We describe a three-qubit quantum phase gate which is implemented by passing a four-level atom in a cascade configuration initially in its ground state through a three-mode optical cavity. The three qubits are represented by the photons in the three modes of the cavity. Under appropriate detunings, coupling coefficients, and interaction times, this system exhibits like a three-qubit quantum phase gate. Such a quantum phase gate has potential applications in quantum search.

We describe the results of stimulated Raman spectroscopy between the fine-structure levels, specifically $3d^2{D}_{3/2}$ and $3d^2{D}_{5/2}$ metastable states, in a single trapped ${{}^{40}\text{C}\text{a}}^{+}$. Transitions between different Zeeman sublevels, split by an applied magnetic field, are clearly observed and the fine-structure level separation of $\nu =1819599021504\pm 37\text{Hz}$ is determined. This measurement provides a direct observation of this level separation. From the spectroscopic data, a prospect of using the $D$-fine structure levels as a qubit for the quantum information processing is reviewed.

The exact-exchange energy density and energy density of a semilocal density-functional approximation are two key ingredients for modeling the static correlation, a strongly nonlocal functional of the electron density, through a local hybrid functional. Because energy densities are not uniquely defined, the conventional (Slater) exact-exchange energy density $e_{\text{x}}^{\text{ex}\left(\text{conv}\right)}$ is not necessarily well suited for local mixing with a given semilocal approximation. We show how to transform $e_{\text{x}}^{\text{ex}\left(\text{conv}\right)}$ in order to make it compatible with an arbitrary semilocal density functional, taking the nonempirical meta-generalized-gradient approximation of Tao, Perdew, Staroverov, and Scuseria as an example. Our additive gauge transformation function integrates to zero, satisfies exact constraints, and is most important where the density is dominated by a single orbital shape. We show that, as expected, the difference between semilocal and exact-exchange energy densities becomes more negative under bond stretching in $\text{He}_2{}^{+}$ and related systems. Our construction of $e_{\text{x}}^{\text{ex}\left(\text{conv}\right)}$ by a resolution-of-the-identity method requires uncontracted basis functions.

The Schwinger multichannel method is applied to study the influence of polarization effects on the electronic excitation of the furan molecule by low-energy electron impact. We discuss the importance of inclusion of these effects through the comparison of theoretical results for the electronic excitation of the ${{}^{3}B}_2$ state of furan obtained with and without the proper treatment of the polarization of the target. The electron-furan scattering presents two prominent shape resonances in the ${{}^{2}A}_2$ and ${{}^{2}B}_1$ symmetries at around the electronic excitation threshold of the ${{}^{3}B}_2$ state (3.7 eV). At this low-energy, the inclusion of polarization effects in the calculation moves to lower energies the resonances positions obtained either in the close-coupling or in the static-exchange level of approximation. This phenomenon strongly influences the electronic excitation process. The present results show that a simple close-coupling calculation cannot be applied for molecular systems with low-energy electronic excitation thresholds around misplaced resonances.

The high-order above-threshold ionization (ATI) by a few-cycle pulse in asymmetric molecules has been investigated by solving the time-dependent Schrödinger equation. The resulting high-energy ATI spectra are very sensitive to the laser’s carrier-envelope phase (CEP) and analyzed in terms of the classical model. The left-right asymmetry of ATI yields of asymmetric molecules for high energies is different from that of atoms, resulting from the existence of an asymmetric potential well, and is explained by studying the molecules in the presence of a static electric field. The asymmetry for asymmetric molecules is expected to be used for measuring the CEP more accurately than for atoms.

The interaction of near-resonant laser radiation with atoms immersed in a magnetic $\mathbf{B}$ field is calculated using a quantum electrodynamic model. In this model, the magnetic field is assumed to produce a small perturbation such that the degeneracy of the magnetic substates is lifted while maintaining the usual quantum numbers that define the states (the Zeeman effect). The laser radiation is considered to have a narrow bandwidth and to be temporally and spatially coherent. The model produces three general coupled differential equations that describe the state populations and their relative coherences and the optical coherences between levels coupled by the laser radiation. The model can therefore be directly applied to different experiments ranging from atom trapping and cooling experiments through to collision experiments carried out in magnetic and laser fields.

We investigate the high-order harmonic generation (HHG) from diatomic molecules with large internuclear distance using a strong-field approximation model. We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum and the location of this striking structure is sensitive to the laser intensity. Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories is responsible for the unusual enhanced or suppressed harmonic yield at a certain order, and these interference effects are greatly influenced by laser parameters such as intensity.

The intraband tunneling of a Bose-Einstein condensate between three degenerate high-symmetry $X$ points of the Brillouin zone of a cubic optical lattice is studied in the quantum regime by reduction to a three-mode model. The mean-field approximation of the deduced model is described. Compared to the previously reported two-dimensional (2D) case [V. S. Shchesnovich and V. V. Konotop, Phys. Rev. A 75, 063628 (2007)], which is reducible to the two-mode model, in the case under consideration there exist a number of new stable stationary atomic distributions between the $X$ points and a new critical lattice parameter. The quantum collapses and revivals of the atomic population dynamics are absent for the experimentally realizable time span. The 2D stationary configurations, embedded into the 3D lattice, turn out to be always unstable, while the existence of a stable 1D distribution, where all atoms populate only one $X$ state, may serve as a starting point in an experimental study of nonlinear tunneling in a 3D lattice.

The squeezing and entanglement properties of a one-component Bose-Einstein condensate trapped in optical lattices are theoretically studied. A two-mode squeezing parameter for the system is found, which is identical with Einstein-Podolsky-Rosen correlation, indicating the quantum correlation between excitation modes. Its dynamics and relation to the Hamiltonian parameters are quantitatively shown, and some constructive relation between squeezing and condensation is pointed out. For entanglement, the entanglement of formation of the two-mode system is also presented. For the probing of such a correlation, relevant experimental issues about atom shot noise are also discussed.

We study the conversion efficiency of heteronuclear Feshbach molecules in population imbalanced atomic gases formed by ramping the magnetic field adiabatically. We extend the recent work [J. E. Williams et al., New J. Phys. 8, 150 (2006)] on the theory of Feshbach molecule formations to various combinations of quantum statistics of each atomic component. A simple calculation for a harmonically trapped ideal gas is in good agreement with the recent experiment [S. B. Papp and C. E. Wieman, Phys. Rev. Lett. 97, 180404 (2006)] without any fitting parameters. We also give the conversion efficiency as an explicit function of initial peak phase space density of the majority species for population imbalanced gases. In the low-density region where Bose-Einstein condensation does not appear, the conversion efficiency is a monotonic function of the initial peak phase space density, but independent of statistics of a minority component. The quantum statistics of majority atoms has a significant effect on the conversion efficiency. In addition, Bose-Einstein condensation of an atomic component is the key element determining the maximum conversion efficiency.

In two nearby atoms, the dipole-dipole interaction can couple transitions with orthogonal dipole moments. This orthogonal coupling accounts for a number of interesting effects, but strongly depends on the geometry of the setup. Here, we discuss several setups of interest where the geometry is not fixed, such as particles in a trap or gases, by averaging over different sets of geometries. Two averaging methods are compared. In the first method, it is assumed that the internal electronic evolution is much faster than the change of geometry, whereas in the second, it is vice versa. We find that the orthogonal coupling typically survives even extensive averaging over different geometries, albeit with qualitatively different results for the two averaging methods. Typically, one- and two-dimensional averaging ranges modeling, e.g., low-dimensional gases, turn out to be the most promising model systems.

We derive the properties of polaritons in single-$\Lambda$ and double-$\Lambda$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\Lambda$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.

The dynamic properties of two-photon pumped blue lasing $(\sim 470\mathrm{nm})$ in the solution of an organic chromophore [2-acetyl-6-(dimethylamino)naphthalene], excited by $\sim 160\text{−}\mathrm{fs}$ laser pulses at $\sim 775\mathrm{nm}$, have been studied. Both the forward and backward stimulated emission are enhanced by feedback from the reflection at the two optical windows of the solution filled cuvette. Under current experimental conditions, the lasing wavelengths in the forward and backward directions were almost the same, but both blueshifted compared to the fluorescence peak wavelength of the sample solution. The temporal behavior of the lasing output was recorded by a high-speed streak camera system. The multipulse structure and spectral properties of the output lasing are semiquantitatively explained. In addition, excellent optical phase-conjugation properties of the backward stimulated emission were observed; the aberration influences from an aberrator on the backward lasing beam were automatically removed.

The projectile charge-state dependence of methane fragmentation is studied at a constant projectile (${\mathrm{Ar}}^{q+}$, $1\le q\le 7$) velocity of $0.42\text{a.u.}$ using the technique of time-of-flight mass spectroscopy. The relative cross sections for fragment production are reported as a function of the incident projectile charge state. The fragments appearing as molecular ions show a decrease in cross sections with increasing projectile charge state as opposed to the carbon ions which show an increase with increasing projectile charge state.

We clarify the internal relationship between the coherent destruction of tunneling (CDT) for a two-state model and the dynamic localization (DL) for a one-dimensional tight-binding model, under the periodical driving field. The time evolution of the tight-binding model is reproduced from that of the two-state model by a mapping of equation of motion onto a set of SU(2) operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the SU(2) operators. We also show that both of the CDT and the DL can be interpreted as a result of destructive interference in repeated Landau-Zener level crossings.

We study how a Rabi oscillation is affected by a periodic pulsed perturbation. Unlike a continuous perturbation, which simply shifts the resonance frequency, a pulsed perturbation splits the Rabi resonance into two lines separated by the pulse repetition rate. When the perturbation integrated over one pulse is equal to $\pi$, the resonance splits into two symmetrically placed lines at ± half the pulse repetition rate. When it is $2\pi$, the Rabi oscillation is unaffected by the perturbation. We demonstrate these behaviors using the ground hyperfine transition of cesium atoms in a magneto-optical trap. The pulsed perturbation is introduced by a periodic magnetic field pulse. The $2\pi$ case is compared with the self-induced transparency, and its implications for optical frequency metrology using a pulsed optical trap is discussed.

Using recent results in the field of quantum chaos we derive explicit expressions for the time scale of decoherence induced by the system-environment entanglement. For a generic system-environment interaction and for a generic quantum chaotic system as environment, conditions are derived for energy eigenstates to be preferred states in the weak coupling regime. A simple model is introduced to numerically confirm our predictions. The results presented here may also help with understanding the dynamics of quantum entanglement generation in chaotic quantum systems.

Quantum lithography proposes to adopt entangled quantum states in order to increase resolution in interferometry. In the present paper we experimentally demonstrate that the output of a high-gain optical parametric amplifier can be intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as proposed by [Agarwal et al., Phys. Rev. Lett. 86, 1389 (2001)]. We investigate multiphoton states generated by a high-gain optical parametric amplifier operating with a quantum vacuum input for gain values up to 2.5. The visibility has then been increased by means of three-photon absorption. The present paper opens interesting perspectives for the implementation of such an advanced interferometrical setup.

The heating effect—i.e., photon fluctuation—occurs in the geometric logic gating in cavity QED due to a noisy environment. We propose an efficient scheme to suppress this heating by combining the displacementlike operator method [Phys. Rev. A 73, 032344 (2006)] with the method of double-Hamiltonian evolution [Phys. Rev. Lett. 90, 217901 (2003)]. Discussions about the fidelity and the success probability of the proposed scheme as well as the experimental feasibility are made in detail.