This paper investigates the relationship, if any, which may exist between the electron-electron correlation and spin entanglement of two electrons ejected simultaneously from a linear molecule following the absorption of a single photon. In order to properly learn about the influence of the molecular dynamics on this relationship and also to take into account the parity of the molecular states, double photoionization has been studied by including rotational degrees of freedom in the Hund’s coupling schemes (a) and (b). Entanglement properties of the ejected pair of electrons with respect to their spins have been investigated in each of these coupling schemes without or with taking spin dependent interactions into account. The existence, or otherwise, of the entanglement is predicted on the basis of the negativity of the partial transpose of the density matrix calculated for each case considered in this paper.

We present studies of resonance-enhanced photoionization for isotope-selective loading of ${\mathrm{Ca}}^{+}$ into a Paul trap. The ${4s}^2{}^1{S}_0\leftrightarrow 4s4p{}^1{P}_1$ transition of neutral calcium is driven by a 423 nm laser and the atoms are photoionized by a second laser at 389 nm. Isotope selectivity is achieved by using crossed atomic and laser beams to reduce the Doppler width significantly below the isotope shifts in the 423 nm transition. The loading rate of ions into the trap is studied under a range of experimental parameters for the abundant isotope ${}^{40}{\mathrm{Ca}}^{+}.$ Using the fluorescence of the atomic beam at 423 nm as a measure of the Ca number density, we estimate a lower limit for the absolute photoionization cross section of 170(60) Mb. We achieve loading and laser cooling of all the naturally occurring isotopes, without the need for enriched sources. Laser heating/cooling is observed to enhance the isotope selectivity. In the case of the rare species ${}^{43}{\mathrm{Ca}}^{+}$ and ${}^{46}{\mathrm{Ca}}^{+},$ which have not previously been laser cooled, the loading is not fully isotope selective, but we show that pure crystals of ${}^{43}{\mathrm{Ca}}^{+}$ may nevertheless be obtained. We find that for loading ${}^{40}{\mathrm{Ca}}^{+}$ the 389 nm laser may be replaced by an incoherent source.

We present a detailed experimental study of the velocity distribution of atoms cooled in an optical lattice. Our results are supported by full-quantum numerical simulations. Even though the Sisyphus effect, the responsible cooling mechanism, has been used extensively in many cold atom experiments, no detailed study of the velocity distribution has been reported previously. For the experimental as well as for the numerical investigation, it turns out that a Gaussian function is not the one that best reproduces the data for all parameters. We also fit the data to alternative functions, such as Lorentzians, Tsallis functions, and double Gaussians. In particular, a double Gaussian provides a more precise fitting to our results.

Quantum states of a two-component Fermi trapped gas are described by introducing an effective trap frequency, determined via variational techniques. Closed expressions for the contribution of a contact interaction potential to the total energy and the pairing interaction are derived. They are valid for both few and large number of particles, given the discrete nature of the formulation, and therefore richer than the continuous expressions, which are perfectly matched. Pairing energies within a shell are explicitly evaluated and its allowed values at a given energy level delimited. We show the importance of the interaction over the trap energy as the number of particles N grows and the temperature decreases. At zero temperature we find a polynomial dependence of the interaction energy on the Fermi energy, whose dominant term at large N corresponds to the mean-field approximation result. In addition, the role of the strength of an attractive potential on the total energy is exhibited.

Using a $\omega -2\omega$ combination scenario, we investigate the spectra of two-color ultrashort laser pulses in a two-level medium. It is found that higher spectral components can be produced even for small area pulses due to the interference effect of the two laser pulses. Moreover, these higher spectral components depend crucially on the relative phase $\phi$ of the two laser pulses: continuum and distinct peaks can be achieved through the control of the relative phase.

We report ab initio interaction potentials, transition dipole moments, and radiative lifetimes for the four lowest triplet states of ${\mathrm{H}}_2:$ $b$ ${}^3{\Sigma }_u^{+},$ $c$ ${}^3{\Pi }_u,$ $a$ ${}^3{\Sigma }_g^{+},$ and $e$ ${}^3{\Sigma }_u^{+},$ and their response to the perturbation due to approaching ground state He atom. Hybrid density functional–quantum Monte Carlo calculations employing the ab initio interaction potentials are then used for calculating the liquid structure around the molecular excimers in bulk superfluid ${}^4\mathrm{He}.$ Calculations demonstrate a wide variety of possible solvation structures, both spherical and highly anisotropic in geometry, depending on the electronic state of ${\mathrm{H}}_2.$ The experimentally observed ${\mathrm{H}}_2$ ${(}^3{e}^{3}a)$ emission bands [Trottier et al., Phys. Rev. A 61, 052504 (2000)] are simulated and the origins of the line shifts discussed. Absorption spectra of the same system are predicted to be broader and more blue shifted compared to the gas phase. Feasibility of the metastable ${}^3$$c$ state for absorption experiments in liquid helium is proposed.

A generalized method of using feedback to control multimode behavior in Bose-Einstein condensates is introduced. We show that for any available control, there is an associated moment of the atomic density and a feedback scheme that will remove energy from the system while there are oscillations in that moment. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of nonlinear controls. If the nonlinear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.

We present a quantum theory of a coherently pumped two-level atom in a photonic band gap (PBG), coupled to both a multimode waveguide channel and a high-quality microcavity embedded within a photonic crystal. One mode is engineered to exhibit a sharp cutoff within the PBG, leading to a large discontinuity in the local photon density of states near the atom, and the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence. Another mode of the waveguide channel is used to propagate the pump beam. We derive analytical expressions for the optical amplitude, intensity, second-order correlation functions, and conjugate quadrature variances for the light emitted by the atom into the microcavity. The quantum degree of second-order coherence in the cavity field reveals enhanced, inversionless, nearly coherent light generation when the photon density of states jump between the Mollow spectral components is large. The cavity field characteristics are highly distinct from that of a corresponding high-$Q$ cavity in ordinary vacuum. In the case of a vanishing photon density of states on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian, and the cavity field exhibits quadrature coherence.

A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a $J=\overrightarrow{1}{J}^{\prime }=0\mathrm{}$ transition is presented. The theory is developed for a Doppler-free transition and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium $D1\mathrm{}$ line.

We discuss the problem of estimating a qubit mixed state. We give the optimal estimation that can be inferred from any given set of measurements. For collective measurements and for a large number N of copies, we show that the error in the estimation varies as $1/N.$ For local measurements, we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that the error using plain tomography varies as ${1/N}^{1/4},$ while our approach leads to an error proportional to ${1/N}^{3/4}.$

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? It has been shown that all two-body Hamiltonian evolutions can be simulated using any fixed two-body entangling n-qubit Hamiltonian and fast local unitaries. By entangling we mean that every qubit is coupled to every other qubit, if not directly, then indirectly via intermediate qubits. We extend this study to the case where interactions may involve more than two qubits at a time. We find necessary and sufficient conditions for an arbitrary n-qubit Hamiltonian to be dynamically universal, that is, able to simulate any other Hamiltonian acting on n qubits, possibly in an inefficient manner. We prove that an entangling Hamiltonian is dynamically universal if and only if it contains at least one coupling term involving an even number of interacting qubits. For odd entangling Hamiltonians, i.e., Hamiltonians with couplings that involve only an odd number of qubits, we prove that dynamic universality is possible on an encoded set of $n-1$ logical qubits. We further prove that an odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify the algebras that such Hamiltonians generate. Thus, our results show that up to local unitary operations, there are only two fundamentally different types of entangling Hamiltonian on n qubits. We also demonstrate that, provided the number of qubits directly coupled by the Hamiltonian is bounded above by a constant, our techniques can be made efficient.

We analyze a reversibility of optimal Gaussian $\overrightarrow{1}2$ quantum cloning of a coherent state using only local operations on the clones and classical communication between them and propose a feasible experimental test of this feature. Performing Bell-type homodyne measurement on one clone and anticlone, an arbitrary unknown input state (not only a coherent state) can be restored in the other clone by applying appropriate local unitary displacement operation. We generalize this concept to a partial reversal of the cloning using only local operations and classical communication (LOCC) and we show that this procedure converts the symmetric cloner to an asymmetric cloner. Further, we discuss a distributed LOCC reversal in optimal $\overrightarrow{1}M$ Gaussian cloning of coherent states which transforms it to optimal $\overrightarrow{1}{M}^{\prime }$ cloning for $M^{\prime }<M.\mathrm{}$ Assuming the quantum cloning as a possible eavesdropping attack on quantum communication link, the reversibility can be utilized to improve the security of the link even after the attack.

We perform a nonlinear study of the energy loss of light and heavy ions in solids using the quantum transport-cross-section method based on numerical solution of the Schrödinger equation. The charge of the ion—the relevant parameter in this calculation—is considered equal to the average ion charge measured after emergence from solid foils. When the calculated energy loss values are analyzed within the framework of the effective charge approach, the results of the present calculations are in excellent agreement with the empirical values and also show the expected scaling properties. Through this analysis, we find a relationship between the charge state inside the solid and the effective charge related to energy loss studies, which solves a seaming contradiction between these values. The implications of this study with respect to the Bohr-Lindhard and Betz-Grodzins models are discussed.

We investigate the deceleration and bunching of cold molecules in a pulsed supersonic jet using a far-off-resonant optical lattice traveling with a constant velocity. Using an analytical treatment, we show that by choosing the lattice velocity equal to half the supersonic beam velocity and by optimizing the pulse duration, a significant fraction $(\sim 33\%)$ of translationally cold (1 K) CO molecules from a supersonic molecular beam can be decelerated to zero velocity, and simultaneously bunched in velocity space. Due to the large difference of polarizability to mass ratio between the buffer gas and the CO molecules in the pulsed jet, the buffer gas can be precluded from the fraction of stationary molecules by choosing a suitable pulse duration. Furthermore, we find that spatial bunching within the optical lattice is induced and the position of the bunch within the lattice can be chosen by varying the lattice velocity.

We study an aggregate of N identical two-level atoms (TLA’s) coupled by the retarded interatomic interaction, using the Lehmberg-Agarwal master equation. First, we calculate the entangled eigenstates of the system; then, we use these eigenstates as a basis set for the projection of the master equation. We demonstrate that in this basis the equations of motion for the level populations, as well as the expressions for the emission and absorption spectra, assume a simple mathematical structure and allow for a transparent physical interpretation. To illustrate the use of the general theory in emission processes, we study an isosceles triangle of atoms, and present in the long wavelength limit the (cascade) emission spectrum for a hexagon of atoms fully excited at $t=0.\mathrm{}$ To illustrate its use for absorption processes, we tabulate (in the same limit) the biexciton absorption frequencies, linewidths, and relative intensities for polygons consisting of $N=2,\dots ,9\mathrm{}$ TLA’s.

We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of a number of different arrays of N identical two-level atoms (TLA’s) or qubits, including polygons, “diamond” structures, polygon multilayers, icosahedra, and dodecahedra. We assume only that the coupling occurs via an exchange interaction which depends on the separation between the atoms. We include the interactions between all pairs of atoms, and our results are valid for arbitrary separations relative to the radiation wavelength.

In this paper we describe a scheme for performing a nonorthogonal projective positive-operator-value measurement of any arbitrary single-photon polarization input state with unit probability of success. While this probability is reached in the limit of infinite cycles of states through the apparatus, only one actual physical setup is required for a feasible implementation. Specifically, our setup implements a set of three nonorthogonal measurement operators at angles of 120° to each other.

We explore the character of a novel set of “field-linked” states that were predicted by Avdeenkov and Bohn [Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field’s strength. We clarify the nature of these quasibound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as functions of both the intermolecular distance and the angle that the intermolecular axis makes with the electric field. Within an adiabatic approximation we solve the two-dimensional Schrödinger equation to find bound states, whose energies correlate well with resonance features found in fully converged multichannel scattering calculations.

The spontaneous decay rate of an excited atom placed near a dielectric cylinder is investigated. Special attention is paid to the case when the cylinder radius is small in comparison with radiation wavelength (nanofiber or photonic wire). In this case, the analytical expressions of the transition rates for different orientations of a dipole are derived. It is shown that the main contribution to decay rates is due to the quasistatic interaction of the atom dipole momentum with the nanofiber, and the contributions of guided modes are exponentially small. On the contrary, in the case when the radius of the fiber is only slightly less than the radiation wavelength, the influence of guided modes can be substantial. The results obtained are compared with the case of a dielectric nanospheroid and an ideally conducting wire.

We investigate continuous-variable entangling resources on the basis of two-mode squeezing for all operational regimes of a nondegenerate optical parametric oscillator with allowance for quantum noise of an arbitrary level. The results for the quadrature variances of a pair of generated modes are obtained by using the exact steady-state solution of the Fokker-Planck equation for the complex-$P$-representation quasiprobability distribution function. We find a simple expression for the squeezed variances in the near-threshold range and conclude that the maximal two-mode squeezing reaches 50% relative to the level of vacuum fluctuations and is achieved at the pump field intensity close to the generation threshold. The distinction between the degrees of two-mode squeezing for monostable and bistable operational regimes is cleared up.