We present a method of generating collective multiqubit entanglement via global addressing of an ion chain performing blue and red Tavis-Cummings interactions, where several qubits are coupled to a collective motional mode. We show that a wide family of Dicke states and irradiant states can be generated by single global laser pulses, unitarily or helped with suitable postselection techniques.

In this paper, a numerically stable method of calculating atomic integrals is suggested. The commutation relations among the components of the angular momentum and the Runge-Lenz vector are used to deduce recurrence relations for the Sturmian radial functions. The radial part of the one- and two-electron integrals is evaluated by means of these recurrence relations. The product of two radial functions is written as a linear combination of the radial functions. This enables us to write the integrals over four radial functions as a linear combination of the integrals over two radial functions. The recurrence relations for the functions are used to derive the recursion relations for the coefficients of the linear combination and for the integrals over two functions.

There is a natural orthogonal basis of the 6-qubit decoherence-free (DF) space robust against collective noise. Interestingly, most of the basis states can be obtained from one another just permuting qubits. This property (a) is useful for encoding qubits in DF subspaces, (b) allows the implementation of the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting qubits, which completes the method for quantum key distribution using DF states proposed by Boileau et al. [Phys. Rev. Lett. 92, 017901 (2004)], and (c) points out that there is only one 6-qubit DF state which is essentially new (not obtained by permutations) and therefore constitutes an interesting experimental challenge.

We present a general scheme for implementing bidirectional quantum state transfer in a quantum swapping channel. Unlike many other schemes for quantum computation and communication, our method does not require qubit couplings to be switched on and off. The only control variable is the bias acting on individual qubits. We show how to derive the parameters of the system (fixed and variable) such that perfect state transfer can be achieved. Since these parameters vary linearly with the pulse width, our scheme allows flexibility in the time scales under which qubits evolve. Unlike quantum spin networks, our scheme allows the transmission of several quantum states at a time, requiring only a two qubit separation between quantum states. By pulsing the biases of several qubits at the same time, we show that only eight bias control lines are required to achieve state transfer along a channel of arbitrary length. Furthermore, when the information to be transferred is purely classical in nature, only three bias control lines are required, greatly simplifying the circuit complexity.

Experimental cross sections are reported for the ${\mathrm{Fe}}^{13+}$ coronal green line transition $3s^{2}3p{}^{2}P_{1∕2}^o-3s^{2}3p{}^{2}P_{3∕2}^o$ at $\lambda 5303\mathrm{\AA }\left(2.338\mathrm{eV}\right)$. The center-of-mass interaction energies are in the range $1.7\mathrm{eV}$ (below threshold) through threshold, to $6.6\mathrm{eV}$ ($2.9\times$threshold). Data are compared with results of a 135-level Breit-Pauli $R$-matrix theory. Present experiment detects a strong maximum in the excitation cross section of magnitude $15\times {10}^{-16}{\mathrm{cm}}^2$ at $2.6\mathrm{eV}$. Smaller structures are observed between $3\mathrm{eV}$ and $6.6\mathrm{eV}$, with a maximum cross section never exceeding about $1.2\times {10}^{-16}{\mathrm{cm}}^2$. All features are due to enhancement of the direct excitation via a multitude of narrow, closely-spaced resonances calculated by the theory, the effects of which are convoluted by the $125\mathrm{meV}$ energy resolution of the present experiment. Iron is present in practically every astrophysical object, as well as being an impurity in fusion plasmas. Present results are the highest charge state in any ion for which an absolute excitation cross section has been measured.

The oscillator strength distribution in the discrete and continuous regions of the spectrum of lithium has been determined by employing the saturation technique in conjunction with a thermionic diode ion detector. The photoionization cross section from the $3s{}^{2}S$ excited state at the ionization threshold has been determined by the direct absorption of the $614\mathrm{nm}$ laser and also from extrapolating the photoabsorption cross sections measured for eight transitions of the $3s{}^{2}S\to np$ ${}^{2}P$ $(n=14,16,18,20,22,24,26,28)$ Rydberg series. The average value of the photoionization cross section measured at the ionization threshold has been used to extract the $f$ values for the $3s{}^{2}S\to np$ ${}^{2}P$ Rydberg series of lithium from $n=14$ to $n=56$. The measured $f$ values of the observed Rydberg series decrease smoothly with an increase of the principal quantum number. The oscillator strength densities in the continuum region have also been determined from the measured values of the photoionization cross section from the $3s{}^{2}S$ excited state at four ionizing laser wavelengths above the first ionization threshold. Continuity has been found between the discrete and the continuous spectrum across the ionization threshold.

We study the influence of atom-surface interactions close to the surface on the confinement properties in a recently proposed model [A. Jurisch and H. Friedrich, Phys. Lett. A 349, 230 (2006)] for quantum reflection traps and test the reliability of the sharp-step approximation used there. Accurate numerical calculations show a dependence of the surviving particle fraction on characteristic potential lengths determined by the behavior of the interaction in the limits $r\to 0$ and $r\to \infty$ of the atom-surface distance $r$. For interactions dominated by the retarded potential proportional to $1∕r^4$ we find that the simplified sharp-step potential reproduces the behavior of the trapped atoms well, both qualitatively and quantitatively.

A hierarchical ordering is demonstrated for the periodic orbits in a strongly coupled multidimensional Hamiltonian system, namely the hydrogen atom in crossed electric and magnetic fields. It mirrors the hierarchy of broken resonant tori and thereby allows one to characterize the periodic orbits by a set of winding numbers. With this knowledge, we construct the action variables as functions of the frequency ratios and carry out a semiclassical torus quantization. The semiclassical energy levels thus obtained agree well with exact quantum calculations.

We investigate collective modes and free expansions of quasi-one- and quasi-two-dimensional (Q1D and Q2D) ultracold Fermi gases in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). We solve a superfluid order parameter equation valid for the BCS-BEC crossover by employing a time-dependent variational method. We take a trial wave function of hybrid Gaussian-parabolic type, which not only reflects the low-dimensional character of the system but also allows an essentially analytical approach for the problem. We present Q1D and Q2D criteria that are valid in various superfluid regimes and show clearly the relation between the maximum condensed particle number and the parameters of the trapping potential as well as the atom-atom interaction. We demonstrate that, due to the small particle number in Q1D and Q2D condensates, the contribution to oscillating frequencies of collective modes by the quantum pressure in the strong-confinement direction is significant and hence the Thomas-Fermi approximation cannot be used. We also show that the free expansion of Q1D and Q2D superfluid Fermi gases in the strong-confinement direction is much faster than that in the weak-confinement direction.

We present a detailed analysis of the two-channel atom-molecule effective Hamiltonian for an ultracold two-component homogeneous Fermi gas interacting near a Feshbach resonance. We particularly focus on the two-body and many-body properties of the dressed molecules in such a gas. An exact result for the many-body T matrix of the two-channel theory is derived by both considering coupled vertex equations and functional-integral methods. Making use of this result allows us to incorporate exactly into the many-body theory the two-body physics of the Feshbach scattering by means of simple analytical formulas without any fitting parameters. New interesting many-body effects are discussed in the case of narrow resonances. We give also a description of the BEC-BCS crossover above and below $T_C$. The effects of different approximations for the self-energy of the dressed molecules are discussed. The single-channel results are derived as a special limit for broad resonances. Moreover, through an analytic analysis of the BEC limit, the relation between the composite boson of the single-channel model and the dressed-molecule of the two-channel model is established.

Spin-averaged static exchange potential and modified semiclassical exchange potential have been used in the distorted-wave Born approximation to calculate the triple differential cross section of Mg $\left(3s^2\right)$ in the coplanar symmetric geometry. The calculations have been carried out at impact energies ranging from $(R=)$ 1.78 to 8.84 times the first ionization potential for Mg. The effect of post-collision interactions has been included by making use of the Gamow factor introduced by Whelan et al. [Phys. Rev. A 50, 4394 (1994)]. Present results have been compared with recent experiments of Murray [Phys. Rev. A 72, 062711 (2005)] and are found to be in excellent agreement with the same except for the lowest impact energy (that is, for $R=1.78$ times above the first ionization potential).

We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only preselected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain nontrivial bipartite ensembles which do satisfy causality. These ensembles give rise to a violation of the Clauser-Horne-Shimony-Holt inequality, which exceeds the maximal quantum violation given by Tsirelson’s bound $B_{\mathrm{CHSH}}\le 2\sqrt{2}$ and obtains the Popescu-Rohrlich bound for the maximal violation, $B_{\mathrm{CHSH}}\le 4$. This may be regarded as an a posteriori realization of supercorrelations, which have recently been termed Popescu-Rohrlich boxes.

We use a multimode description of polarization-encoded qubits to analyze the quantum teleportation protocol. Specifically, we investigate how the teleportation fidelity depends on the spectral correlations inherent to polarization-entangled photons generated by type-II spontaneous parametric down conversion. We find that the maximal obtainable fidelity depends on the spectral entanglement carried by the joint probability amplitude, a result which we quantify for the case of a joint spectrum approximated by a correlated Gaussian function. We contrast these results with a similar analysis of the visibility obtained in a polarization-correlation experiment.

The Groverian entanglement measure of pure quantum states of $n$ qubits is generalized to the case in which the qubits are divided into any $p⩽n$ parties. The entanglement between these parties is evaluated numerically using an efficient parametrization. To demonstrate this measure we apply it to symmetric states such as the Greenberg-Horne-Zeiliner state and the W state. Interestingly, this measure is equivalent to an entanglement measure introduced earlier [H. Barnum and N. Linden, J. Phys. A 34, 6787 (2001)], using different considerations.

We prove a no-broadcasting theorem for the Holevo information of a noncommuting ensemble stating that no operation can generate a bipartite ensemble such that both copies have the same information as the original. We argue that upper bounds on the average information over both copies imply lower bounds on the quantum capacity required to send the ensemble without information loss. This is because a channel with zero quantum capacity has a unitary extension transferring at least as much information to its environment as it transfers to the output. For an ensemble being the time orbit of a pure state under a Hamiltonian evolution, we derive such a bound on the required quantum capacity in terms of properties of the input and output energy distribution. Moreover, we discuss relations between the broadcasting problem and entropy power inequalities. The broadcasting problem arises when a signal should be transmitted by a time-invariant device such that the outgoing signal has the same timing information as the incoming signal had. Based on previous results we argue that this establishes a link between quantum information theory and the theory of low power computing because the loss of timing information implies loss of free energy.

A recent advance in the theory of the contracted Schrödinger equation (CSE), in which only the anti-Hermitian part of the equation is solved, permits the direct determination of ground-state two-electron reduced density matrices (2-RDM’s) that yield 95%–100% of the correlation energy of atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Here we discuss in detail the anti-Hermitian contracted Schrödinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDM’s, the role of Nakatsuji’s theorem, and the structure of the wave function. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules including ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{CH}}_2$, ${{\mathrm{NH}}_4}^{+}$, $\mathrm{HF}$, and ${\mathrm{N}}_2$, and potential energy and dipole-moment surfaces are computed for boron hydride in a polarized double-$\zeta$ basis set. The computed 2-RDM’s very closely satisfy known $N$-representability conditions.

Charge transfer and electronic excitation processes for ${\mathrm{H}}^{+}+{\mathrm{H}}_2\mathrm{O}$ collisions are investigated theoretically below $10\mathrm{keV}$. Molecular-orbital close-coupling approach is employed for scattering dynamics, while an ab initio multireference single- and double-configuration interaction method is used for the determination of molecular states. The present results for charge transfer show rather weak energy dependence in the energy range from $10\mathrm{keV}$ down to a few tens of eV with very slowly varying cross-section value of $4–13\times {10}^{-16}{\mathrm{cm}}^2$, and are found to be in excellent agreement with experimental measurements by Lindsay et al. [Phys. Rev. A 55, 3945 (1997)] where the energy in the experiment and theory overlaps. The electronic-excitation cross sections are found to be much smaller than those for the charge transfer, but increase rapidly and become comparable to charge transfer at a few keV. Most of the water molecular ions and excited species produced in the collision are unstable and soon undergo dissociation; some insight into the fragmentation process and the fragmented species is given.

We have determined the scattering length of the $a{}^3\Sigma ^{+}$ potential of ${}^{87}\mathrm{RbCs}$ based on experimental observations from the literature and the known value for the long-range dispersion coefficient. Our analysis uses quantum defect theory and analytical solutions of the Schrödinger equation for a van der Waals potential. We find that the scattering length is either ${700}_{-300}^{+700}{a}_0$ or $(176\pm 2)a_0$ with more confidence associated with the first value, where $a_0=0.05292\mathrm{nm}$ is the Bohr radius. An independent value of the van der Waals coefficient could not be determined and the best theoretically determined $C_6$ value was used.