quantum imaging” effects) which are generated by nonlinear devices inserted in resonant optical cavities have been calculated using the “thin-crystal approximation,” i.e., taking into account the effect of diffraction only inside the empty part of the cavity, and neglecting its effect in the nonlinear propagation inside the nonlinear crystal. We introduce in the present paper a theoretical method which is not restricted by this approximation. It allows us in particular to treat configurations closer to the actual experimental ones, where the crystal length is comparable to the Rayleigh length of the cavity mode. We use this method in the case of the confocal optical parametric oscillator, where the thin-crystal approximation predicts perfect squeezing on any area of the transverse plane, whatever its size and shape. We find that there exists in this case a “coherence length” which gives the minimum size of a detector on which perfect squeezing can be observed, and which gives therefore a limit to the improvement of optical resolution that can be obtained using such devices.

A recent paper [] presented a bound for the three-qubit Mermin inequality such that the violation of this bound indicates genuine three-qubit entanglement. We show that this bound can be improved for a specific choice of observables. In particular, if spin observables corresponding to orthogonal directions are measured at the qubits (e.g., $X$ and $Y$ spin coordinates), then the bound is the same as the bound for states with a local hidden variable model. As a consequence, it can straightforwardly be shown that in the experiment described by ], genuine three-qubit entanglement was detected.