We can uniquely calculate almost all entangled state vectors of tripartite systems $ABC$ if we know the reduced states of any two bipartite subsystems, e.g., of $AB$ and of $BC$. We construct the explicit solution.

In this paper we report an experimental realization of an ancilla-free $1\to 2$ phase-covariant quantum cloner. The cloner is realized by interfering a linearly polarized photon, which we wish to clone with a circularly polarized photon at a beam splitter. The two-photon effect can be understood in light of Hong-Ou-Mandel interference. The fidelity of the cloner was measured as $0.829\pm 0.008$ for the $0∕90$ basis and $0.835\pm 0.006$ for the $45∕135$ basis, which is in good agreement with the theoretical prediction of $5∕6$ fidelity. The experimental scheme is straightforward and has a high cloning success rate.

We present linear optical schemes to perform generalized measurements for conclusive teleportation when the sender and the receiver share nonmaximal entanglement resulting from amplitude errors during propagation or generation. Three different cases are considered for which the states to be teleported are unknown superpositions of (a) single-photon and vacuum states, (b) vertically polarized and horizontally polarized photon states, and (c) two coherent states of opposite phases. The generalized measurement scheme for each case is analyzed, which indicates that the success probability is much more resistant to amplitude errors for case (c) than for case (a) or (b).

This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulas, written in terms of matrix coefficients, characterizing operators implementable with exactly zero, one, or two controlled-NOT (CNOT) gates and all other gates being one-qubit gates. We give an algorithm for synthesizing two-qubit circuits with an optimal number of CNOT gates and illustrate it on operators appearing in quantum algorithms by Deutsch-Josza, Shor, and Grover. In another application, our explicit numerical tests allow timing a given Hamiltonian to compute a CNOT modulo one-qubit gate, when this is possible.

Absolute double differential cross section spectra of $\mathrm{NO}$ below $135\mathrm{eV}$ have been determined by an angle-resolved electron-energy-loss spectrometer with an incident electron energy of $2500\mathrm{eV}$ and an energy resolution of $100\mathrm{meV}$. Some features above the first ionization threshold, which are too weak to be observed in the photoabsorption spectrum, stand out at large scattering angles. The present measured features and those unassigned ones in the fluorescence spectra [Chem. Phys. 293, 65 (2003)] are assigned based on the present experimental work and theoretical analysis. The energy levels of $4{\sigma }^{-1}\left(c{}^3\Pi \right)ns\sigma \left(n=3–5\right)$, $4{\sigma }^{-1}\left(B{}^1\Pi \right)ns\sigma \left(n=3–5\right)$, a vibrational resolved doubly excited state, and the inner-valence transition $2\pi \leftarrow 3\sigma$ are determined. Meanwhile, the ionization threshold $\left(22.1\mathrm{eV}\right)$ of ${\left(4\sigma \right)}^{-1}B{}^1\Pi$ is estimated.

We demonstrate the bidirectional propagation of more than ${10}^7\mathrm{atoms}$ ${(}^{87}\mathrm{Rb})$ around a “stadium”-shaped magnetic ring that encloses an area of $10.9{\mathrm{cm}}^2$, with a flux density exceeding ${10}^{11}\text{atom}{\text{s}}^{-1}{\mathrm{cm}}^{-2}$. Atoms are loaded into the guide from a two-dimensional (and higher) magneto-optical trap at one side of the “stadium.” An optical standing wave pulse is applied to increase the propagation velocity of atoms along the waveguide. The atom sample fills the entire ring in $200\mathrm{ms}$ when counterpropagating atom sections of the original atom cloud recombine at their initial positions after a full revolution.

We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of ${}^{87}\mathrm{Rb}$ atoms in a harmonic trap. Focusing primarily on condensed fraction and expansion energy, we measure unambiguous deviations from ideal-gas thermodynamics and obtain good agreement with a Hartree-Fock description of the mixed cloud. Our results offer clear evidence of the mutual interaction between the condensed and thermal components. To probe the low-temperature region unaccessible to the usual time-of-flight technique, we use coherent Bragg scattering as a filtering technique for the condensate. This allows us to separate spatially the condensed and normal components in time of flight and to measure reliably temperatures as low as $0.2T_c^0$ and thermal fractions as low as 10%. Finally, we observe evidence for the limitations of the usual image analysis procedure, pointing out to the need for a more elaborate model of the expansion of the mixed cloud.

We have designed interferometers that sort Bose-Einstein condensates into their vortex components. The Bose-Einstein condensates in the two arms of the interferometer are rotated with respect to each other through fixed angles; different vortex components then exit the interferometer in different directions. The method we use to rotate the Bose-Einstein condensates involves asymmetric phase imprinting and is itself new. We have modeled rotation through fixed angles and sorting into vortex components with even and odd values of the topological charge of two-dimensional Bose-Einstein condensates in a number of states (pure or superposition vortex states for different values of the scattering length). Our scheme may have applications for quantum information processing.

The electron transfer process in the interaction of a slow highly charged ion with a metal surface has been studied employing a microcapillary foil as a target. The combination of the target and a visible light spectroscopy allows us to directly evaluate the initial $(n,\ell )$ distributions of the first transferred electrons. It was found that observed lines were primarily attributed to $\Delta n=1$ transitions with relatively high angular momenta $\left({\ell }_i\gtrsim 4\right)$. A cascade analysis revealed that the electron is selectively transferred to $n\approx q_{in}+1$ states with a narrow distribution width of $\delta n\approx 2$ (full width at half maximum). The average initial principal quantum number is consistent with the prediction of the classical over-barrier model.

Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.

We propose a measurement scheme that allows determination of even moments of a Bose-Einstein condensate (BEC) atom number, in a ring cavity, by continuous photodetection of an off-resonant quantized optical field. A fast cavity photocounting process limits the heating of atomic samples with a relatively small number of atoms, being convenient for BECs on microchip scale applications. The measurement back-action introduces a counting-conditioned phase damping, suppressing the condensate typical collapse and revival dynamics.

We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if they are orthogonal. The sufficient and necessary condition under which nonorthogonal mixed quantum states can be unambiguously discriminated is also presented. Furthermore, we derive a series of lower bounds on the inconclusive probability of unambiguous discrimination of states from a mixed state set with a priori probabilities.

We show that the poor performance of approximate Kohn-Sham (KS) density functional theory for highly charged atomic ions is improved dramatically by ensuring that (i) the exchange functional recovers the correct leading term in the $Z$ expansion of the exchange energy ($Z$ is the nuclear charge) and (ii) the correlation functional is bounded under uniform scaling of the density to the high-density limit—i.e., ${\lim }_{\lambda \to \infty }{E}_{\mathrm{c}}^{\mathrm{KS}}\left[n_{\lambda }\right]>-\infty$, where $n_{\lambda }\left(\mathbf{r}\right)={\lambda }^{3}n\left(\lambda \mathbf{r}\right)$. The performance of several density functionals (BLYP, BP86, VS98, HCTH/407, PBE, PKZB, and TPSS) is compared for the 4-, 10-, and 18-electron atomic series spanning values of $Z$ from 4 to 28. Especially accurate results are obtained with the nonempirical metageneralized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS). High-$Z$ limits of selected exchange and correlation functionals are evaluated and compared with the exact values.

We analyze the role of nonlinear Hamiltonians in bosonic channels. We show that the information capacity as a function of the channel energy is increased with respect to the corresponding linear case, although only when the energy used for driving the nonlinearity is not considered as part of the energetic cost and when dispersive effects are negligible.

Hyperspherical close-coupling calculations for $S$- and $P$-wave positron scattering by ${\mathrm{He}}^{+}$ ions produce no full resonances in the eigenphase sum $\delta \left(E\right)$ in the two regions of energy $E$ where stable eigenvalues $E_r-i\Gamma ∕2$ with large $\Gamma$ were found previously by the complex-rotation method (CRM); $\delta \left(E\right)$ increases only by one radian in the lower-$E$ region, and even decreases almost monotonically in the higher-$E$ region, implying time advance, rather than time delay, due to the collision. However, the peaks found in the trace of time-delay matrix, $\mathrm{Tr}Q\left(E\right)$, are consistent with the CRM eigenvalues. This suggests that these eigenvalues indeed represent $S$-matrix poles in the complex-$E$ plane, but that their effects on scattering are almost masked by the background $\delta$ due to the large $\Gamma$. This work uses a general relation $\mathrm{Tr}Q\left(E\right)=2\hslash (d\delta ∕dE)$, proved here for any functional form of $\delta \left(E\right)$, and hence, both on and off resonance. This is a generalization of the well-known single-channel time-delay formula and of the multichannel formula proved previously for the Breit-Wigner resonance with a constant background $S$ matrix.

Relative angle-differential cross sections and spin-asymmetry parameters are presented for spin-polarized electron-impact excitation of spin-polarized cesium atoms for incident projectile energies ranging from $5\mathrm{eV}$ to $25\mathrm{eV}$. The experimental data, obtained in the angular range of $40°$ to $140°$, are compared with predictions from a nonrelativistic convergent close-coupling treatment for the differential cross section and the (spin) exchange asymmetry and from a semirelativistic $R$ matrix with pseudostates approach. The latter also yields nonzero values for two other spin asymmetries that require the presence of explicitly relativistic effects such as the spin-orbit interaction. The overall agreement between the experimental data and the theoretical predictions is satisfactory.

We derive closed analytic expressions for intrashell transitions in Rydberg atoms exposed to linearly polarized or circularly polarized periodic electromagnetic fields. The resonance energies and transition probabilities are calculated using multichannel Landau-Zener-Stueckelberg theory. The theory provides formulas for the resonance widths and positions for arbitrary field strength and frequency. The formulas are in excellent agreement with numerical solution of the evolution equations.

We investigated the recombination of electrons with ions in an ultrashort, intense laser pulse by numerically solving the time-dependent Schrödinger equation. The inverse above-threshold ionization (IATI) phenomenon, which shows the recombination probability peaked at specific energies of the injected electron wave packet, is explicitly elucidated. Furthermore, these IATI peaks which are separated by the laser photon energy also show up in processes of recombination to excited states.

We investigate the effects of dimensional reduction in Bose gases induced by a strong harmonic confinement in the transverse cylindric radial direction. By using a generalized Lieb-Liniger theory, based on a variational treatment of the transverse width of the Bose gas, we analyze the transition from a three-dimensional Bose-Einstein condensate to the one-dimensional Tonks-Girardeau gas. The sound velocity and the frequency of the lowest compressional mode give a clear signature of the regime involved. We also study the case of negative scattering length deriving the phase diagram of the Bose gas (uniform, single soliton, multisoliton, and collapsed) in toroidal confinement.

We investigate exciton emission of a quantum well embedded in a semiconductor microcavity. The analytical expressions of the light intensity for the cases of the excitonic number state and the coherent state are presented by using secular approximation. Our results show that the effective exciton-exciton interaction leads to the appearance of collapse and revival of the light intensity. The revival time is twice compared the coherent state case with that of the number state. The dissipation of the exciton-polariton lowers the revival amplitude but does not alter the revival time. The influences of the detuning and the phase-space filling are studied. We find that the effect of higher-order exciton-photon interaction can be removed by adjusting the detuning.