Recently, Karimipour and Memarzadeh [Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space, each of dimension $D$, with the following properties: (i) The family continuously interpolates between a product basis and a maximally entangled basis as some parameter $t$ is varied, and (ii) for a fixed $t$, all basis states have the same amount of entanglement. The authors derived a necessary condition and provided explicit solutions for $D⩽5$, but the existence of a solution for arbitrary dimensions remained an open problem. We prove that such families exist in arbitrary dimensions by providing two simple solutions, one that employs the properties of quadratic Gauss sums and the other that uses graph states. The latter can be generalized to more than two parties—we can construct equally entangled families that vary continuously between a product basis and a graph-state basis.

A rigorous quantum electrodynamics theory of the multiphoton decay of excited states in a hydrogen atom is presented. The “two-photon” approximation is formulated which is limited by the one- and two-photon transitions including cascade transitions with two-photon links. This may be helpful for the strict description of the recombination process in a hydrogen atom and, in principle, for the history of hydrogen recombination in the early universe.

Doubly excited states below the $N=2$ ionization threshold are populated by exciting helium atoms in a supersonic beam with monochromatized synchrotron radiation. The fluorescence decay of these states triggers a radiative cascade back to the ground state with large probability to populate long lived singlet and triplet helium metastable states. The yield of metastables is measured using a multichannel plate detector after the beam has passed a singlet-quenching discharge lamp. The variation of the yield observed with the lamp switched on or off is related to the triplet-singlet mixing of the doubly excited states.

The normalized orthopositronium quenching rate, ${}_1{Z}_{\mathrm{eff}}$, has been measured for CH${}_3$F, CH${}_3$Cl, CH${}_3$Br, and CH${}_3$I in the gas phase. Silica aerogel was used as the positronium formation medium and the microchambers. The ${}_1{Z}_{\mathrm{eff}}$ values obtained are ${}_1{Z}_{\mathrm{eff}}({\mathrm{CH}}_3\mathrm{F})=0.46\pm 0.03$, ${}_1{Z}_{\mathrm{eff}}({\mathrm{CH}}_3\mathrm{Cl})=0.58\pm 0.05$, ${}_1{Z}_{\mathrm{eff}}({\mathrm{CH}}_3\mathrm{Br})=0.70\pm 0.04$, and ${}_1{Z}_{\mathrm{eff}}({\mathrm{CH}}_3\mathrm{I})=2.1\pm 0.2$. The ${}_1{Z}_{\mathrm{eff}}$ value for CH${}_3$I is significantly larger than expected for pick-off quenching. It is probably caused by spin-conversion quenching through spin-orbit interaction.

The charge transfer in collisions of ${\mathrm{C}}^{2+}$ ions with the HF molecule has been studied by means of ab initio quantum chemistry molecular methods followed by a semiclassical dynamical treatment in the keV collision energy range. The mechanism of the process, in particular its anisotropy, has been investigated in detail in connection with nonadiabatic interactions around avoided crossings between states involved in the reaction. The vibration of the molecular target has been analyzed and cross sections on different vibrational levels of ${\mathrm{HF}}^{+}$ have been estimated in the Franck-Condon approximation.

We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, pressure, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.

The possible ground states of spin-2 Bose-Einstein condensates in an external magnetic field are obtained analytically and classified systematically according to the population of the condensed atoms at the hyperfine sublevels. It is shown that the atoms can populate simultaneously at four hyperfine sublevels in a weak magnetic field with only the linear Zeeman energy, in contrast to that in a stronger magnetic field with the quadratic Zeeman energy, where condensed atoms can at most populate at three hyperfine sublevels in the ground states. Any spin configuration we obtained will give a closed subspace in the order parameter space of the condensates.

We consider the operator product expansions for unitarity fermions. We compute the dynamic structure factor $S(\mathbf{q},\omega )$ at large frequency and wave number away from the one-particle peak. The overall normalization of $S(\mathbf{q},\omega )$ is determined by Tan’s contact parameter, and the dependence on $\mathbf{q}$ and $\omega$ is obtained in closed analytic form. We also find energy deposited into the system by small, rapid variations of the inverse scattering length.

We performed a series of simulations of resonant high-order harmonic generation (HHG) by means of a multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach for three-dimensional fullerenelike systems. The results proved the theory of resonant recombination proposed in this article and showed the ways of resonant HHG optimization. The results of MCTDHF calculation of the HHG for ${\mathrm{C}}_{60}$ were in good qualitative agreement with reported experimental data.

We present a direct measurement of the Kirkwood-Rihaczek (KR) distribution for spatial properties of a coherent light beam in terms of position and momentum (angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne detection (BHD) to simultaneously extract the distribution of the transverse position and momentum of a light beam. The two-LO BHD can measure the KR distribution for any complex wave field (including quantum mechanical wave function) without applying tomography methods (inverse Radon transformation). The transformation of the KR distribution to the Wigner, Glauber-Sudarshan $P$, and Husimi or $Q$ distributions in spatial coordinates are illustrated through experimental data. The KR distribution can provide the local information of a wave field, which is suitable for studying particle properties of a quantum system. Meanwhile, the Wigner function is suitable for studying wave properties such as interference, and hence provides nonlocal information of the wave field. The method developed here can be used for exploring the spatial quantum state for information processing and optical phase-space imaging for biomedical applications.

Alkaline-earth-metal-like atoms with ultranarrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications, it is crucial to understand the noise properties of this device. In this paper, we present a detailed analysis of the intensity fluctuations by means of Monte Carlo simulations and semiclassical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.

We consider scattering of a single particle from an interaction-bound pair of particles in the one-dimensional Bose-Hubbard model. We show that the transmission probability of the single particle is always significantly smaller than unity. This invalidates the main result of L. Jin et al. [Phys. Rev. A 79, 032108 (2009)], where it is claimed that a single-particle wave packet can pass with unit probability through a bound-particle pair and coherently shift its position by one lattice site.

We report correlated two-electron ab initio calculations for the hydrogen molecule ${\mathrm{H}}_2$ in interaction with intense ultrashort laser pulses, via a solution of the full three-dimensional time-dependent Schrödinger equation. Our results for ionization and excitation probabilities (at 800 and 400 nm) as a function of internuclear distance $R$ show strong evidence of enhanced ionization, in both single and double ionization, as well as enhanced excitation, in single and double excitation, as the internuclear distance $R$ increases from the equilibrium value $R_e$. The enhancement of all these molecular processes exhibits a maximum at a critical distance $R_c$, which can be predicted from simple electrostatic and recollision models.

By means of the method of the effective potential, the phase transitions from the Mott insulating state to either the atomic or the dimer superfluid state in the three-body constrained attractive Bose lattice gas are analyzed. Because of the appearance of the Feshbach resonance coupling between the two kinds of order parameters in the derived Ginzburg-Landau function, it is found that the continuous Mott-insulator–superfluid transitions can be preempted by first-order ones. Since the employed approach can provide accurate predictions of phase boundaries in the strong coupling limit, where the dimer superfluid phase can emerge, our work sheds light on the search of this phase in real ultracold Bose gases in optical lattices.

We propose a method of indirect measurements where a probe is able to read, in short interaction times, the quantum state of a remote system through an incoherent third party, hereafter called a mediator. The probe and system can interact briefly with the mediator in an incoherent state but not directly among themselves and, nevertheless, the transfer of quantum information can be achieved with robustness. We exemplify our measurement scheme with a paradigmatic example of this tripartite problem—a qubit-oscillator-qubit setup—and discuss different physical scenarios, pointing out the associated advantages and limitations.

In this article we treat the subject of chaotic environments with few degrees of freedom in quantum communication by investigating a conservative dynamical map as a model of a dephasing quantum channel. When the channel’s dynamics is chaotic, we investigate the model’s semi-classical limit and show that the entropy exchange grows at a constant rate which depends on a single parameter (the interaction strength), analogous to stochastic models of dephasing channels. We analyze memory effects in the channel and present strong physical arguments to support that the present model is forgetful in the chaotic regime while memory effects in general cannot be ignored when channel dynamics is regular. In order to render the nonchaotic channel forgetful, it becomes necessary to apply a reset to the channel and this reset can efficiently be modeled by application of a chaotic map. We may then refer to encoding theorems (valid in the case of forgetful channels) to present evidence of a transition from noiseless to noisy channel due to the environment’s transition from regular to chaotic dynamics.

We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of ${\mathrm{Sr}}^{+}$ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. ac Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminating the need for an additional laser. Quantum process tomography is implemented on atomic and motional states by use of conditional pulse sequences. With these techniques, we demonstrate a Cirac-Zoller controlled-not gate in a single ion with a mean fidelity of $91(1)\%$.

The three-pulse photon echo is a well-known technique to store intense light pulses in an inhomogeneously broadened atomic ensemble. This protocol is attractive because it is relatively simple and it is well suited for the storage of multiple temporal modes. Furthermore, it offers very long storage times, greater than the phase relaxation time. Here, we consider the three-pulse photon echo in both two- and three-level systems as a potential technique for the storage of light at the single-photon level. By explicit calculations, we show that the ratio between the echo signal corresponding to a single-photon input and the noise is smaller than one. This severely limits the achievable fidelity of the quantum state storage, making the three-pulse photon echo unsuitable for single-photon quantum memory.

Photoexcited electrons and holes in molecules or in semiconductors constitute a bipartite entangled system. We show that this entanglement can be coherently controlled by broadband x-ray pulses which create valence excitation wave packets through a stimulated Raman process. A novel measure of electron correlations in excited states is then provided by the time dependence of the concurrence. In a simulation study we demonstrate the control of entanglement of electrons and holes in CO that can be achieved by tuning a soft x-ray pulse to different core transitions: the carbon $K$ edge (296 eV), the oxygen $K$ edge (540 eV), and the $2\sigma \to 1{\pi }^{*}$ transition (191 eV).

Many-body states whose wave functions admit a representation in terms of a uniform binary-tree tensor decomposition are shown to obey power-law two-body correlation functions. Any such state can be associated with the ground state of a translationally invariant Hamiltonian which, depending on the dimension of the systems sites, involves at most couplings between third-neighboring sites. Under general conditions it is shown that they describe unfrustrated systems which admit an exponentially large degeneracy of the ground state.