A method for the solution of the two-electron problem in a strong magnetic field is presented that combines the well-known hyperspherical close-coupling and finite element methods and applied to helium in a magnetic field of up to ${10}^5$ T, giving energy levels of low-lying $S$ and $P$ states up to a principal quantum number of $n=4\mathrm{}$ as well as wavelengths of selected transitions.

We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with recent experiments and predict that the decoherence rate will depend on vibrational quantum number in different ways depending on which vibrational excitation sideband is used.

Ortho-para separations of ${}^7{\mathrm{Li}}_2$ and ${}^6{\mathrm{Li}}_2$ molecules were achieved by using a monochromatic laser beam to align atoms into a single nuclear spin state. This approach is unlike the cryogenic cooling technique, which has been successful only on very light molecules (such as ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$), which have large energy gaps between the lowest rotational states. The atoms were “pumped into” a single hyperfine Zeeman state with defined electron and nuclear spin orientations. The well-resolved rotational structures of the lithium molecules, as shown by laser-induced fluorescence spectra, revealed the enrichment of ortho-components over para-components. Using laser radiation with a power density of $\sim 10{\mathrm{m}\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ can increase the amount of ortho-components by a factor of 2 for ${}^7{\mathrm{Li}}_2$ vapor and by a factor of 3 for ${}^6{\mathrm{Li}}_2$ vapor on a time scale of milliseconds. This paper proposes a model to account for the experimental observations. These increases in the concentrations of ortho-components to para-components are explained by a combined effect of (i) a decrease in molecular density due to the electron spin orientation and (ii) a transfer of nuclear spin momenta from oriented atoms to molecules. The exchange reaction, ${\mathrm{Li}}^{\prime }{+\mathrm{L}\mathrm{i}}_2{\to \mathrm{Li}}_3{\to \mathrm{Li}}^{\prime }\mathrm{L}\mathrm{i}+\mathrm{L}\mathrm{i},$ appears to transfer the spin orientation from atoms to molecules. A substantial number of ortho-para separations can be achieved through multiple exchange collisions. Applications of this technique to other homonuclear diatomic molecules and polyatomic molecules with nuclear exchange symmetry are predicted.

We study the scattering of an atomic beam slowly passing through a standing laser wave with an amplitude periodically modulated in time. The formal analysis of the problem involves the theory of interacting nonlinear resonances, developed earlier in the field of quantum chaos. Two different diffraction regimes are distinguished: a quasiregular regime, where the atoms are Bragg-like scattered by a primary or secondary nonlinear resonance, and a chaotic regime, where the scattering can be regarded as (quasi)random.

An improved two-electron approach is proposed to investigate electron-correlation effects in intense-field ionization of hydrogen molecules. Different from the single-active-electron approximation and the partially correlated approach, our model describes the interaction between two electrons through use of a pair of time-dependent Coulomb mean potentials. With the correlated two-electron approach, we have explored the mechanisms of electron correlation in intense-field ionization of molecular hydrogen for different laser intensities.

Dark magnetic resonance in the solid state is observed and is shown to be analogous to electromagnetically induced transparency in coherent optics. The basis of the two effects is coherent population trapping, which can conveniently be described by the product operator formalism. It is demonstrated that pulse electron paramagnetic resonance experiments on electron-nuclear spin systems provide a simple means for studying the physics of these types of coherence phenomena.

We study the Autler-Townes absorption spectrum of the upper and intermediate levels of a three-level cascade atom in which the intermediate and ground levels are strongly driven by a laser field as well as weakly coupled by a cavity mode [Phys. Rev. 100, 703 (1955)]. Surprisingly, one of the Autler-Townes peaks may be greatly suppressed or enhanced by tuning the cavity resonant frequency. The larger the Rabi frequency, the more pronounced the cavity-induced suppression or enhancement. The Autler-Townes spectrum carries full information on the cavity-induced modification of the strongly driven levels. A physical interpretation is presented in the dressed-state basis.

We analyze a stimulated revival (echo) effect for the breathing modes of atomic oscillations in optical lattices. The effect arises from the dephasing due to the weak anharmonicity being partly reversed in time by means of additional parametric excitation of the optical lattice. The shape of the echo response is obtained by numerically simulating the equation of motion for the atoms with subsequent averaging over the thermal initial conditions. A qualitative analysis of the phenomenon shows that the suggested echo mechanism combines the features of both spin and phonon echoes.

The ground and some excited states of the Li atom in external uniform magnetic fields are calculated by means of our two-dimensional mesh Hartree-Fock method for field strengths ranging from zero up to $2.35\times {10}^8\mathrm{T}$. With increasing field strength, the ground state undergoes two transitions involving three different electronic configurations: for weak fields, the ground-state configuration arises from the field-free ${1s}^{2}2s$ configuration; for intermediate fields, it arises from the ${1s}^2{2p}_{-1}$ configuration, and in high fields, the ${1s2p}_{-1}{3d}_{-2}$ electronic configuration is responsible for the properties of the atom. The transition field strengths are determined. Calculations on the ground state of the ${\mathrm{Li}}^{+}$ ion allow us to describe the field-dependent ionization energy of the Li atom. Some general arguments on the ground states of multielectron atoms in strong magnetic fields are provided.

Atom optic techniques are proposed to control the excitation of a Bose-Einstein condensate in an atomic trap. We show that by employing the dipole potential induced by four highly detuned traveling-wave laser beams with appropriate phases and frequencies, one can coherently excite a trapped Bose-Einstein condensate composed of ultracold alkali-metal atoms into a state rotating around the trap center. Pure vortex states can be created with this scheme if the condensate is trapped in an anharmonic trap.

We propose an optical method for increasing the number of atoms in a pair of dilute-gas Bose-Einstein condensates. The method uses laser-driven Raman transitions which scatter atoms between the condensate and noncondensate atom fractions. For a range of condensate phase differences there is destructive quantum interference of the amplitudes for scattering atoms out of the condensates. Because the total atom scattering rate into the condensates is unaffected, the condensates grow.

We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low-lying excitation energies and the ground-state energy and density profile. We discuss the dependence of these quantities on both interaction strength $g$ and particle number $N$. The ground-state properties are compared to the predictions of the Gross-Pitaevskii equation, and the agreement is surprisingly good even for relatively low particle numbers. We also calculate the specific heat based on the obtained energy spectra.

We use a one-dimensional time-dependent nonlinear Schrödinger equation (NLSE) to study the temporal evolution of excited-state populations of an inhomogeneous Bose condensate. We show how one can decompose an arbitrary single-particle wave function into a condensate and a collection of quasiparticles and we use this method to analyze simulations in which the initial wave function contains a finite amount of excitation in a single mode. The nonlinear mixing of the quasiparticles is dominated by processes that approximately conserve energy and we see the reversible transfer of excitation between energetically matched modes. We show analytically how the time scale for nonlinear mixing depends on the amount of initial excitation and the size of the nonlinearity. We propose that, by averaging over the phase of the excitations, the NLSE can be used as a simple tool for the simulation of incoherent excitations. This will allow the techniques presented here to be used to explore finite-temperature mixing effects.

An atom interferometer comprised of four copropagating traveling laser beams has been developed using a thermal calcium atomic beam and the performance of the interference fringes was investigated experimentally. The interference fringes with a visibility of 0.2 were observed at an excitation power of 0.6 mW. The signal-to-noise ratio was about 100 at an integration time of 5 ms. The equations for the interference signal were derived from the evolution matrices of spinors and the visibility was calculated in consideration of the divergent thermal atomic beam. The experimental results were described well by the present calculation.

We obtain analytic solutions to the Gross-Pitaevskii equation with negative scattering length in highly asymmetric traps. We find that in these traps the Bose-Einstein condensates behave like quasiparticles and do not expand when the trapping in one direction is eliminated. The results can be applicable to the control of the motion of Bose-Einstein condensates.

We consider the statistical properties of the fluctuations in the orientation of the vector laser field for a nearly isotropic laser, addressing the competition between the randomizing influence of noise and the preference for linearly or circularly polarized emission induced by saturation in the laser medium and/or cavity anisotropies. We describe, through a nonperturbative analysis, a crossover regime from diffusion-induced polarization-isotropic emission to emission of nearly fixed polarization characteristics. In this crossover the linewidth of intensity fluctuations associated with one of the circularly polarized components of the vector field amplitude changes from decreasing to increasing with output power. This behavior can be expressed in terms of a single parameter that measures the pump or the total output intensity in terms of the ratio of the noise amplitude to the degree of cross saturation of the amplitudes of the circularly polarized components of the vector field amplitude. Analytical results are given for the linewidth of the intensity fluctuations. When the laser has a preference for linearly polarized emission, there is a weakly non-Lorentzian spectrum in the crossover region. When the laser has a “preference” for circularly polarized emission the crossover regime is characterized by a non-Lorentzian spectrum due to fast hopping between two circularly polarized eigenstates. We also describe ellipticity fluctuations induced by the diffusion of the direction of the main axis of the polarization ellipse in the presence of cavity birefringence.

We analyze the general conditions and limitations for the realization of frequency up-conversion via lasing without inversion (LWI). Based on this analysis we propose a class of schemes in which LWI can be achieved via optical- or microwave-frequency driving on a weakly allowed transition. A noninversion amplification process based on this system is studied with particular emphasis on propagation effects and Doppler broadening. Amplification of both monochromatic and bichromatic fields is considered and a possible implementation in realistic atoms and ions is discussed.

The Mollow and Autler-Townes probe absorption spectra of a three-level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed-vacuum field are studied. Analytical studies of the modifications caused by the finite squeezed-vacuum bandwidth to the spectra are made for the case when the Rabi frequency of the driving field is much larger than the natural linewidth. The squeezed vacuum center frequency and the driving laser frequency are assumed equal. We show that the spectral features depend on the bandwidth of a squeezed vacuum field and whether the sources of the squeezing field are degenerate (DPA) or nondegenerate (NDPA) parametric amplifiers. In a broadband or narrow bandwidth squeezed vacuum generated by a NDPA, the central component of the Mollow spectrum can be significantly narrower than that in the normal vacuum. When the source of the squeezed vacuum is a DPA, the central feature is insensitive to squeezing. The Rabi sidebands, however, can be significantly narrowed only in the squeezed vacuum produced by the DPA. The two lines of the Autler-Townes absorption spectrum can be narrowed only in a narrow bandwidth squeezed vacuum, whereas they are independent of the phase and are always broadened in a broadband squeezed vacuum.

We examine the dynamical evolution of wave packets in a large class of quantum systems where two quantum numbers determine the energy spectrum and consequently the dynamical behavior. Using a generic Hamiltonian, we study the formation of coherent structures. The ratio of two time scales as well as the symmetry of the initial wave packet decisively determines the revival and fractional revivals of the system for which we give analytical results. The theory is applicable to a wide class of systems from diatomic molecules to ions in two-dimensional traps and two interacting Bose condensates.

The operational theory of homodyne detection by nonideal detectors, used in quantum tomography, was recently modified in order to incorporate the preamplification (before homodyne detection) of the input signal, thus enabling one to beat the handicap of the lower than 0.5 detector efficiency. In the present work we set expressions for the Mandel $Q$ parameter and the signal-to-noise ratio in terms of the operational (measured) moments of the preamplified homodyne detection formalism. These quantities furnish important information on the statistical properties of the input signal field and the photocounts at the output. We illustrate the theory by considering several kinds of fields (for the input signal) and determine the effects of the preamplification on the output signal-to-noise ratios. Here we essentially verify that (i) the preamplification shifts the statistics towards the super-Poissonian limit, without jeopardizing the capacity of reconstructing a sub-Poissionan input signal, and (ii) the preamplification is more effective, i.e., the rate of increase of the signal-to-noise ratio of the output photocount is larger for low-efficiency detectors than for ideal ones.