We revisit the criterion of multiparticle entanglement based on the overlaps of a given quantum state $\rho$ with maximally entangled states. For a system of m particles, each with N distinct states, we prove that $\rho$ is m-particle negative partial transpose entangled, if there exists a maximally entangled state $|\mathrm{MES}〉,$ such that $〈\mathrm{MES}|\rho |\mathrm{MES}〉>1/N.\mathrm{}$ While this sufficiency condition is weaker than the Peres-Horodecki criterion in all cases, it applies to multi-particle systems, and becomes especially useful when the number of particles (m) is large. We also consider the converse of this criterion and illustrate its invalidity with counter examples.

A protocol for quantum secure direct communication using blocks of Einstein-Podolsky-Rosen (EPR) pairs is proposed. A set of ordered N EPR pairs is used as a data block for sending secret message directly. The ordered N EPR set is divided into two particle sequences, a checking sequence and a message-coding sequence. After transmitting the checking sequence, the two parties of communication check eavesdropping by measuring a fraction of particles randomly chosen, with random choice of two sets of measuring bases. After insuring the security of the quantum channel, the sender Alice encodes the secret message directly on the message-coding sequence and sends them to Bob. By combining the checking and message-coding sequences together, Bob is able to read out the encoded messages directly. The scheme is secure because an eavesdropper cannot get both sequences simultaneously. We also discuss issues in a noisy channel.

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a $\mathrm{}(2n+1)\mathrm{}\times \mathrm{}(2n+1)\mathrm{}$ binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.

We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and “small” coherent superposition resource states.

In this paper we propose a scheme for creating a three photons Greenberger-Horne-Zeilinger-type (GHZ) state using only linear optics elements and single-photon detectors. We furthermore generalize the scheme for producing any GHZ-like state of n photons. The input state of the scheme consists of a nonentangled state of n photons. Experimental aspects regarding the implementation of the scheme are presented. Finally, the role of such schemes in quantum information processing with photons is discussed.

We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off-resonant optical lattice. Raman lasers provide the “Josephson” tunneling, and the collision interaction between atoms represent the “capacitive” couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single-qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.

The quantal density-functional theory (Q-DFT) of nondegenerate excited-states maps the pure state of the Schrödinger equation to one of noninteracting fermions such that the equivalent excited state density, energy, and ionization potential are obtained. The state of the model S system is arbitrary in that it may be in a ground or excited state. The potential energy of the model fermions differs as a function of this state. The contribution of correlations due to the Pauli exclusion principle and Coulomb repulsion to the potential and total energy of these fermions is independent of the state of the S system. The differences are solely a consequence of correlation-kinetic effects. Irrespective of the state of the S system, the highest occupied eigenvalue of the model fermions is the negative of the ionization potential. In this paper we demonstrate the state arbitrariness of the model system by application of Q-DFT to the first excited singlet state of the exactly solvable Hookean atom. We construct two model S systems: one in a singlet ground state ${(1s}^2),$ and the other in a singlet first excited state $\mathrm{}\left(1s2s\right).$ In each case, the density and energy determined are equivalent to those of the excited state of the atom, with the highest occupied eigenvalues being the negative of the ionization potential. From these results we determine the corresponding Kohn-Sham density-functional theory (KS-DFT) “exchange-correlation” potential energy for the two S systems. Further, based on the results of the model calculations, suggestions for the KS-DFT of excited states are made.

X-ray absorption spectrum of cesium vapor in the K-edge region is measured in a stainless steel cell. The spectrum is free of the x-ray absorption fine structure signal and shows small features analogous to those in the spectrum of the neighbor noble gas Xe. Although the large natural width of the K vacancy $(>\mathrm{}10\mathrm{}\mathrm{eV})$ washes out most of the details, fingerprints of multielectron excitations can be recognized at energies close to Dirac-Fock estimates of doubly excited states $1s4(d,p,s)\mathrm{}$ and $1s3(d,p).$ Among these, the $1s3p$ excitation 1000 eV above the K edge in both spectra is the deepest double excitation observed so far. Within the K-edge profile, some resolution is recovered with numerical deconvolution of the spectra, revealing the coexcitation of the $5(p,s)\mathrm{}$ electrons, and even the valence $6s$ electron in Cs. As in homologue elements, three-electron excitations, either as separate channels or as configuration admixtures are required to explain some spectral features in detail.

We report the calculation of the interspecies scattering length for the sodium-rubidium (Na-Rb) system. We present improved hybrid potentials for the singlet $X^1\Sigma {}^{+}$ and triplet $a^3{\Sigma }^{+}$ ground states of the NaRb molecule, and calculate the singlet and triplet scattering lengths $a_s$ and $a_t$ for the isotopomers ${}^{23}{\mathrm{Na}}^{87}\mathrm{Rb}$ and ${}^{23}{\mathrm{Na}}^{85}\mathrm{Rb}.$ Using these values, we assess the prospects for producing a stable two-species Bose-Einstein condensate in the Na-Rb system.

Calculations of the photoelectron angular distribution from atoms confined in a fullerene cage have been performed using a recently developed theory of inner-shell near-threshold molecular photoionization. Trends uncovered in the modification of near-threshold photoelectron angular distribution of the $\mathrm{A}@{\mathrm{C}}_{60}$ molecules as a function of the displacement of the confined atom from the center of the ${\mathrm{C}}_{60}$ cage are demonstrated. Specific results for Li $1s$ from $\mathrm{Li}@{\mathrm{C}}_{60},$ and Ar $1s,$ $2s,$ and $3s$ from $\mathrm{Ar}@{\mathrm{C}}_{60}$ molecules are presented. In addition, the situation where the encapsulated atom lies in the vicinity of the center of one of the carbon hexagons of ${\mathrm{C}}_{60}$ and also when it is displaced beyond the fullerene cage, has been studied. It has been found that the photoelectron spectra are extremely sensitive, both qualitatively and quantitatively, to even a small displacement of the confined atom from the center of the cage. The existence of the ${\mathrm{C}}_{60}$ molecule even affects the atom’s photoelectron angular distribution when it is a significant distance away.

We present a first-principles study of ionization and high-order harmonic generation by benzene aligned in the polarization plane of a short circularly polarized laser pulse. Time-dependent density-functional theory within the adiabatic local-density approximation is employed to describe the 30 valence-electron dynamics in three dimensions. The multielectron approach enables us to study the effect of very strong laser fields, ${10}^{14}–{10}^{15}{\mathrm{W}\mathrm{}\mathrm{cm}}^{-2},$ where multiple ionization and high-order harmonic generation interplay. Large ionization currents are formed, causing ionization of 1–4 electron charges, while strong high-order harmonic generation is observed. The well-known recollision mechanism of high-order harmonic generation plays a part for moderate laser intensities but is fully suppressed for strong laser fields. The harmonic generation spectra are characterized by two distinguishable plateaus, where the structure of the first plateau is dominated by the $6k\pm 1$ $(k=0,1,\dots )$ selection rule. The number of harmonics in the second plateau is insensitive to the duration of the pulse. The peaks appear in pairs or in threesomes, depending on the pulse duration.

We present a detailed analysis of short-pulse detachment processes using few-cycle pulses with the aim of demonstrating means for controlling such processes. We first generalize the standard Keldysh-type formalism for laser-target interactions (in which final-state interaction between the detached electron and the core is ignored) to include the possibility that the vector potential is nonzero at the end of the interaction between a short laser pulse and the target. With this formalism in hand, we examine the effects of half-cycle pulses (HCPs) on detachment of the prototypical negative ion ${\mathrm{H}}^{-},$ and show that detachment by pairs of oppositely-directed (i.e., “bidirectional”) HCPs allows one to understand the interference pattern seen in detachment by single-cycle pulses. We also examine in detail the transition from few-cycle pulses to many-cycle pulses as various experimental parameters are varied, i.e., the laser frequency, the laser-pulse duration, and the absolute phase of the carrier wave with respect to the pulse envelope. Finally, we examine the use of pairs of single-cycle pulses, differing in phase by $180°,$ together with a modest static electric field to control coherently the extent of ${\mathrm{H}}^{-}$ detachment as the delay between the pulses is varied. Our simulations show that this scheme allows one to modulate the ${\mathrm{H}}^{-}$ detachment probability by $\sim 30\%,$ which is far higher than has been achieved for similar schemes using many-cycle pulses. Although our results are presented specifically for ${\mathrm{H}}^{-},$ they apply to detachment of any negative ion having s-state valence electrons; in addition, the qualitative information on half-cycle, single-cycle, and few-cycle pulse interactions should be generally applicable to short-pulse detachment or ionization of other target atoms or ions.

We solve exactly the three-dimensional time-dependent Schrödinger equation for the ${\mathrm{H}}_2^{+}$ molecular ion in a combination of intense short laser pulses and static magnetic fields using a newly developed adaptive grid method. This allows for a study of the control of high-order harmonic generation in molecules by various orientations of the magnetic and laser fields in order to control electron recollision with nuclei. In particular, we find regimes of pure even harmonic or even and odd harmonic generation for particular field and frequency configurations. Furthermore, magnetic fields are found to extend harmonic generation plateaus to higher order as a result of further nonlinear coupling between charges and fields.

We investigate rotational properties of a system of attractive bosons confined in a one-dimensional torus. Two kinds of ground states, uniform-density and bright soliton, are obtained analytically as functions of the strength of interaction and of the rotational frequency of the torus. The quantization of circulation appears in the uniform-density state, but disappears upon formation of the soliton. By comparing the results of exact diagonalization with those predicted by the Bogoliubov theory, we show that the Bogoliubov theory is valid at absolute zero over a wide range of parameters. At finite temperatures we employ the exact diagonalization method to examine how thermal fluctuations smear the plateaus of the quantized circulation. Finally, by rotating the system with an axisymmetry-breaking potential, we clarify the process by which the quantized circulation becomes thermodynamically stabilized.

We numerically solve the time-dependent Gross-Pitaevskii equation (GPE) that describes the evolution of an elongated dilute repulsive atomic Bose-Einstein condensate trapped in a one-dimensional (1D) nonharmonic potential. We find that the gray solitons, which are propagative solutions of the 1D GPE, traveling at an initial constant velocity, smaller than the speed of sound, oscillate through the trapped condensate, but that this oscillatory motion is accompanied by a spontaneous emission of small sound waves. By examining the gray soliton trajectory and its velocity in the trapped repulsive Bose-Einstein condensate, we show that the oscillatory motion is uniform and nondissipative except at the returning points of the gray soliton, where it exhibits a slight radiative acceleration (antidamping). Our numerical results are in good agreement with previous theoretical predictions, but show the need to take radiation emission into account.

We have developed a three-level atom interferometer using three-level atoms coupled with bichromatic fields in order to investigate the phase information between two excited states. First, we presented a theoretical description of the interaction of three-level atoms with bichromatic fields based on single-transition operators. Using the time evolution of a wave function, the equations of the interference fringes and the visibility were derived and calculated for several types of the three-level atom interferometers with bichromatic fields. Optimum excitation conditions were evaluated. Next, several types of three-level atom interferometers were demonstrated experimentally using a thermal calcium atomic beam with two Zeeman substates of $m=1\mathrm{}$ and $m=-1$ in the long-lived excited state coupled with bichromatic resonant fields between the ground state and the excited states. The behaviors of the interference fringes were compared among them along with the calculated results. The three-level atom interferometer excited by two bichromatic laser beams separated in space was found to produce the largest visibility among them when the excitation power of each frequency component was the same.

Spin squeezing of an ensemble of N atoms in a high-Q cavity is enhanced by continuous measurement of photons in the cavity. A degree of spin squeezing proportional to $N^{-1/3}$ is achieved as a quasi-steady-state over a broad set of initial states of atoms and photons. Our method of spin squeezing is robust against the imperfect photodetection efficiency in current experiments.

The production of conditional quantum states and quantum operations based on the result of measurement is now seen as a key tool in quantum information and metrology. We propose a different type of photon number detector. It functions nondeterministically, but when successful, it has high fidelity. The detector, which makes use of an n-photon auxiliary Fock state and high efficiency homodyne detection, allows a tunable trade-off between fidelity and probability. By sacrificing probability of operation, an excellent approximation to a photon-number detector is achieved.

In an earlier study, the exchange energy density ${\epsilon }_x\mathrm{}\left(r\right)\mathrm{}$ has been calculated analytically for Ne-like atomic ions in the nonrelativistic limit of large atomic number Z. Here, though now by numerical methods based on the optimized exchange potential approximation, corresponding results are obtained for $V_x\mathrm{}\left(r\right)\mathrm{}$ for such ten-electron ions at large Z. The approach to the bare Coulomb limiting form of the $1/Z$ expansion is considered in some detail, as are corrections to the Slater potential $V_x^{\mathrm{Sl}}\mathrm{}\left(r\right),$ given in terms of the exchange energy density and ground-state density $\rho \mathrm{}\left(r\right)\mathrm{}$ by $2{\epsilon }_x\mathrm{}\left(r\right)/\rho \mathrm{}\left(r\right).$