We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase-transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two-level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener-like problems.

Quantum phases of hard core bosons (HCBs) confined in a one-dimensional quasiperiodic (QP) potential are studied within the theoretical framework of Hanbury-Brown-Twiss interferometry. The QP potential induces a cascade of Mott-like band-insulator phases in the extended regime, in addition to the Mott insulator, Bose glass, and superfluid phases. The new phases are incompressible and have zero superfluid fraction. At critical filling factors, the appearance of these insulating phases is heralded by a peak to dip transition in the interferogram, which reflects the fermionic aspect of HCBs. In the localized phase, the interference pattern exhibits an hierarchy of peaks at the reciprocal lattice vectors of the system. Our study demonstrates that in contrast to the momentum distribution, HBTI provides an effective method to distinguish Mott and glassy phases.

Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level $\Lambda$-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ${\omega }_1∕{\omega }_2=3$. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of $2\pi$, for pulse frequencies close to resonance with the transitions of a three-level $\Lambda$ medium. Also, phase-sensitive phenomena are discussed in the case of two-color $\omega \text{−}3\omega$ pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ${\omega }_{13}∕{\omega }_{12}=3$. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color $\omega \text{−}3\omega$ pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a $\Lambda$-type system by competition effects between optical transitions.

Absolute measurements of differential cross sections for the elastic scattering of positrons from xenon are made at 2, 5 and $8\mathrm{eV}$ using a trap-based beam and the technique of measuring scattering cross sections in a strong magnetic field. Calculations are carried out using the relativistic Dirac equations with a static plus polarization potential. Generally good absolute agreement is found between experiment and theory.

The lifetimes of three isotopologs of the molecular hydrogen anion have been measured using an electrostatic ion-beam trap. Much longer lifetimes (up to $\sim 2\mathrm{ms}$ for $\mathrm{D}_2{}^{-}$) than predicted by the most recent calculation are found, and it is proposed that more than one electronic state contributes to the overall lifetimes of these species.

We present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states, the root-mean square of the estimation scales as ${\left(2\sqrt{\overline{n}}\right)}^{-1}$ versus the average photon number $\overline{n}$, while it can be improved to ${\left(2\overline{n}\right)}^{-1}$ by using displaced squeezed states.

By embedding an atom capable of electromagnetically induced transparency inside an appropriate photonic-crystal microcavity it may become possible to realize an optical nonlinearity that can impart a $\pi$-rad-peak phase shift in response to a single-photon excitation. Such a device, if it operated at high fidelity, would then complete a universal gate set for all-optical quantum computation. It is shown here that the causal, noninstantaneous behavior of any ${\chi }^{\left(3\right)}$ nonlinearity is enough to preclude such a high-fidelity operation. In particular, when a single-photon-sensitive ${\chi }^{\left(3\right)}$ nonlinearity has a response time that is much shorter than the duration of the quantum computer’s single-photon pulses, essentially no overall phase shift is imparted to these pulses by cross-phase modulation. Conversely, when this nonlinearity has a response time that is much longer than this pulse duration a single-photon pulse can induce a $\pi$-rad overall phase shift through cross-phase modulation, but the phase noise injected by the causal, noninstantaneous response function precludes this from being a high-fidelity operation.

We study a system of two qubits interacting with a common environment, described by a two-spin boson model. We demonstrate two competing roles of the environment: inducing entanglement between the two qubits and making them decoherent. For the environment of a single harmonic oscillator, if its frequency is commensurate with the induced two-qubit coupling strength, the two qubits could be maximally entangled and the environment could be separable. In the case of the environment of a bosonic bath, the gap of its spectral density function is essential to generate entanglement between two qubits at equilibrium and for it to be used as a quantum data bus.

Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction $⟨{\Psi }_{\mathrm{ground}}\left(t\right)\mid \dot{H}\left(t\right)\mid {\Psi }_{\mathrm{excited}}\left(t\right)⟩∕\mathrm{\Delta }{E}^2\left(t\right)⪡1$. However, it is demonstrated that this first-order correction does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections as well, and shows that the computational error can be made exponentially small—which facilitates significantly shorter evolution times than the above first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time $T$ of order of the inverse minimum energy gap $\mathrm{\Delta }{E}_{\min }$ is sufficient and necessary, i.e., $T=O\left(\mathrm{\Delta }{E}_{\min }^{-1}\right)$. For some examples, these analytical investigations are confirmed by numerical simulations.

A strong entanglement monotone, which never increases under local operations and classical communications (LOCC), restricts quantum entanglement manipulation more strongly than the usual monotone since the usual one does not increase on average under LOCC. We propose strong monotones in mixed-state entanglement manipulation under LOCC. These are related to the decomposability and one-positivity of an operator constructed from a quantum state, and reveal geometrical characteristics of entangled states. These are lower bounded by the negativity or generalized robustness of entanglement.

A formalism for energy-dependent many-body perturbation theory (MBPT), previously indicated in our recent review articles [Lindgren et al., Phys. Rep. 389, 161 (2004); Can. J. Phys. 83, 183 (2005)], is developed in more detail. The formalism allows for an arbitrary mixture of energy-dependent (retarded) and energy-independent (instantaneous) interactions and hence for a merger of quantum-electrodynamics (QED) and standard (relativistic) MBPT. This combined many-body-QED procedure is particularly important for light elements, such as light heliumlike ions, where electron correlation is pronounced. It can also be quite significant in the medium-heavy mass range, as recently discussed by Fritzsche et al. [J. Phys. B 38, S707 (2005)], with the consequence that the effects might be significant also in analyzing the data of experiments with highly charged ions. A numerical procedure is described, and some preliminary results are given for heliumlike ions with a single retarded photon. This represent the first numerical evaluation of the combined many-body-QED effect on an atomic system. It is found that for heliumlike neon the effect of one retarded photon with correlation represents more than 99% of the nonradiative effects beyond energy-independent MBPT. The new procedure also allows for the inclusion of radiative effects (self-energy and vacuum polarization) in a more systematic fashion than has previously been possible.

State-dependent quantum electrodynamic corrections are evaluated for the hyperfine splitting of $nS$ states for arbitrary principal quantum number $n$. The calculations comprise both the self-energy and the vacuum-polarization correction of order $\alpha (Z\alpha {)}^2{E}_F$ and the recoil correction of order $\left(Z\alpha {)}^2\right(m∕M)E_F$. Higher-order corrections are summarized and partly reevaluated as well. Accurate predictions for hydrogen hyperfine splitting intervals of $nS$ states with $n=2,\dots ,8$ are presented. The results obtained are important due to steady progress in hydrogen spectroscopy for transitions involving highly excited $S$ states.

A numerical investigation of the doubly excited states of ${\mathrm{H}}_2$ converging to the $\mathrm{H}(n=2)+\mathrm{H}(n^{\prime }=2)$ limit was performed. Special emphasis was put on the accurate description of the range of intermediate internuclear distances in order to correctly connect the short range with the asymptotic van der Waals regime where perturbation theory is applicable. The present nonperturbative calculation extends to internuclear separations $R=200a_0$ and is sufficiently accurate to achieve a connection between the two extreme regimes without any need for an interpolation procedure. The high precision of the ab initio results revealed a long range dipole-quadrupole interaction that had been omitted in two earlier calculations. In addition to revised first-order perturbation theory results the leading second-order term varying as $R^{-6}$ was obtained. The impact of the present findings for cold $\mathrm{H}(n=2)$ collisions is briefly discussed.

We present a theoretical and computational study of the effects of the laser light intensity attenuation, due to absorption by an assembly of ${\left(D_2\right)}_{n∕2}$ $(n=250–{3\times 10}^4)$ clusters in ultraintense laser fields (peak intensity $I_M={10}^{16}–{10}^{18}\mathrm{W}{\mathrm{cm}}^{-2}$). The laser intensity attenuation was described by a relation between the local, time-integrated energy flow of the laser pulse and the energy deposited per ion in the Coulomb explosion products. In the cluster vertical ionization (CVI) domain, the local laser intensity manifests a linear decrease along the plasma filament, so that under the conditions of partial light absorption the energy absorbed by the plasma filament is independent of the incident laser intensity. In the non-CVI domain, the local laser intensity decreases exponentially across the plasma filament and the energy absorbed is proportional to the incident intensity. Cluster sizes for total light absorption were established on the basis of numerical solutions of our first-order differential equation for the local laser intensity. The effect of strong light absorption on the kinetic energy distribution of the ions from Coulomb explosion in an assembly of clusters results in a marked deviation from the energy distribution under CVI conditions. This exhibits a sharp rise in the range of low energies with the location of a low-energy maximum in the energy distribution providing a benchmark for the assessment of the contributions of laser absorption effects. Finally, we consider the effects of laser light absorption in a single cluster, demonstrating that both in the CVI and in the non-CVI domains the attenuation of the laser intensity is small for the cluster sizes considered in this work, while in the non-CVI domain laser light absorption by a single large ($R_0=330\mathrm{\AA }$ and $n\sim {5\times 10}^6$) deuterium cluster can be realized.

We use the Lee-Yang cluster expansion method to study quantum-statistical properties of a mixture of interconvertible atoms and dimers, where the dimers form in a two-body bound state of the atoms. We point out an infinite series of cluster diagrams whose summation leads to the Bose-Einstein condensation of the dimers below a critical temperature. Our theory captures some important features of a cold atom-dimer mixture such as interconversion of atoms and dimers and properties of the mixture at the unitarity limit.

We consider the Landau-Zener problem for a Bose-Einstein condensate in a linearly varying two-level system, for the full many-particle system as well as in the mean-field approximation. Novel nonlinear eigenstates emerge in the mean-field description, which leads to a breakdown of adiabaticity: The Landau-Zener transition probability does not vanish even in the adiabatic limit. It is shown that the emergence of nonlinear eigenstates and thus the breakdown of adiabaticity corresponds to quasi-degenerate avoided crossings of the many-particle levels. The many-particle problem can be solved approximately within an independent crossings approximation, which yields an explicit generalized Landau-Zener formula. A comparison to numerical results for the many-particle system and the mean-field approximation shows an excellent agreement.

We introduce a Hamiltonian formulation of electromagnetic fields in dispersive and absorptive structured media of arbitrary dimensionality; the Kramers-Kronig relations are satisfied by construction. Our method is based on an identification of the photonic component of the polariton modes of the system. Although the medium degrees of freedom are introduced in an oscillator model, only the susceptibility of the medium appears in the derived eigenvalue equation for the polaritons; the theory is applicable to both classical and quantum optics. A discrete polariton spectrum is obtained in the transparent regime below the absorption cutoff frequency, and the normalization condition contains the material dispersion in a simple way. In the absorptive regime, a continuous polariton spectrum is obtained. The expressions for the full electromagnetic field of the system can be written in terms of the modes of a limiting, nondispersive, nonabsorptive system, so the theory is well suited to studying the effect of dispersion or absorption on photonic dispersion relations and mode structure. Available codes for dispersive photonic modes can easily be leveraged to obtain polariton modes in both the transparent and absorptive regimes.

We analyze low-energy scattering of positrons on Ar atoms and ${\mathrm{N}}_2$ molecules using the modified effective-range theory (MERT) developed by O’Malley, et al. [J. Math. Phys. 2, 491 (1961)]. We use the formulation of MERT based on exact solutions of the Schrödinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes the experimental data well, provided that effective-range expansion is performed both for $s$- and $p$-wave scattering, which dominate in the considered regime of positron energies $(0.4–2\mathrm{eV})$. We estimate the values of the $s$-wave scattering length and the effective range for $e^{+}\text{−}\mathrm{Ar}$ and $e^{+}\text{−}{\mathrm{N}}_2$ collisions.

We prove the existence of topological quantum error correcting codes with encoding rates $k∕n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.