We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of localizable entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-$1∕2$ and spin-1 systems, we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.

A programmable quantum-state discriminator is implemented by using nuclear magnetic resonance. We use a two-qubit spin-$1∕2$ system, one for the data qubit and one for the ancilla (program) qubit. This device does the unambiguous (error-free) discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and elliptically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla qubit. It is also shown that the probability of discrimination depends on the angle of the unitary operator of the protocol and ellipticity of the data qubit state.

We propose feasible implementations of basic continuous-variable (CV) interactions (squeezer, parametric amplifier, and quantum nondemolition interaction) between light modes without the requirement for in-line nonlinear couplings in a strongly pumped optical medium. The method is based entirely on linear optics, homodyne detection, and off-line squeezed ancillary states and therefore represents the CV analog of the measurement-induced nonlinearity approach, previously used in single-photon qubit experiments to probabilistically implement a controlled-NOT gate.

For two two-level atoms coupled to a single Bosonic mode that is driven and heavily damped, the steady state can be entangled by resonantly driving the system [S. Schneider and G. J. Milburn, Phys. Rev. A 65, 042107 (2002)]. We present a scheme to significantly increase the steady-state entanglement by using homodyne-mediated feedback, in which the Bosonic mode is that of an electromagnetic cavity, the output of which is measured and the resulting homodyne photocurrent is used to modulate the field driving the qubits. Such feedback can increase the nonlinear response to both the decoherence process of the two-qubit system and the coherent evolution of individual qubits. We present the properties of the entangled states using the SO(3) $Q$ function.

A large-scale dynamical simulation of the superfluid–Mott-insulator transition in a gas of ultracold atoms placed in an optical lattice is performed using the time-dependent Gutzwiller mean-field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Greiner et al., Nature (London) 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap only.

We present a quantum mechanical treatment for both atomic and field fluctuations of an atomic ensemble interacting with propagating fields, either in electromagnetically induced transparency (EIT) or in a Raman situation. The atomic spin noise spectra and the outgoing field spectra are calculated in both situations. For suitable parameters both EIT and Raman schemes efficiently preserve the quantum state of the incident probe field in the transfer process with the atoms, although a single-pass scheme is shown to be intrinsically less efficient than a cavity scheme.

We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks, we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such a reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.

We show in this note that, in the coherent Rayleigh-Brillouin scattering (CRBS) experiment [X. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004)], the vibrational modes of the $\mathrm{C}{\mathrm{O}}_2$ molecules are frozen. When the gas dynamic parameters are chosen accordingly, the model predicts a line shape that matches with the experimental data. Fitting the theoretical curve to the CRBS data represents a method to measure the speed of high-frequency sound, bulk viscosity, and the rotational relaxation time of molecular gases.

We present an ab initio stochastic method for calculating thermal properties of a trapped, one-dimensional Bose gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard–type Hamiltonian, whose imaginary time evolution is made computationally accessible by stochastic factorization of the kinetic energy. To achieve convergence for low enough temperatures such that quantum fluctuations are essential, the stochastic factorization is generalized to blocks, and ideas from density-matrix renormalization are employed. We compare our numerical results for density and first-order correlations with analytic predictions.

We propose a different scheme to realize holonomic quantum computation with rf superconducting quantum interference device (SQUID) qubits in a microwave cavity. In this scheme associated with the non-Abelian holonomies, the single-qubit gates and a two-qubit controlled-PHASE gate as well as a controlled-NOT gate can be easily constructed by tuning adiabatically the Rabi frequencies of classical microwave pulses coupled to the SQUIDs. The fidelity of these gates is estimated to be possibly higher than 90% with the current technology.

Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] have recently defined a class of discrete Wigner functions $W$ to represent quantum states in a finite Hilbert space dimension $d$. I characterize the set $C_d$ of states having non-negative $W$ simultaneously in all definitions of $W$ in this class. For $d⩽5$ I show $C_d$ is the convex hull of stabilizer states. This supports the conjecture that negativity of $W$ is necessary for exponential speedup in pure-state quantum computation.

The early study of Schwartz [Ann. Phys. (N.Y.) 6, 156 (1959)] led to an explicit expression for the ground-state electron density $\rho \left(r\right)$ of He-like atomic ions with nuclear charge $Ze$ in the limit of large $Z$. Much later, Gál, March, and Nagy [Chem. Phys. Lett. 305, 429 (1999)] derived a third-order linear homogeneous differential equation satisfied by the Schwartz limiting density. Our aim here has been to solve a still correlated model more closely related to the He atom itself. Motivated by semiclassical studies (as by Handke [Phys. Rev. A 50, R3561 (1994)]), we have solved a fully quantal model in which the Coulomb repulsion energy $e^2∕r_{12}$ of the two electrons at separation $r_{12}$ is expanded in a one-center form about the atomic nucleus and only the $s$-wave term is retained. From the resulting analytical ground-state density, a differential equation has been derived, which is contrasted with that satisfied by the large-$Z$ limiting form of Schwartz. Suggestions are finally made as to the way the density of the He atomic ion series may be characterized, the ionization potential $I\left(Z\right)$ being proposed as crucial input data.

Ionization and multifragmentation of ${\mathrm{C}}_{60}$ in ${\mathrm{Ar}}^{+}$ impact at $7\mathrm{keV}$, $14\mathrm{keV}$, and $20\mathrm{keV}$ have been investigated. Fragment mass spectra differentiated according to the $\mathrm{C}_{60}{}^{r+}$ parent ion charge state are interpreted in terms of a transition from the nonstatistical fast multifragmentation in a time range of about $500\mathrm{fs}$ induced by nuclear interaction at low collision velocity $(v<0.1\mathrm{a.u.})$ to the statistical multifragmentation induced by nuclear and electronic interaction at higher collision velocities. Prompt ejection of a carbon atom due to the direct momentum transfer is observed.

We present analytical and numerical results of the relativistic calculation of the transition matrix element $S_{fi}$ and differential cross sections for Mott scattering of initially polarized Dirac particles (electrons) in the presence of a strong laser field with linear polarization. We use exact Dirac-Volkov wave functions to describe the dressed electrons and the collision process is treated in the first Born approximation. The influence of the laser field on the degree of polarization of the scattered electron is reported.

We consider electron-ion recombination in the presence of a very short laser pulse and we analyze the spectrum of x rays generated during this process. In particular, we investigate the development of the $x$-ray spectrum as a function of time within the duration of the laser pulse. We compare our results with the spectra we obtained in our earlier work on this topic, describing the laser pulse by an electromagnetic plane wave and we also relate our results to our classical investigation of this process based on Bohr’s correspondence principle. As we can show, our classical model of laser-assisted electron-ion recombination can still be successfully applied in the case of a very short laser pulse of a few cycles.

Toluene fragmentation by intense femtosecond laser pulses is experimentally investigated. A strong increase of the toluene fragmentation appears to correlate with an increase of the focal area due to changes in the focal geometry and nonlinear small-scale self-focusing. The scenario of Raman modes excitation proposed in an earlier publication [A.M. Müller et al., Phys. Rev. Lett. 88, 023001 (2002)] is ruled out as the dominant effect for the enhancement.

Nonperturbative analytical and numerical methods are presented for the solution of the coupled nonlinear Maxwell-Schrödinger equations. The theory has been derived within the Hamiltonian or canonical formalism. The canonical approach to dynamics, starting from the Maxwell and Schrödinger Lagrangians with a Lorenz gauge fixing term, yields a set of first order Hamilton equations. They form a well-defined initial value problem. The Maxwell-Schrödinger equations of motion are then represented in a spatial basis of Gaussian functions. In the limit of a complete basis this representation is exact. For any choice of finite basis it provides an approximate system of dynamical equations that can be integrated in time and made systematically more accurate by enriching the basis. The basis form of the theory has been implemented numerically and is used to investigate the dynamics of a single nonrelativistic spinless one electron atom interacting with the electromagnetic modes of a cavity.

To construct an $N$-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained-search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schrödinger equation. The original Runge-Gross (RG) formulation is subsumed within the current formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.

We present experimental results of $\mu$-atomic and $\mu$-molecular processes induced by negative muons in pure helium and helium-deuterium mixtures. The experiment was performed at the Paul Scherrer Institute (Switzerland). We measured relative intensities of muonic x-ray $K$ series transitions in ${\left(\mu {}^{3,4}\mathrm{He}\right)}^{*}$ atoms in pure helium as well as in helium-deuterium mixtures. The $d\mu {}^3\mathrm{He}$ radiative decay probabilities for two different helium densities in ${\mathrm{D}}_2+{}^3\mathrm{He}$ mixture were also determined. Finally, the $q_{1s}^{\mathrm{He}}$ probability for a $d\mu$ atom formed in an excited state to reach the ground state was measured and compared with theoretical calculations using a simple cascade model.

Differential cross sections for the elastic scattering of $1.115\text{−}\mathrm{MeV}$ photons from tungsten $(Z=74)$ and lead $(Z=82)$ have been measured at angles ranging from 30° to 135°, using a high purity coaxial germanium detector. The experimental results are compared with $S$-matrix theoretical calculations of Rayleigh scattering cross sections, which also include contributions arising from the nuclear Thomson amplitudes and the Delbrück amplitude in lowest order Born approximation. The present experimental data at $1.115\mathrm{MeV}$ indicates that Delbrück amplitudes calculated with lowest-order Born approximation, when combined with $S$-matrix Rayleigh scattering amplitudes, are sufficient, as has previously been observed at $1.332\mathrm{MeV}$ for a number of high-$Z$ elements, and at $1.121\mathrm{MeV}$ and $1.173\mathrm{MeV}$ for $Z=92$. This result for $Z=74$ and $Z=82$ at $1.115\mathrm{MeV}$ provides further confirmation that the Delbrück amplitudes calculated with lowest-order Born approximation are sufficient for energies at and below $1.332\mathrm{MeV}$, in contrast to the situation at $2.754\mathrm{MeV}$ where Coulomb corrections to the Delbrück amplitudes are significant for high-$Z$ elements.