A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge.

Accurate QED evaluations of the one- and two-photon interelectron interaction for the configurations ${1s}_{1/2}{2s}_{1/2}{}^1{S}_0$ and ${1s}_{1/2}{2s}_{1/2}{}^3{S}_1$ in He-like ions and for the configurations ${\mathrm{}\left(1s\right)\mathrm{}}^2{2s}_{1/2}$ and ${\mathrm{}\left(1s\right)\mathrm{}}^2{2p}_{1/2}$ in Li-like ions with nuclear charge numbers $30<~Z<~92$ are performed. The three-photon interaction is also partly taken into account. The QED theory of these corrections is provided by the adiabatic S matrix and by the line-profile approach. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations.

A variational wave function constructed with correlated hyperspherical harmonic functions is used to describe the Helium trimer. This system is known to have a deep bound state. In addition, different potential models predict the existence of a shallow excited state that has been identified as an Efimov state. Using the Rayleigh-Ritz variational principle, the energies and wave functions of both bound states have been obtained by solving a generalized eigenvalue problem. The introduction of a suitable correlation factor reduces considerably the dimension of the basis needed to accurately describe the structure of the system. The most recent helium-helium interactions have been investigated.

Ab initio potential-energy curves and rotational and radial coupling matrix elements of the ${}^2{\Sigma }^{+}$ and ${}^2\Pi$ molecular states involved in the collision of ${\mathrm{N}}^{4+}$ with He are determined by means of configuration interaction methods. In the 1–50-keV laboratory energy range, the total and the partial electron capture cross sections have been obtained using a semiclassical approach. Comparison with experiment shows the importance of the double capture channels.

The potential energy surfaces for ${\mathrm{H}}_2-\mathrm{N}$ and ${\mathrm{N}}_2-\mathrm{N}$ interactions are calculated by accurate ab initio methods and applied to determine transport data. The results confirm that an effective potential energy for accurately determining transport properties can be calculated using a single predetermined orientation. A simple method is developed to determine the dispersion coefficients of effective potential energies. Effective potential energies required for ${\mathrm{O}}_2-\mathrm{O}$ collisions are determined. The ${\mathrm{H}}_2-\mathrm{N},$ ${\mathrm{N}}_2-\mathrm{N},$ ${\mathrm{O}}_2-\mathrm{H},$ and ${\mathrm{O}}_2-\mathrm{O}$ collision integrals are calculated and tabulated for a broad range of temperatures. The theoretical values of the ${\mathrm{N}}_2-\mathrm{N}$ and ${\mathrm{O}}_2-\mathrm{O}$ diffusion coefficients compare well with measured data available at room temperature.

We show that a ferromagnetic Bose-Einstein condensate has not only line-like vortex excitations, but in general, also allows for pointlike topological excitations, i.e., skyrmions. We discuss the thermodynamic stability and the dynamic properties of these skyrmions for both spin-1/2 and ferromagnetic spin-1 Bose gases.

Photonic de Broglie wave interferometers display interesting, qualitatively nonclassical effects. We present theory and simulations demonstrating a photonic de Broglie interferometer based on nonlinear directional couplers. The Kerr nonlinearity in the couplers allows an N-photon pulse to tunnel between waveguides. Our calculations show the characteristic $\lambda /N$ fringes of this device even in the presence of photon number uncertainty, albeit with reduced contrast.

We present a method to remove, using only linear optics, exactly one photon from a field mode. This is achieved by putting the system in contact with an absorbing environment, which is under continuous monitoring. A feedback mechanism then decouples the system from the environment as soon as the first photon is absorbed. We propose a possible scheme to implement this process and provide the theoretical tools to describe it.

The dynamical response of a laser to frequency-shifted optical feedback is investigated both theoretically and experimentally. The ultrahigh sensitivity of a class-B laser (i.e., a laser with a cavity damping rate ${\gamma }_c$ higher than the population damping rate ${\gamma }_1)$ to external light injection is demonstrated by the optical detection of weak optical feedback. Compared to a conventional optical beating, the intensity modulation induced by the coherent interaction between the laser electric field and the frequency-shifted reinjected electric field can be several orders of magnitude higher. This method permits high sensitive interferometry and hence imaging. We call this laser detection technique laser optical feedback imaging (LOFI). When the optical frequency shift is resonant with the laser relaxation frequency, the intracavity amplification of the beating is maximum and the enhancement is given by the laser damping rate ratio ${\gamma }_c/{\gamma }_1.$ This amplification is of the order of ${10}^6$ for a microchip laser. We also show that without optical feedback the strong fluctuations of the laser output power are well described by the Langevin noise process. In a broad range around the laser relaxation frequency the laser quantum noise is also resonantly amplified and is then several orders of magnitude higher than the detector noise. In these conditions, the LOFI is a shot noise limited detection technique. Reflectivity as low as ${10}^{-13}$ is then easily detectable with a laser output power of a few milliwatts with a detection bandwidth of 1 kHz. Experimentally, for weak optical feedback the laser fluctuations are principally composed of the LOFI modulation signal at the shifted frequency and of the laser quantum noise amplified at the relaxation frequency. For strong optical feedback, nonlinear effects appear in the laser dynamics. In these conditions, harmonics and parametrics peaks appear in the power spectrum. The LOFI detection system is then saturated.

Resonance profiles of spectroscopically resolved radiative transitions from ${\mathrm{}\left(2pnd\right)\mathrm{}}^1{P}^o,$ ${\mathrm{}(sp,2n+)\mathrm{}}^1{P}^o,$ and $(sp,2n-{)}^1{P}^o$ doubly excited He states with $n=3,\dots ,7\mathrm{}$ were investigated. The ${\mathrm{}\left(2p3d\right)\mathrm{}}^1{P}^o–{\mathrm{}\left(1s3d\right)\mathrm{}}^1{D}^e–{\mathrm{}\left(1s2p\right)\mathrm{}}^1{P}^o–{1s}^2{}^1{S}^e$ cascade transitions were observed using photon induced fluorescence spectroscopy in the vacuum ultraviolet and the visible spectral range. The $\mathrm{}\left(2pnd\right)\mathrm{}$ levels populate predominantly ${\mathrm{}\left(1snd\right)\mathrm{}}^{1}D$ levels, while for the $(sp,2n+or-)$ levels, $n^{1}S$ levels are populated as well. The experiments demonstrate that further quantitave branching ratio measurements are needed in order to test matrix elements for radiative transitions from ${\mathrm{He}}^{**}.$

Measurement-induced decoherence and its consequent effect on the time evolution of the measured system is investigated via the Wigner representation W. Using a discrete-state computer model put forward by Wallace [D. Wallace, Phys. Rev. A 63, 022109 (2001)], we simulate a free particle moving in a periodic space, which is subjected to repeated projection-valued measurements of position. The measurements are made at rapid intervals, such as to induce a Zeno effect in the motion of the particle. We construct a discrete form of the Wigner distribution, which is used to represent the system ensemble at various times during its evolution. In addition, we calculate the entropy of the system ensemble and compare its time development with the Wigner distribution of the system state. We conclude that, in accordance with the findings of other similar investigations, the attenuation of negative W is a measure of the increasing decoherence in the system density operator, and is characteristic of the transition from the quantum to the classical descriptions of the system.

We propose a self-consistent quantum mechanical approach to study the dynamics of a two-level system subject to random time evolution. This randomness gives rise to competing effects between dissipative and nondissipative decoherence with a consequent slowdown of the atomic decay rate.

The Larmor precession of a neutral spinning particle in a magnetic field confined to the region of a one-dimensional rectangular barrier is investigated for both a nonrelativistic and a relativistic incoming particle. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of a general spin coherent state it is explicitly shown that the precession time is equal to the dwell time in both the nonrelativistic and relativistic cases. We also present a numerical estimation of the precession time showing an apparent superluminal tunneling.

We propose quantitative measures of wave properties and particle properties for multibeam interferometers. We show that these quantities are connected by a few fundamental inequalities which express wave-particle duality. Our analysis includes which-way detection schemes and quantum erasure. The inequalities derived here are a generalization of similar limits which were studied previously in the special case of two-beam interferometers. In addition, we propose alternative measures that express the available information more efficiently, and we show that these measures fulfill similar inequalities.

We investigate separability and entanglement of mixed states in $C^2\otimes C^2\otimes C^N$ three party quantum systems. We show that all states with positive partial transposes that have $\mathrm{rank}<~N$ are separable. For the three-qubit case $\mathrm{}(N=2\mathrm{})\mathrm{}$ we prove that all states ρ that have positive partial transposes and rank three are separable. We also provide constructive separability checks for the states ρ that have the sum of the rank of ρ and the ranks of partial transposes with respect to all subsystems smaller than $15N-1.$

The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some results. Most notably, we show that the dimension of the required catalyst is, in general, unbounded; there is no integer k such that it suffices to consider catalysts of dimension k or less in determining which states can be catalyzed into a given state. We also show that almost all bipartite entangled states are potentially useful as catalysts.

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters’s concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a “universal inverter,” which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of $D_1\times D_2$ bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT superoperator.

After summarizing a recent calculation of the maximum Renyi information loss (for fixed error and inconclusive rates) from a positive operator valued measure (POVM) quantum cryptographic receiver to a general unitary probe, I calculate the worst inconclusive rate for the legitimate receiver. Disturbed inconclusive rates are considered which are less, as well as greater, than the unperturbed inconclusive rate. I also demonstrate that for an optimized individual attack there is a minimum induced error rate which is fixed by the induced inconclusive rate.

We explore quantum search from the geometric viewpoint of a complex projective space $C\mathcal{P},$ a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a target state, an element of the computational basis, and such an initial state as overlaps equally, up to phases, with all the elements of the computational basis. Second, we calculate the entanglement through the algorithm for any number of qubits n as the minimum Fubini-Study distance to the submanifold formed by separable states in Segre embedding, and find that entanglement is used almost maximally for large n. The computational time seems to be optimized by the dynamics as the geodesic, running across entangled states away from the submanifold of separable states, rather than the amount of entanglement itself.

Nonrelativistically forbidden, single-photon transition rates between low-lying states of the helium atom are rigorously derived within quantum electrodynamics theory. Equivalence of velocity and length gauges, including relativistic corrections is explicitly demonstrated. Numerical calculations of matrix elements are performed with the use of high-precision variational wave functions and compared to former results.