We consider the task of estimating the randomly fluctuating phase of a continuous-wave beam of light. Using the theory of quantum parameter estimation, we show that this can be done more accurately when feedback is used (adaptive phase estimation) than by any scheme not involving feedback (nonadaptive phase estimation) in which the beam is measured as it arrives at the detector. Such schemes not involving feedback include all those based on heterodyne detection or instantaneous canonical phase measurements. We also demonstrate that the superior accuracy of adaptive phase estimation is present in a regime conducive to observing it experimentally.

Kerr-lens mode-locked, femtosecond Ti:sapphire lasers can operate in two coexistent pulsed modes of operation, named $P1$ (transform limited output pulses) and $P2$ (chirped output pulses). We study, both theoretically and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that $P1$ reaches chaos through a quasiperiodic route, while $P2$ does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter’s space, and the embedding and correlation dimensions of the attractors (and also the kurtosis for the intermittent regime) are theoretically predicted and also measured, showing a satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics.

A scheme is presented for generating entangled states of the $\mathrm{W}$ type for trapped ions in thermal motion. In the scheme the ions are simultaneously excited by a laser. Our scheme is insensitive to both the initial motional state and heating as long as the system remains in the Lamb-Dicke regime.

The time-dependent wave packet method has been used to compute full-dimensional, initial-state selected total reaction probabilities for $\mathrm{O}\mathrm{H}+\mathrm{C}\mathrm{O}\to \mathrm{H}+\mathrm{C}{\mathrm{O}}_2$, for the total angular momentum $J=0$. The results show a large increase in reactivity upon vibrational excitation of the CO bond. A comparison to results of an approximate model, in which the CO bond is treated diabatically, shows that the increase in reactivity with vibrational excitation is mostly due to a vibrationally inelastic energy transfer from CO to the reaction coordinate. The nonreactive CO bond does not act as a spectator in the reaction.

Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum state relative to an observable set. For the algebra of local observables on multi-qubit systems, the resulting local purity measure is equivalent to a recently introduced global entanglement measure [Meyer and Wallach, J. Math. Phys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of Lie-algebraic purity is exploited to identify and characterize the quantum phase transitions present in two exactly solvable models, namely the Lipkin-Meshkov-Glick model and the spin-$\frac{1}{2}$ anisotropic $XY$ model in a transverse magnetic field. For the latter, we argue that a natural fermionic observable set arising after the Jordan-Wigner transformation better characterizes the transition than alternative measures based on qubits. This illustrates the usefulness of going beyond the standard subsystem-based framework while providing a global disorder parameter for this model. Our results show how generalized entanglement leads to useful tools for distinguishing between the ordered and disordered phases in the case of broken symmetry quantum phase transitions. Additional implications and possible extensions of concepts to other systems of interest in condensed-matter physics are also discussed.

Within the framework of zero-temperature Fock-space density-functional theory (DFT), we prove that the Gâteaux functional derivative of the universal density functional, ${\delta F^{\lambda }\left[\rho \right]∕\delta \rho \left(\mathit{r}\right)\mid }_{\rho ={\rho }_0}$, at ground-state densities with arbitrary normalizations $(⟨{\rho }_0\left(\mathit{r}\right)⟩=n∊{\mathcal{R}}_{+})$ and an electron-electron interaction strength $\lambda$, is uniquely defined, but is discontinuous when the number of electrons $n$ becomes an integer, thus providing a mathematically rigorous confirmation for the “derivative discontinuity” initially discovered by Perdew et al. [Phys. Rev. Lett. 49, 1691 (1982)]. However, the functional derivative of the exchange-correlation functional is continuous with respect to the number of electrons in Fock space; i.e., there is no “derivative discontinuity” for the exchange-correlation functional at an integer electron number. For a ground-state density ${\rho }_{0,n}^{v,\lambda }\left(\mathit{r}\right)$ of an external potential $v\left(\mathit{r}\right)$, we show that ${\delta F^{\lambda }\left[\rho \right]∕\delta \rho \left(\mathit{r}\right)\mid }_{\rho ={\rho }_{0,n}^{v,\lambda }}={\mu }_{\mathrm{SM}}^n-v\left(\mathit{r}\right)$, where the constant ${\mu }_{\mathrm{SM}}^n$ is given by the following chain of dependences: ${\rho }_{0,n}^{v,\lambda }\left(\mathit{r}\right)\mapsto \left[v\right]\mapsto E_0^{v,\lambda }\left(n\right)\mapsto {\mu }_{\mathrm{SM}}^n={\partial E_0^{v,\lambda }\left(k\right)∕\partial k\mid }_{k=n}$. Here $\left[v\right]$ is the class of the external potential $v\left(\mathit{r}\right)$ up to a real constant, and ${\mu }_{\mathrm{SM}}^n$ is the chemical potential defined according to statistical mechanics. At an integer electron number $N$, we find that there is no freedom of adding an arbitrary constant to the value of the chemical potential ${\mu }_{\mathrm{SM}}^N$, whose exact value is generally not the popular preference of the negative of Mulliken’s electronegativity, $-\frac{1}{2}(I+A)$, where $I$ and $A$ are the first ionization potential and the first electron affinity, respectively. In addition, for any external potential converging to the same constant at infinity in all directions, we resolve that ${\mu }_{\mathrm{SM}}^N=-I$. Finally, the equality ${\mu }_{\mathrm{DFT}}={\mu }_{\mathrm{SM}}^n$ is rigorously derived via an alternative route, where ${\mu }_{\mathrm{DFT}}$ is the Lagrangian multiplier used to constrain the normalization of the density in the traditional DFT approach.

Elastic scattering and spin exchange cross sections in ${\mathrm{H}}^{+}+\mathrm{H}$ collisions are computed using accurate adiabatic potential curves for the center-of-mass energy range ${10}^{-4}<E<100\mathrm{eV}$. Both cross sections show considerable structure which necessitates computation on a fine energy grid to resolve them. We analyze the structures using a comparison equation method to find the poles of the scattering matrix in the complex energy plane. We show that many features of the cross sections can be correlated with these poles and tabulate the positions of the most important poles. Finding stationary phases in the partial wave cross sections, we also explain in all details the glory oscillations of the elastic cross section that extends below $100\mathrm{eV}$ down to the lowest energies.

We examine excitation (by a short laser pulse) of a hydrogen atom in parallel electric and magnetic fields, from an initial tightly bound state to a state above the classical ionization threshold. We predict that the atom ionizes by emitting a train of electron pulses. This prediction is based on the classical dynamics of electron escape. In particular, the pulse train is due to classical chaos, which occurs for nonvanishing magnetic field. We connect the structure of the pulse train to fractal structure in the escape dynamics, and discuss several issues of experimental interest, with a particular emphasis on understanding the resolution of individual pulses. A brief account of this work appeared previously as a Letter [Phys. Rev. Lett. 92, 073001 (2004)].

We report on ground-state laser cooling of single ${}^{111}\mathrm{Cd}^{+}$ ions confined in radio-frequency (Paul) traps. Heating rates of trapped ion motion are measured for two different trapping geometries and electrode materials, where no effort was made to shield the electrodes from the atomic $\mathrm{Cd}$ source. The low measured heating rates suggest that trapped ${}^{111}\mathrm{Cd}^{+}$ ions may be well suited for experiments involving quantum control of atomic motion, including applications in quantum information science.

We investigate electronically excited atoms in a magnetic guide. It turns out that the Hamiltonian describing this system possesses a wealth of both unitary as well as antiunitary symmetries that constitute an uncommon extensive symmetry group. One consequence is the twofold degeneracy of any energy level. The spectral properties are investigated for a wide range of field gradients and the spatial distributions of the spin polarization are analyzed. Wavelengths, oscillator strengths, and selection rules are provided for the corresponding electromagnetic transitions. The effects due to an additional homogeneous bias field constituting a Ioffe-Pritchard trap are explored equally.

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by the intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter $\mid \Delta \mid$, while simpler rectilinear (quasi-1D) DWs exist only for values of $\mid \Delta \mid$ essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers $N_{1,2}$ of atoms in the two species. In rotating traps, “propellers” (stable revolving crosses) are found too. A full stability region for the crosses and propellers in the system’s parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger values of $\mid \Delta \mid$. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical “propellers” are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used for applications to switching and routing.

Hollow-core photonic-crystal fibers are shown to offer the unique possibility of coherent excitation and probing of Raman-active vibrations in molecules by isolated air-guided modes of electromagnetic radiation. A $3\text{−}\mathrm{cm}$ section of a hollow photonic-crystal fiber is used to prepare isolated air-guided modes of pump and probe fields for a coherent excitation of $2331{\text{−}\mathrm{cm}}^{-1}$ $Q$-branch vibrations of molecular nitrogen in the gas filling the fiber core, enhancing coherent anti-Stokes Raman scattering through these vibrations by a factor of 15 relative to the regime of tight focusing.

Theoretical investigation on the temporal and spectral distributions of cascade third harmonic generation in a quasiperiodically optical superlattice is presented. Pulse shaping and integrated energy conversion are studied, for both input transform-limited and chirped pulses, as well as for both phase matched and phase mismatched configurations. Not only the phase mismatch between the center frequencies of the fundamental and harmonic pulses but also the group velocity mismatches (GVM) among the interacting pulses are considered. The pulse shaping features consisting of a multiplicity in phase and amplitude are observed. Additionally, there are some interesting phenomena in harmonic energy conversion, which provide more flexibility for harmonic generations in the ultrashort pulse range.

Ionization of multielectron systems is investigated by using one-dimensional, multiconfiguration time-dependent Hartree-Fock calculations. Our analysis reveals the key physical processes underlying ionization of complex systems. The laser-induced multielectron dynamics, and therewith the ionization process, depend on the ratio of laser frequency $\left({\omega }_0\right)$ to plasmon frequency $\left({\omega }_p\right)$. In the overresonant limit $({\omega }_0⪢{\omega }_p)$, tunnel ionization is destroyed and ionization takes place by a classical over the barrier mechanism. In the underresonant regime $({\omega }_0⪡{\omega }_p)$, tunnel ionization remains dominant, but is weakened by a polarization-induced growth of the tunneling barrier.

Motivated by recent experiments, we compare the Tonks (i.e., hard-core boson gas) regime achieved in an optical lattice with the Tonks regime of a one-dimensional Bose gas in the continuum. For the lattice gas, we compute the local (i.e., on-site) two-body correlations as a function of temperature and the filling of the lattice. It is found that this function saturates to a constant value with increasing temperature. Furthermore, the parameter that characterizes the long-distance correlations in the lattice Tonks regime is also obtained, showing that on the lattice the long-distance correlations enter the Tonks regime more rapidly than in the continuum.

Superselection rules severely constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In Phys. Rev. Lett. 92, 087904 (2004) we showed that this resource can be quantified by a single additional number, the superselection-induced variance $\left(\mathrm{SIV}\right)$, without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed-state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that $\mathrm{SIV}$ is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial-wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering $e‐\mathrm{H}$ scattering in the static exchange approximation. The Schrödinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial-wave results.

We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of “quantum orbits,” which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymmetric electron momentum distributions, which strongly depend on the absolute phase, i.e., on the phase difference between the pulse envelope and its carrier frequency. Around a particular value of this parameter, the distributions shift from the region of positive to that of negative momenta, or vice versa, in a radical fashion. This behavior is investigated in detail for several driving-field parameters, and provides a very efficient method for measuring the absolute phase. Both models yield very similar distributions, which share the same physical explanation. There exist, however, minor discrepancies due to the fact that, beyond the region for which electron-impact ionization is classically allowed, the yields from the quantum-mechanical computation decay exponentially, whereas their classical counterparts vanish.

When calculating the ground-state energy of a weakly interacting Bose gas with the help of the customary contact pseudopotential, one meets an artifical ultraviolet divergence which is caused by the incorrect treatment of the true interparticle interactions at small distances. We argue that this problem can be avoided by retaining the actual, momentum-dependent interaction matrix elements, and use this insight for computing both the ground-state energy and the depletions of a binary Bose gas mixture. Even when considering the experimentally relevant case of equal masses of both species, the resulting expressions are quite involved, and they are no straightforward generalizations of the known single-species formulas. On the other hand, we demonstrate in detail how these latter formulas are recovered from our two-species results in the limit of vanishing interspecies interaction.