The electronic structure of Ce${}_2$ is studied in a valence bond model with two $4f$ electrons localized at two cerium sites. It is shown that the low-lying energy spectrum of the simplest cerium chemical bond is determined by peculiarities of the occupied $4f$ states. The model allows for an analytical solution, which is discussed along with the numerical analysis. The energy spectrum is a result of the interplay between the $4f$ valence bond exchange, the $4f$ Coulomb repulsion, and the spin-orbit coupling. The calculated ground state is the even $\Omega =\Lambda =\Sigma =0$ level, the lowest excitations situated at $~$30 K are the odd $\Omega =\Lambda =\Sigma =0$ state and the ${}^3{6}_5$ doublet $(\Omega =\pm 5,\Lambda =\pm 6,\Sigma =\mp 1)$. The calculated magnetic susceptibility displays different behavior at high and low temperatures. In the absence of the spin-orbit coupling the ground state is the ${}^3{\Sigma }_g^{-}$ triplet. The results are compared with other many-electron calculations and experimental data.

The dissociation dynamics of HD${}^{+}$ molecules is studied theoretically by numerically solving the time-dependent Schrödinger equation in which the molecular vibrational and rotational degrees of freedom are included. Based on the Born-Oppenheimer approximation, the ground 1$s$σ${}_g$ state and the excited 2$p$σ${}_u$ state are taken into account, corresponding to two dissociative channels HD${}^{+}$→D $+$ H${}^{+}$ and HD${}^{+}$→H $+$ D${}^{+}$, respectively. Two dissociative nuclear wave packets overlap and interfere after excited by two ultrashort laser pulses. The interference patterns can be controlled by varying the laser parameters and the dissociation probabilities are demonstrated for different laser fields. The kinetic energy-dependent distributions of the fragments are calculated using an asymptotic-flow expression in the momentum space. The branching ratio D${}^{+}$/(H${}^{+}$ $+$ D${}^{+}$), as a function of the delay time and the relative phase between two laser pulses, is also discussed.

We present a method that harnesses coherent control capability to two-dimensional Fourier-transform optical spectroscopy. For this, three ultrashort laser pulses are individually shaped to prepare and control the quantum interference involved in two-photon interexcited-state transitions of a $\mathsf{V}$-type quantum system. In experiments performed with atomic rubidium, quantum control for the enhancement and reduction of the 5$P$${}_{1/2}\to$ 5$P$${}_{3/2}$ transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.

We present molecular above-threshold ionization (MATI) spectra generated by ultrashort intense linearly and circularly polarized laser pulses from nonperturbative numerical solutions of the corresponding time-dependent Schrödinger equation in the molecular-ion ${{\mathrm{H}}_2}^{+}$. It is found that high-order MATI spectra with maximum kinetic energy $32U_p$, where $U_p=I_0/4m_e{\omega }_0^2$ is the ponderomotive energy at intensity $I_0$ and frequency ${\omega }_0$, can be obtained in ${{\mathrm{H}}_2}^{+}$ at great internuclear distances $R$ for both linear and circular polarizations. Quasiclassical laser-induced collision models confirm that such high-order MATIs mainly result from a collision with neighboring ions of the ionized electron. Interference patterns in the high-order MATI spectra are critically sensitive to both the internuclear distance $R$ of the molecules and the polarizations of the driving laser pulses. Moreover, with few-cycle laser pulses, the carrier-envelope phase sensitivity of MATI angular distributions is also investigated for varying internuclear distances $R$. At critical internuclear distances for charge-resonance-enhanced ionization, we also find that enhanced interference patterns occur.

Diffraction experiments with holographic gratings recorded in SiO${}_2$ nanoparticle-polymer composites have been carried out with slow neutrons. The influence of parameters such as nanoparticle concentration, grating thickness, and grating spacing on the neutron-optical properties of such materials has been tested. Decay of the grating structure along the sample depth due to disturbance of the recording process becomes an issue at grating thicknesses of about 100 microns and larger. This limits the achievable diffraction efficiency for neutrons. As a solution to this problem, the Pendellösung interference effect in holographic gratings has been exploited to reach a diffraction efficiency of 83% for very cold neutrons.

We use the Boltzmann equation in the relaxation-time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main findings are the following: (i) In the regime that has been studied experimentally hydrodynamic effects beyond the Navier-Stokes approximation are small. (ii) Mean-field corrections to the Boltzmann equation are not important. (iii) Experimental data imply that freezeout occurs very late, which means that the relaxation time remains smaller than the expansion time during the entire evolution of the system. (iv) The experimental results also imply that the bulk viscosity is significantly smaller than the shear viscosity of the system.

We investigate discrete nondiffracting beams (DNBs) being the foundation of periodic and quasiperiodic intensity distributions. Besides the number of interfering plane waves, the phase relation among these waves is decisive to form a particular intensity lattice. In this manner, we systematize different classes of DNBs and present similarities as well as differences. As one prominent instance, we introduce the class of sixfold nondiffracting beams, offering four entirely different transverse intensity distributions: in detail, the hexagonal, kagome, and honeycomb pattern, as well as a hexagonal vortex beam. We further extend our considerations to quasiperiodic structures and show the changeover to Bessel beams. In addition, we introduce a highly flexible implementation of the experimental analog of DNBs, namely discrete pseudo-nondiffracting beams, and present locally resolved intensity and phase measurements, which underline the nondiffracting character of the generated wave fields.

We study the scattering of linear and nonlinear waves in a long waveguide array with a parity-time ($\mathrm{PT}$)-symmetric defect created by two waveguides with balanced gain and loss. We present exact solutions for the scattering of linear waves on such a defect, and then demonstrate numerically that the linear theory can describe, with a good accuracy, the soliton scattering in the case of weak nonlinearity. We reveal that the reflected and transmitted linear and nonlinear waves can be amplified substantially after interaction with the $\mathrm{PT}$-symmetric defect thus allowing an active control of the wave scattering in the array.

The paper presents a theoretical analysis of the pulse buildup from the spontaneous noise level and variations in the intrinsic polarization state of x-ray lasers, devices utilizing amplified spontaneous emission in a high-gain medium. Maxwell-Bloch equations with incorporated randomness of spontaneous emission, atomic level degeneracy, and time-dependent gain are used to describe the wave nature of the amplification process properly. The dynamics of pulse growth and polarization variation are analyzed for the entire amplification process starting from the initial state of random noise to the full saturation. It is shown that, within the used one-dimensional model, the output pulse can be polarized to a substantial degree. These results provide the basic understanding of x-ray lasers in a wave-optics perspective.

We theoretically investigate the simultaneous formation and stable propagation of slow optical soliton pairs in semiconductor quantum dots with a four-level biexciton-exciton cascade configuration. Owing to the destructive interference set up by two continuous wave control fields that couple to a biexciton state, the linear as well as nonlinear dispersion can be dramatically enhanced simultaneously with the absorptions of two weak probe fields being almost suppressed. These results reveal that the detrimental distortions of the two weak-pulsed probe fields due to dispersion effects can be well balanced by the self-phase modulation effect under very low input light intensity, which leads to the slow temporal optical soliton pairs with matched group velocity and amplitude. We also show that the propagation of slow optical solitons can be strongly modified by the biexciton coherence.

We present a combined experimental-theoretical study of the energy loss of C and O ions in Zn in the energy range 50–1000 keV/amu. This contribution has a double purpose, experimental and theoretical. On the experimental side, we present stopping power measurements that fill a gap in the literature for these projectile-target combinations and cover an extended energy range, including the stopping maximum. On the theoretical side, we make a quantitative test on the applicability of various theoretical approaches to calculate the energy loss of heavy swift ions in solids. The description is performed using different models for valence and inner-shell electrons: a nonperturbative scattering calculation based on the transport cross section formalism to describe the Zn valence electron contribution, and two different models for the inner-shell contribution: the shellwise local plasma approximation (SLPA) and the convolution approximation for swift particles (CasP). The experimental results indicate that C is the limit for the applicability of the SLPA approach, which previously was successfully applied to projectiles from H to B. We find that this model clearly overestimates the stopping data for O ions. The origin of these discrepancies is related to the perturbative approximation involved in the SLPA. This shortcoming has been solved by using the nonperturbative CasP results to describe the inner-shell contribution, which yields a very good agreement with the experiments for both C and O ions.

Using the spatial-temporal symmetry principle we developed recently, we propose an effective scheme for even-harmonics generation in coupled quantum dots. The relative intensity of odd and even harmonic components in the emission spectrum can be controlled by tuning the dipole couplings among the dots, which can be realized in experiments by careful design of the nanostructures. In particular, pure $2n$th harmonics and $(2n+1)$th harmonics (where $n$ is an integer) can be generated simultaneously with polarizations in two mutual perpendicular directions in our systems. An experimental design of the coupled dots system is presented.

Device-independent quantum key distribution does not need a precise quantum mechanical model of employed devices to guarantee security. Despite its beauty, it is still a very challenging experimental task. We compare a recent proposal by Gisin et al. [Phys. Rev. Lett. 105, 070501 (2010)] to close the detection loophole problem with that of a simpler quantum relay based on entanglement swapping with linear optics. Our full-mode analysis for both schemes confirms that, in contrast to recent beliefs, the second scheme can indeed provide a positive key rate which is even considerably higher than that of the first alternative. The resulting key rates and required detection efficiencies of approximately 95% for both schemes, however, strongly depend on the underlying security proof.

We report on the successful extension of production of a Bose-Einstein condensate (BEC) to a rare atomic species. Despite its low natural abundance of 0.13%, ${}^{168}$Yb is directly evaporatively cooled down to a BEC. Our successful demonstration encourages attempts to obtain quantum gases of radioactive atoms, which extends the possibility of quantum many-body physics and precision measurement. Moreover, a stable binary mixture of ${}^{168}$Yb BEC and ${}^{174}$Yb BEC is successfully formed.

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schrödinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a “sudden death.” In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.

We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator $W\left(z\right)$ are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations $z_{\alpha }\ne z_{\beta }$, and since the orthogonality relation does not generally hold at different values of $z$, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the $W\left(z\right)$ projectors regardless of the number of poles. Such a possibility occurs when $W\left(z\right)$, and hence its eigenvectors, is independent of $z$, which corresponds to the Markovian limit of the coupling to the continuum spectrum.

In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A 76, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.

We have studied the relativistic effect on the spin state of a massive Dirac particle under an arbitrary Lorentz transformation using the Foldy-Woutheysen representation. We have obtained the transformation matrix from the state of a massive Dirac particle with an initial momentum to a state with a transformed momentum under an arbitrary homogeneous Lorentz transformation. We have shown moving observers obtain the consistent monotonic behavior between the concurrence and the maximum value of Bell parameter for the spin state of the pair of particles.

We present measurements of the excitation spectra from the 2$p^5$3$p$ [5/2]${}_{3,2}$ levels in neon using two-step laser excitation and ionization in conjunction with an optogalvanic detection in dc and rf discharge cells. The 2$p^5$3$p$ [5/2]${}_{3,2}$ intermediate levels have been approached via the collisionally populated 2$p^5$3$s$ [3/2]${}_2$ metastable level. The Rydberg series 2$p^5$(${}^2$$P_{3/2}$)$\mathit{nd}$ [7/2]${}_4$ (12 ⩽ $n$ ⩽ 44), 2$p^5$(${}^2$$P_{3/2}$)$\mathit{ns}$ [3/2]${}_2$ (13 ⩽ $n$ ⩽ 35) and the parity forbidden transitions 2$p^5$(${}^2$$P_{3/2}$)$\mathit{np}$ [5/2]${}_3$ (13 ⩽ $n$ ⩽ 19) have been observed from the 2$p^5$3$p$ [5/2]${}_3$ level, whereas the 2$p^5$(${}^2$$P_{3/2}$)$\mathit{nd}$ [7/2]${}_3$ (12 ⩽ $n$ ⩽ 44), 2$p^5$(${}^2$$P_{3/2}$)$\mathit{ns}$ [3/2]${}_2$ (13 ⩽ $n$ ⩽ 35), and 2$p^5$(${}^2$$P_{1/2}$)$\mathit{nd}$′ [5/2]${}_3$ (9 ⩽ $n$ ⩽ 12) Rydberg series have been observed from the 2$p^5$3$p$[5/2]${}_2$ level in accordance with the Δ$J$ $=$ Δ$K$ = ± 1 selection rules. The photoionization cross sections from the 2$p^5$3$p$ [5/2]${}_3$ intermediate level have been measured at eight ionizing laser wavelengths (399, 395, 390, 385, 380, 370, 364, and 355 nm) and that from the 2$p^5$3$p$ [5/2]${}_2$ level at 401.8 nm. These measurements are in excellent agreement with the experimental values reported in the literature, while the experimental data lie much below the theoretically calculated photoionization cross sections curve.

We present an ab initio approach to solving the time-dependent Schrödinger equation to treat electron- and photon-impact multiple ionization of atoms or molecules. It combines the already known time-scaled coordinate method with a high-order time propagator based on a predictor-corrector scheme. In order to exploit in an optimal way the main advantage of the time-scaled coordinate method, namely, that the scaled wave packet stays confined and evolves smoothly toward a stationary state, of which the squared modulus is directly proportional to the electron energy spectra in each ionization channel, we show that the scaled bound states should be subtracted from the total scaled wave packet. In addition, our detailed investigations suggest that multiresolution techniques like, for instance, wavelets are the most appropriate ones to represent the scaled wave packet spatially. The approach is illustrated in the case of the interaction of a one-dimensional model atom as well as atomic hydrogen with a strong oscillating field.