The transformation that an attenuator makes on the state of an optical field is the time reverse of that of an amplifier. Thus predicting the output state for an amplifier is equivalent to retrodicting the input state of an attenuator. We explore the consequences of this equivalence for simple optical quantum communication channels. One counterintuitive consequence is that the mean number of photons sent into an amplifier as retrodicted from a measurement of the number of output photons does not include the contribution of the amplifier noise.

In Van den Nest et al. [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as local complementation. It was shown that two graph states are equivalent under the local Clifford group if and only if there exists a sequence of local complementations which relates their associated graphs. In this Brief Report we report the existence of a polynomial time algorithm, published in A. Bouchet [Combinatorica 11, 315 (1991)], which decides whether two given graphs are related by a sequence of local complementations. Hence an efficient algorithm to detect local Clifford equivalence of graph states is obtained.

$P$-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $\mathrm{Sp}(2,R)\otimes \mathrm{Sp}(2,R)$ locally invariant. Although this special class of states can be reached by a convenient $\mathrm{Sp}(2,R)\otimes \mathrm{Sp}(2,R)$ transformation over an arbitrary covariance matrix, it represents a loss of generality, avoiding inference of many general aspects of separability of bipartite Gaussian states.

We study the pairwise entanglement present in a quantum computer that simulates a dynamically localized system. We show that the concurrence is exponentially sensitive to changes in the Hamiltonian of the simulated system. Moreover, concurrence is exponentially sensitive to the “logic” position of the qubits chosen. These sensitivities could be experimentally checked efficiently by means of quantum simulations with less than 10 qubits. We also show that the feasibility of efficient quantum simulations is deeply connected to the dynamical regime of the simulated system.

The electron-impact single-ionization cross sections on the helium isoelectronic targets $\mathrm{He}$, ${\mathrm{Li}}^{+}$, ${\mathrm{B}}^{3+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, ${\mathrm{O}}^{5+}$, ${\mathrm{Ne}}^{8+}$, ${\mathrm{Na}}^{9+}$, ${\mathrm{Fe}}^{24+}$, ${\mathrm{Ag}}^{45+}$, and ${\mathrm{U}}^{90+}$, are calculated using the recent simplified version of the binary-encounter dipole (siBED) model as applied by Huo [Phys. Rev. A 64, 042719 (2001)] to various molecular targets. The simple siBED model is good for the helium atom, but it is inadequate for ionic targets. Our proposed modifications: (i) ionic correction of the siBED model (QIBED) and (ii) relativistic corrections of the siBED model (RQIBED) are examined on a wider group of species and compared with other available experimental and theoretical results. The predictions of QIBED in the nonrelativistic energy domain and of RQIBED for all energies, with the same parameter values of siBED, produce excellent agreement with the experimental data and the results close to those of other theories for all the two-electron systems, neutral or ions on the same footing.

Dissociation of iodine molecules by two phase-locked 110 femtosecond laser pulses creates a wave packet in the repulsive part of the $B$ state. The time-dependent density functions for the internuclear position, $\mid \Psi (R,t){\mid }^2$, and for the internuclear velocity, $\mid \Psi (v_R,t){\mid }^2$, of the wave packet are measured by ionization with a delayed, intense $20\mathrm{fs}$ nonresonant laser pulse. The pronounced interference pattern, observed in both $\mid \Psi \left(R\right){\mid }^2$ and $\mid \Psi \left(v_R\right){\mid }^2$, is controlled by the time separation of the two pump pulses. The experimentally determined internuclear position and velocity distributions are in very good agreement with calculated results for $\mid \Psi \left(R\right){\mid }^2$ and $\mid \Psi \left(v_R\right){\mid }^2$ obtained by numerical wave packet propagation.

Lasing from an erbium-doped high-$Q$ silica toroidal microcavity coupled to a tapered optical fiber is demonstrated and analyzed. Average erbium ion concentrations were in the range $0.009\text{–}0.09\mathrm{at.}\%$, and a threshold power as low as $4.5\mu \mathrm{W}$ and an output lasing power as high as $39.4\mu \mathrm{W}$ are obtained from toroidal cavities with major diameters in the range $25\text{–}80\mu \mathrm{m}$. Controlling lasing wavelength in a discrete way at each whispering-gallery mode was possible by changing the cavity loading, i.e., the distance between the tapered optical fiber and the microcavity. Analytic formulas predicting threshold power and differential slope efficiency are derived and their dependence on cavity loading, erbium ion concentration, and $Q$ factor is analyzed. It is shown that the experimental results are in good agreement with the derived formulas.

We propose a scheme for realizing the Deutsch-Jozsa algorithm in cavity QED. The scheme is based on the resonant interaction of atoms with a cavity mode. The required experimental techniques are within the scope of what can be obtained in the microwave cavity QED setup. The experimental implementation of the scheme would be an important step toward more complex quantum computation in cavity QED.

We have measured the parallel velocity distribution of a lithium supersonic beam produced by seeding lithium in argon. The parallel temperature for lithium is considerably lower than the calculated parallel temperature of the argon carrier gas. We have extended the theory of supersonic cooling to calculate the parallel temperature of the seeded gas, in the limit of high dilution. The theoretical result thus obtained is in good agreement with our observations.

The fully relativistic theory of the $g$ factor of hydrogenlike ions with nonzero nuclear spin is considered. The hyperfine-interaction correction to the atomic $g$ factor is calculated for both point and extended charge-distribution models for nuclei. Both the magnetic dipole and the electric quadrupole interactions are taken into account. This correction is combined with corrections resulting from QED, nuclear recoil, and nuclear size, to obtain theoretical high-precision values for the $g$ factor of hydrogenlike ions with nonzero nuclear spin. The results can be used for a precise determination of nuclear magnetic moments from $g$ factor experiments.

Electron-impact ionization cross sections for helium are calculated using time-dependent close-coupling theory. The total wave function for the three electron system is expanded in nine dimensions, where three dimensions are represented on a radial lattice and a coupled channels expansion is used to represent the other six dimensions. Collision cross sections are obtained by $t\to \infty$ projection onto fully antisymmetric spatial and spin functions, with care as to orthogonality of different representations. Cross sections are also obtained using time-independent first- and second-order perturbative distorted-wave theory. Total cross sections are calculated at incident energies above the double ionization threshold for electron-impact single ionization leaving ${\mathrm{He}}^{+}$ in the $1s$, $2s$, and $2p$ states and for electron-impact double ionization. Both the single ionization cross section, leaving ${\mathrm{He}}^{+}$ in the $1s$ ground state, and the double ionization cross section are in excellent agreement with previous absolute experimental measurements.

We analyze the quantum dynamics of the nonrelativistic two-dimensional isotropic harmonic oscillator in Heisenberg’s picture. Such a system is taken as a toy model to analyze some of the various quantum theories that can be built from the application of Dirac’s quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac’s quantization rule and the usual Copenhagen interpretation of quantum mechanics.

The spectral distributions for the two-photon decay modes of singly $K$-shell ionized silver atoms are determined by x-ray–x-ray coincidence measurements. $\mathrm{Ag}K$-shell vacancies were induced by nuclear electron capture decay of radioactive cadmium isotopes ${}^{109}\mathrm{Cd}$ and two-photon coincidences were taken back to back $(180°)$ and at a $90°$ opening angle for the emission. Each of the two-photon transitions from the $2s$, $3s$, and $3d$ states exhibits unique angular and spectral distributions. The measurements agree nicely with relativistic self-consistent field calculations of Tong et al. Our results also confirm and extend the earlier experimental data of Ilakovac and co-workers with improved accuracy.

Previous resonant dipole-dipole energy-transfer experiments of cold Rydberg gases [Anderson et al., Phys. Rev. Lett. 80, 249 (1998); Mourachko et al., Phys. Rev. Lett. 80, 253 (1998)] have been interpreted as providing evidence of many-body, as opposed to purely binary, effects. Here we separate two-body and many-body interactions by introducing an additional Rydberg state, which does not participate directly in the energy-transfer process, but is strongly coupled to one of the final states. We observe broadening of the energy-transfer resonances due to this added Rydberg state, which clearly demonstrates the many-body nature of the dipole-dipole interactions in such a system.

Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D 44, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve $\mathit{NP}$-complete problems with only a polynomial number of quantum gates.

The problem of the estimation of multiple phases (or of commuting unitaries) is considered. This is a submodel of the estimation of a completely unknown unitary operation where it has been shown in recent works that there are considerable improvements by using entangled input states and entangled measurements. Here it is shown that, when estimating commuting unitaries, there is practically no advantage in using entangled input states or entangled measurements.

We describe an experimental protocol for introducing spin-dependent lattice structure in a cold atomic Fermi gas using lasers. It can be used to realize Hubbard models whose hopping parameters depend on spin and whose interaction strength can be controlled with an external magnetic field. We suggest that exotic superfluidities will arise in this framework. An especially interesting possibility is a class of states that support coexisting superfluid and normal components, even at zero temperature. The quantity of normal component varies with external parameters. We discuss some aspects of the quantum phase transition that arises at the point where it vanishes.

Quantum mechanics in dissipative systems with a magnetic field is discussed. For strong magnetic fields the system exhibits an oscillatory behavior around the classical trajectory of the electron which should generate emissions in the millimeter range of the electromagnetic spectrum.