Cooperative ring exchange is suggested as a mechanism of quantum melting of vortex lattices in a rapidly rotating quasi-two-dimensional atomic Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al. [Phys. Rev. Lett. 56, 873 (1986)] for the fractional quantized Hall effect, we calculate the condition for quantum melting instability by considering large-correlated ring exchanges in a two-dimensional Wigner crystal of vortices in a strong “pseudomagnetic field” generated by the background superfluid Bose particles. BEC may be profitably used to address issues of quantum melting of a pristine Wigner solid devoid of complications of real solids.

In this paper we analyze the steady-state populations and gain lineshape of a V-type three-level atom with a closely spaced excited doublet. The atom is driven by a strong coherent field, a weak probe, and a single broadband squeezed vacuum. We focus our attention in the interplay between the quantum interference and the squeezed field on the probe gain. It is shown that the relative phases between the two coherent fields and the squeezed field play an important role in the optical properties of the atom. Specifically, we find that the probe can experience gain without population inversion for proper values of the parameters characterizing the squeezed field and in the absence of incoherent pumping. The system can be tailored to exhibit multiple dispersion regimes accompanied by negligible gain or absorption over a large bandwidth, a desirable feature for obtaining propagation of pulses with negligible distortion.

We analyze quantum computers which perform Shor’s factoring algorithm, paying attention to asymptotic properties as the number L of qubits is increased. Using numerical simulations and a general theory of the stabilities of many-body quantum states, we show the following: Anomalously fluctuating states (AFSs), which have anomalously large fluctuations of additive operators, appear in various stages of the computation. For large L, they decohere at anomalously great rates by weak noises that simulate noises in real systems. Decoherence of some of the AFSs is fatal to the results of the computation, whereas decoherence of some of the other AFSs does not have strong influence on the results of the computation. When such a crucial AFS decoheres, the probability of getting the correct computational result is reduced approximately proportional to $L^2.$ The reduction thus becomes anomalously large with increasing L, even when the coupling constant to the noise is rather small. Therefore, quantum computations should be improved in such a way that all AFSs appearing in the algorithms do not decohere at such great rates in the existing noises.

Variational and exact estimators for the positron-electron annihilation rate in bound states of systems containing a positron in the framework of quantum Monte Carlo methods are presented. The modification needed to compute the effective number of electrons $Z_{\mathrm{eff}}$ when scattering states are concerned is also discussed. The algorithms are tested against four cases for which close to exact results are available, finding an overall good agreement. The systems are ${\mathrm{Ps}}^{-},$ PsH, and the s-wave scattering component of $e^{+}\mathrm{H}$ and $e^{+}\mathrm{He}.$

We consider a three-level V-type atomic system with the ground state coupled by a laser field to only one of the excited states, and with the two excited states coupled together by a dc field. Although the dipole moments of the two dipole-allowed transitions are assumed perpendicular, we demonstrate that this system emulates to a large degree a three-level system with parallel dipole moments—the latter being a system that exhibits quantum interference and displays a number of interesting features. As examples, we show that the system can produce extremely large values for the intensity-intensity correlation function, and that its resonance fluorescence spectrum can display ultranarrow lines. The dressed states for this system are identified, and the spectral features are interpreted in terms of transitions among these dressed states. We also show that this system is capable of exhibiting considerable squeezing.

Using a ${}^{14}{\mathrm{C}}^{16}{\mathrm{O}}_2$ laser the ${2s}_{1/2}{-2p}_{3/2}$ (fine structure–Lamb shift) transition has been induced in ${}^{14}{\mathrm{N}}^{6+}$ ions trapped in an electron beam ion trap. The transition has been measured to be $835.0\pm 0.5{\mathrm{cm}}^{-1},$ in agreement with QED theory.

The linear response to a space- and time-dependent external disturbance of a system of dilute condensed composite bosons at zero temperature, as obtained from the linearized version of the time-dependent Gross-Pitaevskii equation, is shown to result also from the strong-coupling limit of the time-dependent BCS (or broken-symmetry random-phase) approximation for the constituent fermions subject to the same external disturbance. In this way, it is possible to connect excited-state properties of the bosonic and fermionic systems by placing the Gross-Pitaevskii equation in perspective with the corresponding fermionic approximations.

Recent studies have considered the possibility that the exact ground-state wavefunction from any Hamiltonian with two-particle interactions may be generated from a single finite two-body exponential transformation acting on an arbitrary Slater determinant [Piecuch et al., Phys. Rev. Lett. 90, 113001 (2003)]. Using the Campbell-Baker-Hausdorff relation, we show that it is difficult for the variational minimum of this trial wave function to satisfy the contracted Schrödinger equation which is a necessary and sufficient condition for the wave function to satisfy the Schrödinger equation. A counterexample is presented through the Lipkin quasispin model with 4–50 fermions. When the number of fermions exceeds four, the wave function from a finite two-body exponential transformation is shown to be inexact. If the trial wave function ansatz is extended to include products of finite two-body exponential transformations acting on an arbitrary Slater-determinant reference, then we show that the ansatz includes the exact ground-state wave function from any Hamiltonian with only two-particle interactions. Connections between the two-body exponential transformation of the wave function and recent research on two-body exponential similarity transformations of the Hamiltonian [S.R. White, J. Chem. Phys. 117, 7472 (2002)] are discussed.

The paper describes an experiment aimed at studying muon capture by ${}^3\mathrm{He}$ nuclei in pure ${}^3\mathrm{He}$ and ${\mathrm{D}}_2{+}^3\mathrm{He}$ mixtures at various densities. Energy distributions of protons and deuterons produced via ${\mu }^{-}{+}^3\mathrm{He}\to p+n+n+{\nu }_{\mu }$ and ${\mu }^{-}{+}^3\mathrm{He}\to d+n+{\nu }_{\mu }$ are measured for the energy intervals 10–49 MeV and 13–31 MeV, respectively. Muon capture rates ${\lambda }_{\mathrm{cap}}^p\left(\Delta E_p\right)$ and ${\lambda }_{\mathrm{cap}}^d\left(\Delta E_d\right)$ are obtained using two different analysis methods. The least-squares methods give ${\lambda }_{\mathrm{cap}}^p=(36.7\mathrm{}\pm 1.2){\mathrm{s}}^{-1},$ ${\lambda }_{\mathrm{cap}}^d=(21.3\mathrm{}\pm 1.6){\mathrm{s}}^{-1}.$ The Bayes theorem gives ${\lambda }_{\mathrm{cap}}^p=(36.8\mathrm{}\pm 0.8){\mathrm{s}}^{-1},$ ${\lambda }_{\mathrm{cap}}^d=(21.9\mathrm{}\pm 0.6){\mathrm{s}}^{-1}.$ The experimental differential capture rates, $d{\lambda }_{\mathrm{cap}}^p{(E}_p{)/dE}_p$ and $d{\lambda }_{\mathrm{cap}}^d{(E}_d{)/dE}_d,$ are compared with theoretical calculations performed using the plane-wave impulse approximation with the realistic nearest-neighbor interaction Bonn B potential. Extrapolation to the full energy range yields total proton and deuteron capture rates in good agreement with former results.

Using a scattering length parametrization of the crossover from a BCS state to a Bose-Einstein condensate as well as the local density approximation for the density profile, we calculate the momentum distribution of a harmonically trapped atomic Fermi gas at zero temperature. Various interaction regimes are considered, including the BCS phase, the unitarity limit, and the molecular regime. We show that the relevant parameter which characterizes the crossover is given by the dimensionless combination $N^{1/6}{a/a}_{\mathrm{ho}},$ where N is the number of atoms, a is the scattering length, and $a_{\mathrm{ho}}$ is the oscillator length. The width of the momentum distribution is shown to depend in a crucial way on the value and sign of this parameter. Our predictions can be relevant for experiments on ultracold atomic Fermi gases near a Feshbach resonance.

We theoretically propose a nonperiodic optical superlattice (NOS), in which multiple nonlinear optical parametric processes can be realized simultaneously. The optimal design of the NOS structure is achieved by the combination of stimulated annealing (SA) and genetic algorithm methods. The multiple quasi–phase-matched (QPM) second harmonic generations (SHG’s) in NOS’s are theoretically investigated. The numerical simulations show that NOS’s can be used as a more effective and useful nonlinear optical crystal for multiple nonlinear optical parametric generation.

We propose a simple scheme for the reconstruction of the single-mode cavity field by considering the resonant atom-cavity interaction in the presence of a strong classical field. With the aid of the strong classical field, it is easy to realize the displacement operator for the cavity field correlated to the internal state of the atom. It is shown that the measurement of the population of the lower internal state directly yields the Wigner characteristic function of the cavity field.

We report integral, differential, and momentum-transfer cross sections for elastic scattering of low-energy electrons by ${\mathrm{C}}_4{\mathrm{H}}_6$ isomers, namely, 1,3-butadiene, 2-butyne, and cyclobutene. We use the Schwinger multichannel method with pseudopotentials [M. H. F. Bettega, L. G. Ferreira, and M. A. P. Lima, Phys. Rev. A 47, 1111 (1993)] at the static-exchange approximation to compute the cross sections for energies from 10 to 60 eV. In particular, we discuss the isomer effect, reported by experimental studies for isomers of ${\mathrm{C}}_3{\mathrm{H}}_4$ and ${\mathrm{C}}_4{\mathrm{H}}_6.$ We also calculate the total ionization cross section using the binary-encounter-Bethe model for 2-butyne and 1,3-butadiene, and estimate the inelastic cross section for these two isomers.

The high-energy electron-energy spectra of atoms and atomic ions undergoing direct tunneling or barrier-suppression ionization by superintense linearly polarized femtosecond laser pulse are derived. The Landau-Dykhne adiabatic approximation is used. The new result is the simple analytic expression for the electron momentum spectrum along the polarization axis and along the other directions in the case of the relativistic quiver electron energies. The contribution from the direct tunneling ionization exceeds the contribution from the ionization occurring in the rescattering processes. The energy spectrum is independent of the laser frequency and of the nonrelativistic ionization potential of the atom (atomic ion) considered. The conclusions have been made that (1) the drift electron energy along the polarization axis is much greater than in other directions, (2) the energy distribution depends on the sign of the electron drift momentum along the propagation of laser radiation, and (3) the electron drift energy is the nonrelativistic quantity even when the quiver electron energy has high ultrarelativistic values.

Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom: $e+e+\overrightarrow{p}\mathrm{H}+e)$ in strong magnetic fields. The proton is allowed its full motion whereas the motion of the electron is given by the guiding center approximation. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated anti-hydrogen. When the proton has the same temperature as the electrons, the recombination rate for the more elaborate equations of motion is roughly 60% larger than for the $\overrightarrow{B}\infty$ approximation. The recombination rate decreases as the proton speed approaches the electron thermal speed; the variation of this rate has implications for the directionality of the anti-atoms formed in recent experiments. We report on several properties of the atoms formed by three-body recombination in strong magnetic fields.

A class of silicon carbide cage clusters with two carbon atoms inside the silicon cage and with high stabilities are presented. The theoretical formalism used is Hartree-Fock theory followed by second-order many-body perturbation theory to account for correlation effects, and geometry optimizations at the second-order perturbation theory level are performed without any symmetry constraints. The smallest “cage” is found to be a silicon cube with the carbon dimer inside the cube. Based on the simultaneous criteria of high binding energy, high vertical ionization potential, high [highest occupied–lowest unoccupied molecular orbital (HOMO-LUMO)] gap, and a low vertical electron affinity, ${\mathrm{Si}}_{14}{\mathrm{C}}_2,$ with a close fullerenelike structure, is predicted to be a particularly stable cluster both at the all-electron and at the pseudopotential level of calculations. The $\mathrm{C}—\mathrm{C}$ bond lengths and the HOMO-LUMO gaps of the clusters are both found to oscillate with cluster size.

We report on an experimental and theoretical investigation of the residence time distribution (RTD) of the polarization mode-hopping regime in vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback. The RTD exhibits discontinuity and oscillations, as a result of the fast intensity oscillations at the delay time that accompany the slow mode hopping. We furthermore show numerically that an external noise source on the injection current allows observation of a coherence resonance phenomenon in VCSELs induced by time-delayed feedback.

We report an experimental and computational study of the energy dependence of nonclassical paths in atoms near bifurcations. The experiment employs scaled energy spectroscopy to measure the amplitudes of nonclassical orbits in helium singlet and triplet Stark Rydberg states $\mathrm{}(20<n<\mathrm{}30\mathrm{}),$ close to bifurcations. We have also calculated this behavior for hydrogen. In both cases, the amplitude dependence on energy, just below a bifurcation, is consistent with an exponential function, in accord with theoretical predictions. Five different nonclassical paths have been studied and, in the case of helium but not hydrogen, the effect of interference between real and ghost orbits is found to produce oscillations in the exponential decay with closed orbit type. In the case of hydrogen, the $n$ dependence of the decay exponent has been investigated and a linear relationship is found.

Due to recent advances in quantum information, as well as in mesoscopic and nanoscale physics, the interest in the theory of open systems and decoherence has significantly increased. In this paper, we present an interesting approach to solving a time-convolutionless equation of motion for the open system reduced density matrix beyond the limit of weak coupling with the environment. Our approach is based on identifying an effective, memory-containing interaction in the equations of motion for the representation submatrices of the evolution operator (these submatices are written in a special basis, adapted for the “partial-trace-free” approach, in the $\mathrm{system}+\mathrm{environment}$ Liouville space). We then identify the “memory dressing,” a quantity crucial for solving the equation of motion for the reduced density matrix, which separates the effective from the real physical interaction. The memory dressing obeys a self-contained nonlinear equation of motion, which we solve exactly. The solution can be represented in a diagrammatic fashion after introducing an “information exchange propagator,” a quantity that describes the transfer of information to and from the system, so the cumulative effect of the information exchange results in the memory dressing. In the case of weak system-environment coupling, we present the expansion of the reduced density matrix in terms of the physical interaction up to the third order. However, our approach is capable of going beyond the weak-coupling limit, and we show how short-time behavior of an open system can be analyzed for arbitrary coupling strength. We illustrate the approach with a simple numerical example of single-particle level broadening for a two-particle interacting system on short time scales. Furthermore, we point out a way to identify the structure of decoherence-free subspaces using the present approach.

We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows one to give precise estimates on the regime at which the collapse of the state vector occurs, the reduction and delocalization times, and the reduction probabilities; it also allows one to quantify the effect that a Hamiltonian which does not commute with the reducing terms has on the collapse mechanism. We also give a clear picture of the transition from the “microscopic” regime (when the noise terms are weak and the Hamiltonian prevents the state vector to collapse) to the “macroscopic” regime (when the noise terms are dominant and the collapse becomes effective for very long times). Finally, we clarify the distinction between decoherence and collapse.