The ground and thermal states of a quadratic Hamiltonian representing the interaction of bosonic modes or particles are always Gaussian states. We investigate the entanglement properties of these states for the case where the interactions are represented by harmonic forces acting along the edges of symmetric graphs—i.e., one-, two-, and three-dimensional rectangular lattices, mean-field clusters, and platonic solids. We determine the entanglement of formation (EOF) as a function of the interaction strength, calculate the maximum EOF in each case, and compare these values with the bounds found previously for quadratic Hamiltonians.

We study the robustness of various protocols for quantum key distributions. We first consider the case of qutrits and study quantum protocols that employ two and three mutually unbiased bases. We then derive the optimal eavesdropping strategy for two mutually unbiased bases in dimension 4 and generalize the result to a quantum key distribution protocol that uses two mutually unbiased bases in arbitrary finite dimensions.

The energy and properties of a many-electron atom or molecule may be directly computed from a variational optimization of a two-electron reduced density matrix (2RDM) that is constrained to represent many-electron quantum systems. In this paper we implement a variational 2RDM method with a representability constraint, known as the $T_2$ condition. The optimization of the 2RDM is performed with a first-order algorithm for semidefinite programming [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] which, because of its lower computational cost in comparison to second-order methods, allows the treatment of larger basis sets. We also derive and implement a spin- and symmetry-adapted formulation of the $T_2$ condition that significantly decreases the size of the largest block in the $T_2$ matrix. The $T_2$ condition, originally derived by Erdahl [Int. J. Quantum Chem. 13, 697 (1978)], was recently applied via a second-order algorithm to atoms and molecules [Z. Zhao et al., J. Chem. Phys. 120, 2095 (2004)]. While these calculations were restricted to molecules at equilibrium geometries in minimal basis sets, we apply the 2RDM method with the $T_2$ condition to compute the electronic energies of molecules in both minimal and nonminimal basis sets at equilibrium as well as nonequilibrium geometries. Accurate potential energies curves are produced for BH, HF, and ${\mathrm{N}}_2$. Results are compared with the 2RDM method without the $T_2$ condition as well as several wave-function methods.

We examined nearest-neighbor spacing (NNS) statistics in doubly excited states of helium near the double ionization threshold. Using the Brody parameter $q$ to measure the NNS distribution between the regular Poisson distribution $(q=0)$ and the chaotic Wigner distribution $(q=1)$, we showed that for levels near the $N=20$ threshold of ${\mathrm{He}}^{+}$, or at about $0.13\mathrm{eV}$ below the double ionization threshold, the NNS distribution has $q=0.66$. The result shows the slow approach of the NNS of helium energy levels towards the Wigner distribution vs the excitation energy. Using an $s$-wave model where the angular momentum of each electron is restricted to zero, we also examined the NNS for levels up to the $N=30$ threshold of ${\mathrm{He}}^{+}$. We showed the gradual increase in $q$ as the excitation energy is increased. To generate the theoretical data needed for the NNS analysis, we have used the hyperspherical close-coupling method, with the recently proposed diabatization of potential curves and the truncation of channels, to greatly reduce the complexity in the calculation. We also investigated the dependence of $q$ vs the nuclear charge in the same scaled energy region, and for different symmetries, to assess their relation with the rate of approaching the $q=1$ Wigner distribution.

High-accuracy calculations of term energies and wavelengths of resonance lines in Zn-like ions have been performed as benchmarks in the quest for accurate theoretical treatments of relativity, electron correlation, and quantum electrodynamic effects in multivalence-electron systems. Computed wavelengths of the $4s^2{}^{1}S_0\text{–}4s4p{}^{1}P_1^o$ transitions are compared with the recent high-resolution wavelength measurements using electron-beam ion traps [E. Träbert, P. Beiersdorfer, and H. Chen, Phys. Rev. A 70, 032506 (2004)], a sensitive means of testing electronic structure theory that has revealed the inadequacies in treating multiple valence electrons in the extant relativistic many-body calculations.

The ionization distances $R_c^I$ of slow hydrogenlike Rydberg atoms approaching solid surfaces in the presence of a weak external electric field are calculated. The ionization is treated as resonant electron tunneling in the very vicinity of the top of the potential barrier, created between the ionic core and polarized solid. We obtain both the complex energies and the ionization distances by solving the energy eigenvalue problem under the outgoing wave boundary condition towards the solid. The eigenvalue problem is studied in parabolic coordinates within the framework of an etalon equation method adapted to include the confluence of turning points. It is demonstrated that in a critical region $R\approx R_c^I⪢1\mathrm{a}.\mathrm{u}.$ of ion-surface distances $R$, parabolic quantum numbers $n_1$, $n_2$, and $m$ can serve as approximate, but “sufficiently good” quantum numbers, at least for lower $n_1$ values. The method offers asymptotically exact analytical expressions for the ionization rates and energies, which follow the theoretical predictions of the complex scaling method (CSM). It is also found that the resulting ionization distances $R_c^I$ are in very good agreement with the results of CSM. The implications of using obtained results in analyzing the recent xenon experimental data for $R_c^I$ are briefly discussed.

It was recently remarked by Lutz [Phys. Rev. A 67, 051402(R) (2003)] that the equation for the marginal Wigner distribution in an optical lattice admits a scale-free distribution corresponding to Tsallis statistics. Here we show that this distribution is invariant under an asymptotic symmetry of the equation and hence that this scale-free behavior can be understood in terms of symmetry analysis.

We show that bright solitons exist in quasi-one-dimensional heteronuclear multicomponent Bose-Einstein condensates with repulsive self-interaction and attractive interspecies interaction. They are remarkably robust to perturbations of initial data and collisions and can be generated by the mechanism of modulational instability. Some possibilities for control and the behavior of the system in fully three-dimensional scenarios are also discussed.

Spiral waves appear frequently in nature. They have been studied, e.g., in hydrodynamic systems, chemical reactions, and in a large variety of biological and physical systems [Grill et al., Phys. Rev. Lett. 75, 3368 (1995); Goryachev and Kapral, Phys. Rev. Lett. 76, 1619 (1996)]. In contrast to chemical and hydrodynamic processes where the field amplitude exhibits the spiral patterns (intensity spirals), in optics the spiral structures relate generally to the phase structure of the optical field (so-called “optical vortices” [Lugiato et al., Adv. At., Mol., Opt. Phys. 40, 229 (1999); Arecchi et al., Phys. Rep. 318, 1 (1999); Weiss et al., Appl. Phys. B:Lasers Opt. B68, 151 (1999)]). Thus the question arises whether amplitude spiral patterns can exist also in optics. In [Lodahl et al., Phys. Rev. Lett. 85, 4506 (2000)] the existence of such spiral patterns in optics was theoretically predicted. Experimentally, intensity spiral patterns were shown to exist in an optical feedback system with radially symmetric excitation intensity [Huneus et al., Appl. Phys. B:Lasers Opt. B76, 191 (2000)]. We show here that such spiral patterns occur in a widely studied system, the semiconductor microcavity. The pattern formation is influenced here by the phase- as well as the intensity structure of the exciting light field.

We study the decoherence induced by the environment over a composite quantum system, comprising two coupled subsystems A and B, which may be a harmonic or an upside-down oscillator. We analyze the case in which the B subsystem is in direct interaction with a thermal bath, while the other remains isolated from the huge reservoir. We compare the results concerning the decoherence suffered by the A subsystem.

We demonstrate that, according to a recently suggested Lorentz-force approach to the Casimir effect, the vacuum force on an atom embedded in a material cavity differs substantially from the force on an atom of the cavity medium. The force on an embedded atom is of the familiar (van der Waals and Casimir-Polder) type, however, more strongly modified by the cavity medium than usually considered. The force on an atom of the cavity medium is of the medium-assisted force type with rather unusual properties, as demonstrated very recently [M. S. Tomaš, Phys. Rev. A 71, 060101(R) (2005)]. This implies similar properties of the vacuum force between two atoms in a medium.

We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a time-dependent magnetic field. We prove that this classical system is integrable as a consequence of the underlying unitary quantum dynamics. As a consequence, for the periodic case, (i) rigorous assessment of the validity of the rotating-wave approximation (RWA) becomes possible even beyond the assumptions of resonance and weak coupling (the latter conditions are also shown to follow from the method of averaging); (ii) we determine conditions for the realization of the quantum NOT operation beyond the RWA, by means of classical stroboscopic maps. The results bear upon areas as diverse as quantum optics, nuclear magnetic resonance, and quantum computation.

Quantum mechanics sets a bound between the quality of estimation from measurement of a single copy of a $d$-level system and the degree of disturbance of this system. We show that ideal quantum nondemolition (QND) measurement fed by a properly prepared ancilla saturates this bound. The ratio between the quality of estimation and the degree of disturbance can be continuously controlled by preparation of the ancilla. Further, we show that also nonideal QND measurement achieves this bound if a suitable measurement on the ancilla is performed. Finally, we propose a feasible scheme for such a measurement for optical two-level systems that is based on the controlled-NOT gate.

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics, any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at an arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.

We have used intense few-cycle laser pulses in a pump-probe arrangement to directly map, with high time resolution, the simultaneous evolution on two different potential curves of wave packets created when ${\mathrm{H}}_2$ $\left({\mathrm{D}}_2\right)$ molecules were ionized by a strong laser field. The experimental “snapshots” were obtained by measuring in coincidence the kinetic energy distribution of the proton (deuteron) pairs produced in the Coulomb explosion of the $\mathrm{H}_2{}^{+}$ $\left(\mathrm{D}_2{}^{+}\right)$ molecular ions as a function of the time delay between the pump and the probe pulses. The time resolution was sufficient to reveal not only the evolution of the wave packet centroid but also the fundamentally wavelike features of the packets. A full quantum calculation of observed nuclear motion is in good agreement with the measured spectra.

A matter wave mirror using a single, pulsed, super-Gaussian (SG) optical beam for specular reflection of neutral ground-state molecules is studied. The mirror has a high reflectivity close to 100% and nearly perfect specular reflection over a large incident angle. This mirror avoids the usual problems due to surface roughness and the van der Waals interactions that occur in conventional atomic mirrors. Further, it is capable of reflectance and transmittance with applications to velocity filtering and deceleration of cold molecules.

We present experimental results demonstrating that the flux of a continuous atom laser beam cannot be arbitrarily increased by increasing the strength of output coupling. We find that the continuous atom laser has large density fluctuations when the Rabi frequency becomes greater than the radial trapping frequency, due to the output coupling populating all accessible Zeeman states. In addition, we find that a state-changing output coupler for a continuous atom laser switches off as the output-coupling strength, parametrized in general by the Rabi frequency, is increased above a critical value. The numerical solution of a one-dimensional five-state Gross-Pitaevskii model for the atom laser is in good qualitative agreement with the experiment.

We report on the numerical simulation of the double-slit experiment, where the initial wave packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.

It has been recently pointed out [V. Giovannetti, S. Lloyd, and L. Maccone, Europhys. Lett. 62, 615 (2003)] that, for certain classes of states, quantum entanglement enhances the “speed” of evolution of composite quantum systems, as measured by the time a given initial state requires to evolve to an orthogonal state. We provide here a systematic study of this effect for pure states of bipartite systems of low dimensionality, considering both distinguishable (two-qubits) subsystems, and systems constituted of two indistinguishable particles.

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize the expected probability of a detection error. We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an effective ensemble. In the worst case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.