A theoretical analysis is given for a two-photon subtraction from a continuous-wave squeezed vacuum with finite time separation between two detection events. In the cw photon subtraction process, generated states are inevitably described by temporal multimode states. Our approach is based on analytical formulas that are mathematically simple and provide an intuitive understanding of the multimode structure of the system. We show that, in our process, the photon-subtracted squeezed vacuum is generated in two temporal modes and one of these modes acts as an ancillary mode to make the other one a large-amplitude coherent-state superposition.

We present a feasible and efficient scheme, and its proof-of-principle demonstration, of creating “event-ready” polarization-entangled photon pairs using only simple linear optical elements and single photons. The quality of entangled photon pairs produced in our experiment is confirmed by a strict violation of Bell’s inequality. This scheme and the associated experimental techniques present a step toward linear optics quantum computation.

Groverian and geometric entanglement measures of the $n$-party pure state are expressed by the $\left(n-1\right)$-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure $n$-qudit states have reduced states of $\left(n-1\right)$-qudits, which are equivalent under local unitary transformations, then they have equal Groverian and geometric entanglement measures. Second, both measures have an upper bound for pure states. However, this upper bound is reached only for two-qubit systems. Third, it converts effectively the nonlinear eigenvalue problem for the three-qubit Groverian measure into linear eigenvalue equations. Some typical solutions of these linear equations are written explicitly and the features of the general solution are discussed in detail.

In this paper, we consider the quantum-mechanical phase space patterns on ordered and disordered networks. For ordered networks in which each node is connected to its $2m$ nearest neighbors ($m$ on either side), the phase space quasiprobability of Wigner function shows various patterns. In the long time limit, on even-numbered networks, we find an asymmetric quasiprobability between the node and its opposite node. This asymmetry depends on the network parameters and specific phase space positions. For disordered networks in which each edge is rewired with probability $p>0$, the phase space displays regional localization on the initial node.

We evaluate a Gaussian entanglement measure for a symmetric two-mode Gaussian state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable Gaussian states. The required minimization procedure was considerably simplified by using the remarkable properties of the Uhlmann fidelity as well as the standard form II of the covariance matrix of a symmetric state. Our result for the Gaussian degree of entanglement measured by the Bures distance depends only on the smallest symplectic eigenvalue of the covariance matrix of the partially transposed density operator. It is thus consistent to the exact expression of the entanglement of formation for symmetric two-mode Gaussian states. This non-trivial agreement is specific to the Bures metric.

Planar Coulomb crystals have been recently proposed for implementing large-scale quantum simulation and computation. We investigate the structure and properties of planar Coulomb crystals in both Penning and rf traps. We also analyze in detail the effects of rf-heating and collisions with background gas and estimate the achievable fidelity of quantum gates. The prospects for the experimental implementation of this quantum computation proposal are discussed.

We have performed high-accuracy quantum mechanical calculations for the three lowest $S$ states of the beryllium ion $\left({{}^9\text{B}\text{e}}^{+}\right)$. The nonrelativistic part of the calculations was done with the variational approach and explicitly included the nuclear motion (i.e., the finite-nuclear-mass approach). The nonrelativistic wave functions were expanded in terms of explicitly correlated Gaussian functions. These nonrelativistic functions were subsequently used to calculate the leading ${\alpha }^2$ relativistic corrections $\left(\alpha =1/c\right)$ and the ${\alpha }^3$ and ${\alpha }^4$ QED (quantum electrodynamics) corrections. In the ${\alpha }^4$ QED correction we only accounted for its dominant component typically contributing about 80% of the correction. With those the present results are the most accurate ever obtained for ${{}^9\text{B}\text{e}}^{+}$. They also agree with the experimentally measured transitions within less than $0.1{\text{cm}}^{-1}$.

Optimal control theory is developed for the task of obtaining an objective in a subspace of the Hilbert space while avoiding population transfer to other subspaces. The objective, a state-to-state transition or a unitary transformation, is carried out without loss of coherence, provided the system in the allowed subspace is decoupled from its environment. An optimization functional is introduced that leads to monotonic convergence of the algorithm. This approach becomes necessary for molecular systems which are subject to processes implying loss of coherence such as ionization or predissociation. In the subspaces corresponding to lossy channels, controllability is hampered or even completely lost. A functional constraint that depends on the state of the system at each instant in time keeps the system out of the lossy channels. We outline the resulting algorithm and discuss its convergence properties. The functionality of the algorithm is demonstrated for the examples of a state-to-state transition and of a unitary transformation for a model of cold ${\text{Rb}}_2$.

The states of a boson pair in a one-dimensional double-well potential are investigated. Properties of the ground and lowest excited states of this system are studied, including the two-particle wave function, momentum pair distribution, and entanglement. The effects of varying both the barrier height and the effective interaction strength are investigated.

We study the quantum phases of bosons confined to a combined potential of a one-dimensional double-well optical lattice and a parabolic trap (two-legged ladders). We apply the time-evolving block decimation method to the corresponding ladders described by a two-legged Bose-Hubbard model. In the absence of a parabolic trap, the system of bosons in the double-well optical lattice exhibits a reentrant quantum phase transition between Mott insulator and superfluid phases at unit filling as the tilt of the double wells is increased. We show that this reentrant phase transition still occurs in the presence of a parabolic trap, and we suggest that it can be detected experimentally by measuring matter-wave interference patterns.

The stationary nonlinear Schrödinger equation (or Gross-Pitaevskii equation) for one-dimensional potential scattering is studied. The nonlinear transmission function shows a distorted profile, which differs from the Lorentzian one found in the linear case. This nonlinear profile function is analyzed and related to Siegert-type complex resonances. It is shown that the characteristic nonlinear profile function can be conveniently described in terms of skeleton functions depending on a few instructive parameters. These skeleton functions also determine the decay behavior of the underlying resonance state. Furthermore, we extend the Siegert method for calculating resonances, which provides a convenient recipe for calculating nonlinear resonances. Applications to a double Gaussian barrier and a square-well potential illustrate our analysis.

The temporal history of the x-ray laser output has been measured in dependence of the emission angle of the x-ray laser with respect to the target plane. The results show both the exit time (the time at which the x-ray laser pulse is leaving the plasma) and the pulse duration to depend on the angle of emission. Simulations of the gain in Ni-like Pd combined with ray tracing through the plasma were used to model the dependence of the time of emission on the deflection angle of the individual rays within the laser emission cone. The simulations are in reasonable agreement with the measurements.

The fragmentation pattern and corresponding kinetic energy release distributions from carbon monoxide after collisions with slow, highly charged ions (${\text{C}}^{6+}$ at $v=0.8\text{a}\text{.u}\text{.}$ and ${\text{Ar}}^{11+}$ at $v=0.39\text{a}\text{.u}\text{.}$) are reported. Correlated measurements of the projectile final charge state and all charged molecular fragments were obtained using a coincidence time-of-flight technique coupled to projectile charge state separation. Fragmentation branching ratios for the dominant electron capture processes in these collisions are similar to those resulting from ionization by fast highly charged projectiles. This result can help simplify simulations of astrophysical or artificial plasma environments, as the branching ratio may be considered essentially constant for both electron capture and ionization as long as the relevant impact parameter is large.

We introduce the notion of maximally multipartite entangled states of $n$ qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small $n$ are investigated, both analytically and numerically.

We study the coherent spin-mixing dynamics in a spin-1 atomic condensate coupled with a molecular condensate. A model is proposed to include the photoassociation (PA) interaction in a spinor condensate. If only the $m_F=-1$ spin component can be converted into molecules, the combined dynamics of spin-mixing and PA can be described by nonlinearly coupled pendulums. We performed detailed numerical calculations on the antiferromagnetic spin-1 systems. We find the spin-mixing dynamics can be greatly controlled by the PA field. The PA field can enhance or suppress the period and amplitude of the spin oscillations, which provide more degrees of freedom to control the spin-mixing dynamics.

We analyze decoherence-free (DF) quantum information in the presence of an arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a Markovian master equation. We show that the most appropriate encoding for $N$ qubits is probably contained within the $\sim \frac{2}{9}N$ excitation subspace. We give a time scale over which one would expect to apply other methods to correct for the system Hamiltonian. In order to remain applicable to experiment, we then focus on small systems, and present examples of DF quantum information for three and four qubits. We give an encoding for four qubits that, while quantum information remains in the two-excitation subspace, protects against an arbitrary bath-induced system Hamiltonian. Although our results are general to any system of qubits that satisfies our assumptions, throughout the paper we use dipole-coupled qubits as an example physical system.

We study the effects of an impurity on the magnetic response and the entanglement properties of the infinite $S=\frac{1}{2}$ $XX$ chain in a transverse field $h$ in its quasi-long-range ordered phase, i.e., below the critical point $h=1$. We show that regardless of the sign of the exchange coupling, and for whatever value of the applied field, the impurity generates an oscillating magnetization that displays a power-law decay with the distance from the impurity itself. This effect sensibly modifies the overall magnetic behavior of the chain, as testified by the observed rounding-off of the divergence of the longitudinal susceptibility. Moreover, the emergence of the above alternating structure in the spin configuration entails a substantial change in the pairwise entanglement distribution along the chain, so that concurrences are found either enhanced (up to a factor larger than 2) or quenched, depending on the distance of the spin pair from the impurity, on its strength, and on the value of the magnetic field. Acting on such control parameters, an adiabatic manipulation of both the magnetic and entanglement properties can be performed. We find these effects robust against thermal fluctuations, and we can therefore suggest realistic setups to experimentally probe the predicted behavior.

Electron-impact excitation and ionization cross sections are presented for all atomic ions in the Si, Cl, and Ar isonuclear sequences. These data contribute to the continuing effort to provide accurate collisional data for magnetic fusion and astrophysical modeling. For excitation processes, level-resolved cross section calculations are presented which were made using first-order many-body perturbation theory. For ionization processes, we present calculations made with the configuration-average approximation using a distorted-wave method. A selection of excitation and ionization cross sections are compared with experiment, where available. For ionization of ${\text{Si}}^{2+}$ and ${\text{Si}}^{3+}$, we also compare with calculations made using time-dependent close-coupling theory, to assess the accuracy of the distorted-wave calculations. Our cross sections will be tabulated in several atomic collision databases for use in future kinetics modeling efforts.

We observe a sudden breakdown of the transport of a strongly repulsive Bose-Einstein condensate through a shallow optical lattice of finite width. We are able to attribute this behavior to the development of a self-trapped state by using accurate numerical methods and an analytical description in terms of nonlinear Bloch waves. The dependence of the breakdown on the lattice depth and the interaction strength is investigated. We show that it is possible to prohibit the self-trapping by applying a constant offset potential to the lattice region. Furthermore, we observe the disappearance of the self-trapped state after a finite time as a result of the revived expansion of the condensate through the lattice. This revived expansion is due to the finite width of the lattice.

We consider the propagation of a matter wave packet of two-level atoms through a square potential created by a super-Gaussian laser beam. We explore the matter wave analog of Goos-Hänchen shift within the framework of atom optics where the roles of atom and light are exchanged with respect to conventional optics. Using a vector theory, where atoms are treated as particles possessing two internal spin components, we show that not only large negative but also large positive Goos-Hänchen shifts can occur in the reflected atomic beam.