The wave function for a state of definite angular momentum of the three-dimensional isotropic harmonic oscillator is expressed exactly in terms of the corresponding classical trajectories. In particular, the three-dimensional wave function as well as the radial wave function and the spherical harmonics are obtained as integrals over quantities determined entirely by the classical motion. The expression for the harmonic-oscillator radial wave function is shown also to yield the exact radial wave function for the free particle. The expressions are cast in forms suitable for use as uniform semiclassical approximations for wave functions of other systems. Numerical examples confirm that such wave functions obey boundary conditions appropriate for spherical coordinates and that they are free of caustic singularities. The wave functions obtained by this technique can be quite accurate even for low-energy states where semiclassical approximations are expected to be poor.

Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural fault-tolerant computation) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one- or two-body interactions must leave the code space during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.

We study measurements on various subsystems of the output of a universal $\overrightarrow{1}2$ cloning machine, and establish a correspondence between these measurements at the output and effective measurements on the original input. We show that one can implement sharp effective measurement elements by measuring only two out of the three output systems. Additionally, certain complete sets of sharp measurements on the input can be realized by measurements on the two clones. Furthermore, we introduce a scheme that allows us to restore the original input in one of the output bits, by using measurements and classical communication—a protocol that resembles teleportation.

We analyze models for two intersecting electronic states coupled by one nuclear coordinate. The corresponding model-Hamiltonians depend on a perturbation parameter α. Its variation allows us to switch on the nonadiabatic coupling continuously. We derive analytical expressions for the eigenstates and energies as function of α in the diabatic representation. We rederive the expression for the energy eigenvalues by complete resummation of the Brillouin-Wigner perturbation series in the Born-Oppenheimer basis. We find that the divergences of the nonadiabatic coupling cancel strictly order by order. The admixture of high energy components is shown explicitly.

We present a quasirelativistic method of ab initio calculations on molecular excited states and electronic transition moments within the relativistic effective potential approximation, based on the construction of intermediate Hamiltonians and spin-free one-particle transition density matrices by means of the many-body multipartitioning perturbation theory. The method is applied to describe the electronic transitions involved in the radiative decay of the ${A0\mathrm{}}_u^{+},$ ${B0\mathrm{}}_u^{+},$ and ${B1\mathrm{}}_u$ states of ${\mathrm{Te}}_2.$ Good agreement of the computed transition dipole moment functions with their empirical counterparts is achieved. Theoretical radiative lifetime estimates for several low-lying rovibrational levels of the states under study are reported and compared with experimental collisionless lifetimes.

A fast-beam spectrometer is used to investigate the photofragmentation and autoionization dynamics of laser-excited triatomic hydrogen molecules. The yield of neutral products from rapidly predissociated states of ${\mathrm{H}}_3$ is monitored in parallel with the field ionization signal. Using this spectrometer, we have measured the natural lifetime of low principal quantum number Rydberg states ${\mathrm{nsA}}_1^{\prime }$ and ${\mathrm{npE}}^{\prime }.$ For the ${3sA}_1^{\prime },$ ${4sA}_1^{\prime },$ and ${5sA}_1^{\prime }$ electronic states, we find lifetimes decreasing with increasing principal quantum number. This is unexpected for a Rydberg series and confirms the observations of a previous investigation. In addition, our experiments give direct evidence that even very high principal quantum number Rydberg states of ${\mathrm{H}}_3$ are selectively subject to strong predissociation. This process appreciably shortens their natural lifetimes. In the high principal quantum number $\mathrm{ns}$- and $\mathrm{nd}$ Rydberg series converging to the lowest ionization threshold of ${\mathrm{H}}_3$ we find a significant variation of the predissociation yield with principal quantum number and electronic angular momentum. Windows with enhanced predissociation in the Rydberg series are explained by nonadiabatic couplings of the laser-prepared initial states with the repulsive ground states surface mediated by vibrationally degenerate mode excited ${4pE}^{\prime }$ and ${5pE}^{\prime }$ states. The relevance of the ${\mathrm{H}}_3$ predissociation mechanisms for the dissociative recombination of ${\mathrm{H}}_3^{+}$ is discussed.

The field ionization cross sections for the L-shell states in argon are presented as measured with pulsed-laser radiation at an intensity of up to ${10}^{19}\mathrm{W}/{\mathrm{cm}}^2.$ For ultrahigh intensities, the photoelectron continuum dynamics will be relativistic. However, the measured charge-state yields for ${\mathrm{Ar}}^{9+}$ to ${\mathrm{Ar}}^{16+}$ compare favorably to numerical solutions of the nonrelativistic Schrödinger equation and a widely used Ammosov-Delone-Krainov/WKB tunneling ionization model. The results are interpreted within a two-step, strong-field ionization model, where the initial tunneling ionization process is dominated by nonrelativistic effects while the photoelectron continuum dynamics are strongly relativistic.

Experimental and R-matrix calculated cross sections are reported for the resonance $2\overrightarrow{s}2p$ transition in ${\mathrm{O}}^{5+}.$ Use is made in the measurements of the electron-energy-loss technique, with center-of-mass interaction energies in the range 10.5 (below threshold) through 12.0 (threshold) to 17.0 eV. The present results are in good agreement with calculations using the R matrix with pseudostates theory, which includes nine physical states and 18 pseudostates. They are also in good agreement with near-threshold data of Bell et al. [Phys. Rev. A 49, 4585 (1994)], and with a 41-state calculation of Griffin et al. [J. Phys. B 33, 1013 (2000)].

The quantum-mechanical Baranger-Kolb-Griem theory of pressure broadening is reexamined in order to include both the effects due to overlapping lines and finite duration of collision. A general line-shape formula is derived which for near wings can be presented as a linear combination of the Lorentzian and dispersion profiles. The asymmetry parameter is expressed by means of evolution operators for the initial and final states. It is shown that in the weak-coupling case only the resultant asymmetry parameter can be approximately given as the sum of parameters describing the asymmetry due to line mixing and finite collision time.

The photodetachment cross sections, branching ratios, and angular-distribution asymmetry parameters have been calculated for ${\mathrm{F}}^{\mathrm{-}}$ and ${\mathrm{Br}}^{\mathrm{-}}$ in the relativistic random-phase approximation (RRPA) and modifications of the RRPA that allow for the inclusion of relaxation and core-polarization effects. Photodetachment cross sections are compared with experimental measurements to assess the effectiveness of the various approximations. The effects of core polarization are found to partially cancel relaxation effects.

The effect of total rotational angular momentum on the stochastic characteristics of the internal motion of rare-gas trimers has been studied by the molecular-dynamics method. Results presented for the argon trimer described in a two-parameter phase space characterized by fixed values of the total energy and angular momentum provide insight into the separation of chaotic from regular motions of the system. An important feature of the phase-space structure is that the volume filled by regular trajectories for fixed total energy of the system is not a monotonic function of its total angular momentum. The chaotic motions are characterized by a strong coupling between potential- and kinetic-energy contributions that is not observed for the regular motions.

We discuss electronic population transfer in diatomic molecules. By analyzing time-dependent wave packets on electronic potential-energy surfaces, we investigate the efficiency and robustness of population transfer with intense, chirped laser pulses. Recently, the magnitude of the population transfer was observed to have a remarkable dependence on the sign of the chirp [J. Cao, C. J. Bardeen, and K. R. Wilson, Phys. Rev. Lett. 80, 1406 (1998)]. In this work we explain the reason for this asymmetry, and show how the frequency detuning, intensity, and chirp rate affect the results. In particular, we demonstrate efficient, robust population transfer for both positive and negative chirps. A Landau-Zener model of multiple avoided crossings is invoked to model the results.

In this paper, the quasistatic model is extended to describe the double ionization of helium in an intense linearly polarized field, yielding insight into the two-electron correlation effect in the ionization dynamics. Our numerical calculations reproduce the excessive double ionization and the photoelectron spectra observed experimentally both quantitatively and qualitatively. Moreover, it is shown that the classical collisional trajectories are the main source of the double ionization in the knee regime where the double ionization yield is much higher than that predicted by the sequential single active electron models, and responsible for the unusual angular distribution of the photoelectrons.

We present a self-consistent theory, as well as analytical and numerical results, for the three-photon–one-photon phase control of resonantly enhanced photoionization in an optically dense medium of xenon gas. We show that for an optically thick medium, the standard phase-control technique has a rather limited application since, independently of the initial relative phase between the two fields, over a very short scaled distance of propagation the medium tends to settle such a relative phase that exactly cancels the atomic excitation. Rather unusual results for an optically thin layer of atoms are also found.

The highly accurate series solution of the Schrödinger equation for a hydrogen atom in a uniform magnetic field is used in the calculation of the first-order relativistic correction. For weak magnetic field the results are completed by second- and third-order corrections. The accuracy of the total energy for the ground state of the hydrogen atom matches or exceeds in some cases that of previous fully relativistic calculations.

The quantum nondemolition measurement is applied to a two-dimensional (2D) trapped-ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level system of the ion. The information about the ionic vibrational energy can be detected by the occupation probability of the internal electronic level. The substantial difference of the 2D model from the one-dimensional one is that two orthogonal beams have a fixed phase shift instead of statistical independence. As a result, the atomic Rabi oscillation is involved in the coherent superposition of two sub-Rabi oscillations induced by the corresponding driving beams. This means that, in the bidimensional case, the phase difference between the two laser beams plays the role of an adjustable external parameter which allows us to optimize the measurement scheme itself, in terms of precision and sensitivity. As in the one-dimensional case, our proposal leads to interesting applications as, for example, the cooling and preparation of arbitrary bimodal Fock states. The model can be considered as a cooling method for the trapped ion from the vibrational thermal state to the vacuum state. Due to the coherent superposition of two sub-Rabi oscillations, the Rabi frequency degeneration and offset may occur in this model. This provides the possibility of generating various entangled superposition of Fock states, the pair coherent state, and entangled pair coherent states.

We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two, or three of the scattering lengths $a_{\mathrm{ij}}$ for scattering of boson i with j, $i,j=1,2,$ are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.

We consider a two-component weakly interacting Bose-Einstein condensate in the presence of an external field which couples the two components. We express the Hamiltonian in terms of the energy eigenstates of the single-body part of the Hamiltonian. These eigenstates are the atomic dressed states of quantum optics. When the energy difference between the two dressed states is much larger than the mean-field interactions, two-body interactions in the dressed state basis that do not conserve the number of atoms in each of the two dressed states are highly suppressed. The two-body interactions then take on a simplified form in the dressed basis with effective coupling constants that depend on the intensity and frequency of the external field. This implies that the chemical potential as well as the quasiparticle spectrum may be controlled experimentally in a simple manner. We demonstrate this by showing that one may achieve significant variations in the speed of sound in the condensate, a quantity which has been measured experimentally.

We theoretically study the coherent expansion of a Bose-Einstein condensate in the presence of a confining impenetrable hard-wall potential. The nonlinear dynamics of the macroscopically coherent matter field results in rich and complex spatiotemporal self-interference patterns demonstrating a nonlinear Talbot effect, and the formation of vorticity and solitonlike structures.

A theoretical model that takes into full account the vectorial nature of electromagnetic (EM) fields is developed to investigate various types of quantum electrodynamics (QED) in a three-dimensional (3D) photonic crystal. The EM fields are quantized via solving the eigenproblem of photonic crystals with the use of a plane-wave expansion method. It is found that the light-atom coupling coefficients strongly depend on the Bloch states, and the key physical function concerning the atomic QED is the photon local density of states (LDOS) instead of the DOS. Both the DOS and the LDOS vary slowly near the band edge and no singularity takes place. This vectorial model show that the spontaneous emission from a two-level atom can be solved via the conventional Weisskopf-Wigner approximation theory, which exhibits a pure exponential decay behavior with a rate proportional to the LDOS. The quantum interference effect from a three-level atom is greatly weakened at the band edge, instead of enhanced. Neglecting this vectorial nature will lead to many discrepancies in understanding quantum optics in 3D photonic crystals and other inhomogeneous media.