An approximation to the exchange-hole density is proposed for the evaluation of the exact exchange energy in electronic structure calculations within the density-functional theory and the Kohn-Sham scheme. Based on the localized nature of density matrix, the exchange hole is divided into the short-range (SR) and long-range (LR) parts by using an adequate filter function, where the LR part is deduced by matching of moments with the exactly calculated SR counterpart, ensuring the correct asymptotic $-1/r$ behavior of the exchange potential. With this division, the time-consuming integration is truncated at a certain interaction range, largely reducing the computation cost. The total energies, exchange energies, exchange potentials, and eigenvalues of the highest-occupied orbitals are calculated for the noble-gas atoms. The close agreement of the results with the exact values suggests the validity of the approximation.

Energy-dependent phenomena for positron-lithium scattering in the energy region 1.45–4.5 eV have been investigated using the momentum-space coupled-channels optical method. Positions and widths of resonance states with angular momenta of $J=0$–2 and several threshold behaviors have been obtained. The present results are compared with other theoretical calculations.

We experimentally demonstrate classical-optical logic operations in a solid-state memory, coherently driven by variants of stimulated Raman adiabatic passage (STIRAP). Cyclic transfer of atomic populations permits the implementation of a flip-flop or xor gate, with up to eight optical input operations. Observation of stimulated emission as an additional output channel enables the setup of a STIRAP-driven full adder for three optical input bits (or two input bits and a memory bit).

We investigate the tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at $T=0$, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum $q$, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low-energy limit, the transverse spin wave transmits perfectly only when the momentum $k$ of this mode coincides with $\pm q$. At $k=\pm q$, the wave function of this spin wave has the same form as the condensate wave function in the current-carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of the supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin-rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BEC’s, as well as the anomalous tunneling phenomenon in Bose superfluids.

We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical microcavity. The single atom strongly couples to the high-order transverse vacuum TEM${}_{10}$ mode, instead of the usual TEM${}_{00}$ mode, and the parameters of the system are $(g_{10},\kappa ,\gamma )=2\pi \times (20.5,2.6,2.6)\hspace{0.5em}\text{MHz}$. The atoms simply fall down freely from the magneto-optical trap into the cavity modes, and the trajectories of the single atoms are linear. The transmission spectra of atoms passing through the TEM${}_{10}$ mode are detected by single-photon counting modules and are well fitted. Thanks to the tilted cavity transverse TEM${}_{10}$ mode, which is inclined to the vertical direction $~$${45}^{°}$, it helps us to eliminate the degenerate trajectory of the single atom falling through the cavity and to obtain a unique atom trajectory. An atom position with a high precision of $0.1\hspace{0.5em}\mu \text{m}$ in the off-axis direction (axis $y$) is obtained, and a spatial resolution of $5.6\hspace{0.5em}\mu \text{m}$ is achieved in a time interval of $10\hspace{0.5em}\mu \text{s}$ along the vertical direction (axis $x$). The average velocity of the atoms is also measured from the atom transits, which determines independently the temperature of the atoms in a magneto-optical trap, $186\pm 19\hspace{0.5em}\mu \text{K}$.

We present an experiment of nonclassical interference between an intrinsically pure heralded single-photon state and a weak coherent state. Our experiment demonstrates that, without the use of bandpass filters, spectrally pure single photons can have high-visibility ($89.4\pm 0.5\%$) interference with photons from a weak coherent field. Our scheme lays the groundwork for future experiments requiring quantum interference between photons in nonclassical states and those in coherent states.

The origin of Hund’s multiplicity rule in the low-lying excited states of the helium atom has been studied by considering the two-dimensional helium atom. The internal part of the full configuration interaction wave functions for the $(2s)$ and $(2p)$ singlet-triplet pairs of states has been extracted and visualized in the three-dimensional internal space ($r_1$,$r_2$, ${\varphi }_{-}$). The internal wave function of the singlet states without electron repulsion has a significant probability around the origin of the internal space while the corresponding probability of the triplet wave function is negligible in this region due to the presence of a Fermi hole. The electron-electron repulsion potential has been visualized also in the internal space. It manifests itself by three striking poles penetrating exactly into the spatial region defined by the Fermi hole. Because of the existence of these strong potential poles in the vicinity of the Fermi hole a major part of the singlet probability migrates out of this region. In contrast, the corresponding triplet wave function is less affected by these poles due to the presence of the Fermi hole. The singlet probability is shown to migrate from its original region close to the origin to a region far away where either $r_1$ or $r_2$ are large. This results in a more diffuse electron density distribution and a smaller electron repulsion energy of the singlet state than of the corresponding triplet state. The mechanism of the evolution of the singlet probability toward the region of large $r_i$ ($i$ $=$1, 2) in the presence of the electron repulsion potential has been rationalized on the basis of a new concept called $\mathrm{conjugate}\hspace{0.5em}\mathrm{Fermi}\hspace{0.5em}\mathrm{hole}$.

Spectroscopy of atomic spin noise allows the determination of many sample properties such as energy-level structures and transverse-spin relaxation rates without the need to drive the system away from equilibrium with applied fields. Analysis of noise measurements can also reveal the processes that limit the sensitivity of a measured signal. Standard methods for spectroscopic noise measurements in atomic vapors rely on far-off-resonant optical probing. We present a method for investigating spin noise with a probe beam frequency relatively close to resonance and show how the back action of the probe on the atomic state can be subtracted from the recorded noise spectra. We verify this method experimentally by showing noise data that scale with the square root of the number of atoms, after the probe back action has been properly subtracted.

The Casimir force between a diamagnetic plate and a magnetodielectric plate at finite temperature is considered. Under the condition that the permittivity of the magnetodielectric plate is sufficiently small, we show that the diamagnetic property dominantly determines the asymptotic behavior of the repulsive Casimir force for large separations. On the basis of this simple property, we present numerical results showing that if an effective permeability of a superconductor is much less than one, its diamagnetic response can be indirectly detected by measuring the Casimir force.

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed $A\hspace{0.5em}{}^1{\Sigma }_u^{+}$ and $b\hspace{0.5em}{}^3{\Pi }_u$ states of the cesium dimer. The results are based on data from several sources. Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used some time ago in the Laboratoire Aimé Cotton primarily to study the $X\hspace{0.5em}{}^1{\Sigma }_g^{+}$ state. More recent work at Tsinghua University provides information from moderate resolution spectroscopy on the lowest levels of the $b\hspace{0.5em}{}^3{\Pi }_{0u}^{\pm }$ state as well as additional high-resolution data. From Innsbruck University, we have precision data obtained with cold Cs${}_2$ molecules. Recent data from Temple University was obtained using the optical-optical double resonance polarization spectroscopy technique, and finally, a group at the University of Latvia has added additional LIF FTS data. In the Hamiltonian matrix, we have used analytic potentials (the expanded Morse oscillator form) with both finite-difference (FD) coupled-channel and discrete variable representation (DVR) calculations of the term values. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with ab initio results from Temple and Moscow State universities.

We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (${}^7\Sigma$) in collisions with ${}^3\mathrm{He}$. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with $\Delta M_j>2$ give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.

We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in $1+1$, $2+1,$ and $3+1$ dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to $(2+1)$-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

We investigate the superfluid-insulator quantum phase transition in a disordered one-dimensional Bose gas in the mean-field limit by studying the probability distribution of the density. The superfluid phase is characterized by a vanishing probability to have zero density, whereas a nonzero probability marks the insulator phase. This relation is derived analytically and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments. When a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.

We study theoretically and experimentally the propagation of light beams in chiral nematic liquid crystals. Despite the rather complex refractive index distribution of these crystals, their reorientational nonlinearity can compensate for diffraction, leading to robust solitonlike beams propagating along helical trajectories. We demonstrate that, due to a symmetry-breaking instability of the liquid crystal structure, these beams undergo abrupt switching and bistability, features that are of potential interest for applications to all-optical signal processing.

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multimode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beam splitters, in a transparent manner. For single-mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beam splitter, these conditions turn exactly into signatures of negativity under partial transpose (NPT) entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beam-splitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beam-splitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

In many architectures for fault-tolerant quantum computing universality is achieved by a combination of Clifford group unitary operators and preparation of suitable nonstabilizer states, the so-called magic states. Universality is possible even for some fairly noisy nonstabilizer states, as distillation can convert many noisy copies into fewer purer magic states. Here we propose protocols that exploit multiple species of magic states in surprising ways. These protocols provide examples of previously unobserved phenomena that are analogous to catalysis and activation well known in entanglement theory.

One can uniquely identify an unknown state of a quantum system $S$ by measuring a “quorum” consisting of a complete set of noncommuting observables. It is also possible to determine the quantum state by repeated measurements of a single and factorized observable, when the system $S$ is coupled to an assistant system $A$ whose initial state is known. This is because that the redistribution of the information about the unknown quantum state into the composite system $A+S$ results in a one-to-one mapping between the unknown density matrix elements and the probabilities of the occurrence of the eigenvalues of a single, factorized observable of the composite system. Here we focus on quantum state tomography of high-dimensional quantum systems (e.g., a spin greater than 1/2) via a single observable. We determine the condition for the best determination and the upper bound to achieve the most robust measurements. From the experimental view we require a suitable interaction Hamiltonian to maximize the measure efficiency. For this we numerically investigate a three-level system. Moreover, the error analysis for the different-dimensional quantum states shows that the present measurement method is still very effective in determining an unknown state of a high-dimensional quantum system.