We report the observation of the ${}^{87}\mathrm{Rb}$ ground-state hyperfine transition with a subcollisional linewidth performed in a cell with buffer gas. The transition is observed as a coherent-population-trapping maser-emission profile excited by means of a Λ interaction scheme in the high-atomic-density regime. A theoretical explanation of the phenomenon is given in good agreement with the observed linewidth behavior.

This paper proposes a simple scheme for quantum-bit commitment that is secure against individual particle attacks, where a sender is unable to use quantum logical operations to manipulate multiparticle entanglement for performing quantum collective and coherent attacks. Our scheme employs a cryptographic quantum communication channel defined in a four-dimensional Hilbert space and can be implemented by using single-photon interference. For an ideal case of zero-loss and noiseless quantum channels, our basic scheme relies only on the physical features of quantum states. Moreover, as long as the bit-flip error rates are sufficiently small (less than a few percent), we can improve our scheme and make it fault tolerant by adopting simple error-correcting codes with a short length. Compared with the well-known Brassard-Crepeau-Jozsa-Langlois 1993 (BCJL93) protocol, our scheme is mathematically far simpler, more efficient in terms of transmitted photon number, and better tolerant of bit-flip errors.

Classical and quantum survival probabilities are compared for a truncated radial oscillator undergoing impulsive interactions with periodic laser pulses represented here as kicks. The system is truncated in the sense that the harmonic potential is made valid only within a finite range; the rest of the space is treated as a perfect absorber. Exploring extended values of the parameters of this model [Phys. Rev. A 63, 052721 (2001)], we supplement discussions on classical and quantum features near resonances. The classical system proves to be quasi-integrable and preserves phase-space area despite the momentum transfered by the kicks, exhibiting simple yet rich phase-space features. A geometrical argument reveals quantum-classical correspondence in the locations of minima in the paired survival probabilities while the “ionization” rates differ due to quantum tunneling.

We consider a two-component Bose-Einstein condensate in two spatially localized modes of a double-well potential, with periodic modulation of the tunnel coupling between the two modes. We treat the driven quantum field using a two-mode expansion and define the quantum dynamics in terms of the Floquet Operator for the time periodic Hamiltonian of the system. It has been shown that the corresponding semiclassical mean-field dynamics can exhibit regions of regular and chaotic motion. We show here that the quantum dynamics can exhibit dynamical tunneling between regions of regular motion, centered on fixed points (resonances) of the semiclassical dynamics.

We show that the operator $U=\exp \left[-{ir(Q}_1{P}_2{+Q}_2{P}_3{+Q}_3{P}_1\right)]$ is a three-mode squeezing operator for the three-mode quadratures exhibiting the standard squeezing, the corresponding squeezed vacuum state in three-mode Fock space is derived by virtue of the technique of integration within ordered product of operators. The entanglement involved in such a state is explained. The optical network for producing the three-mode squeezed state is proposed.

We demonstrate, theoretically and experimentally, that statistical mixtures of the vacuum state $|0〉$ and the single-photon Fock state $|1〉$ are nonclassical according to the Vogel criterion [W. Vogel, Phys. Rev. Lett. 84, 1849 (2000)], regardless of the vacuum fraction. The ensembles are synthesized via conditional measurements on biphotons generated by means of parametric down conversion, and their quadrature statistics are measured using balanced homodyne detection. A comparative review of various quantum state nonclassicality criteria is presented.

In this paper, we have calculated the values of the ${\mathrm{C}}_6$ coefficients and the anisotropy parameters $\gamma$ of the leading term of the van der Waals interactions between molecular hydrogen and alkali-metal atoms from Li to Fr. The uncertainties in our results are less than $2\%.$

Classical calculations are used to describe the dynamics of the electron capture to the continuum (ECC) cusp formation in ${\mathrm{H}}^{+}+\mathrm{He}$ collisions. We illustrate the frontier character of the ECC electrons between capture and ionization, and confirm that it is a temporary capture, through projectile focusing, that is responsible for the ECC cusp. Furthermore, the cusp is not a divergence smoothed by the experiment, and is slightly shifted from the impact-velocity value because of the residual pull from the target after ionization. This shift is larger the smaller the nuclear velocity.

We investigate the coupled atom-molecule Bose-Einstein condensate, as would ensue in an attempt to control the scattering length by means of either the Feshbach resonance or coherent photoassociation. In a mean-field model with a photoassociative coupling between the condensates, we demonstrate that the system is structurally stable. The sign of the effective scattering length notwithstanding, neither condensate will collapse.

Two-photon amplification and lasing in laser-driven potassium atoms is investigated theoretically using a rigorous model that takes into account the hyperfine level structure of the atoms for arbitrary intensity drive and lasing fields. The model correctly predicts most features of the recent experiments, such as the characteristics of the multiphoton gain resonances and the two-photon laser emission intensity and line shape. In addition, it constitutes a new tool for exploring behaviors that are difficult to address experimentally, such as interference effects between different quantum pathways. In contrast to single-photon lasers, the laser emission line shape is frequency pushed and has the form of a closed curve composed of a stable and an unstable branch.

Quantum search is a quantum-mechanical technique for searching N possibilities in only $\sqrt{N}$ steps. A similar algorithm applies in a purely classical setting when there are N oscillators, one of which is of a different resonant frequency. We could identify which one this is by measuring the oscillation frequency of each oscillator, a procedure that would take about N cycles. We show, how by coupling the oscillators together in a very simple way, it is possible to identify the different one in only $\sqrt{N}$ cycles. In case there are multiple oscillators of a different frequency, we can estimate the number of these in a time which is the square root of that required by the sampling method. The analog also leads to some energy routing algorithms for mechanical systems.

The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of $4^N-1$ Pauli operators may be partitioned into $2^N+1\mathrm{}$ distinct subsets, each consisting of $2^N-1$ internally commuting observables. Furthermore, each such partitioning defines a unique choice of $2^N+1\mathrm{}$ mutually unbiased basis sets in the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.

We show that quantum entanglement has a very close classical analog, namely, secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogies follow. In particular, teleportation is analogous to the one time pad, the concept of “pure state” exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single-copy-entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement, it allows one to identify those aspects of entanglement that are uniquely quantum mechanical.

We propose an alternative concept for a scalable spin quantum computer that combines aspects of other proposals with the advantageous features of endohedral fullerenes. The key advantages are that electron spins instead of nuclear spins are used and that the manipulation of fullerene molecules is fairly easy. Qubits are set and read out via pulsed electron-spin resonance. Addressing is provided by local magnetic fields or field gradients $(A$ gate). The qubit-qubit interaction is mediated by magnetic dipolar coupling and can be controlled via the direction of the magnetic field with respect to the distance vector of the qubits $(J$ gate). Molecular as well as solid-state architectures are discussed.

A beam splitter is a simple, readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. We conjecture that this is a general property of beam splitters: Nonclassicality of the inputs is a necessary condition for entangling fields in a beam splitter.

High-resolution angle-resolved photoabsorption spectra of HBr below the Br $3d$ ionization thresholds were recorded in the total ion yield. By applying adequate selection rules for excitations from core holes with a strong spin-orbit interaction, we demonstrate for the ${3d}_{{j,m}_j}^{-1}\mathrm{nl}\lambda$ states that this technique is a powerful tool to study the multiplet splitting of the Rydberg states into the different sublevels $M_j.$ We report a multiplet splitting of $\cong 50\hspace{0.5em}\mathrm{meV}$ between the $M_j=1\mathrm{}$ and $0^{+}$ substates of the ${3d}_{5/2,1/2}^{-1}5s\sigma$ and ${3d}_{3/2,1/2}^{-1}5s\sigma$ excitations. As a consequence of this observation, an assignment of the photoabsorption spectrum different to those of earlier studies is derived in the low-energy region. In addition, the orientation parameter ${\beta }_m$ is derived from the spectra.

An algorithm was recently presented to utilize emerging time-dependent probability density data to extract molecular potential-energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. In addition, results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double-well system to illustrate the various points.

An asymptotically adjusted self-consistent $\alpha$ $\left(\mathrm{AASC}\alpha \right)$ method is advanced for the purpose of constructing an accurate orbital-dependent local exchange potential with correct asymptotic behavior. This local potential is made up of the Slater potential plus an additional term containing a multiplicative parameter ${\alpha }_x$ (a self-consistently determined orbital functional) times a local response potential that is approximated using standard exchange-energy functionals. Applications of the $\mathrm{AASC}\alpha$ functionals to diatomic molecules yield significantly improved total, exchange, and atomization energies that compare quite well, but at a much lower computational cost, with those obtained by the exact orbital-dependent exchange energy treatment [S. Ivanov, S. Hirata, and R. J. Bartlett, Phys. Rev. Lett. 83, 5455 (1999); A. Görling, Phys. Rev. Lett. 83, 5459 (1999)] (in fact, the present results are very close to the Hartree-Fock ones). Moreover, because in the $\mathrm{AASC}\alpha$ method the exchange potential tends toward the correct $(-1/r)$ asymptotic behavior, the ionization potentials approximated by the negative of the highest-occupied-orbital energy have a closer agreement with experimental values than those resulting from current approximate density functionals. Finally, we show that in the context of the present method it is possible to introduce some generalizations to the Gritsenko-van Leeuwen-van Lenthe-Baerends model [O. Gritsenko, R. van Leeuwen, E. van Lenthe, and E. J. Baerends, Phys. Rev. A 51, 1944 (1995)].

A numerical calculation, based on full QED, of the energy shift due to the effect of two-photon exchange in the $1s2s{\hspace{0.5em}}^{1}S$ and ${}^{3}S$ states in heliumlike ions is presented. At low Z, the QED effects are compared with the known analytical $(Z\alpha {)}^3$ contributions, and we find good agreement. The calculations have been performed in the range $Z=10\mathrm{}–92.$ Already in the medium-$Z$ range, the effects beyond the leading $(Z\alpha {)}^3$ order are found to be dominant.

Calculations are reported for positronium (Ps) scattering by atomic hydrogen (H) in the energy range 0–6.5 eV in a coupled-pseudostate approximation in which excitation and ionization channels of both the Ps and the H are taken into account. The approximation contains an accurate representation of the van der Waals coefficient. Results are presented for phase shifts, scattering lengths, effective ranges, and various cross sections including partial wave, total, and ortho-para conversion cross sections. An analysis of the possible spin transitions is provided and the energy of the positronium hydride (PsH) bound state is determined. Substantial differences are found from earlier work within the frozen target approximation, now clearly confirming the importance of target excitation channels. Good agreement is obtained with recent calculations of S-wave phase shifts and scattering lengths using the stabilization method. Convergence to the exact binding energy for PsH appears to be slow. Resonances corresponding to unstable states of the positron orbiting ${\mathrm{H}}^{-}$ are seen in the electronic spin singlet partial waves. The importance of the ${\mathrm{H}}^{-}$ formation channel is discussed.