We report a quantitative assessment of the ac Stark effect induced in the NO $3s\sigma A{}^2{\Sigma }^{+}$ Rydberg state by femtosecond laser pulses at intensities up to $I<~6\times {10}^{13}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2}.$ The $n^{\prime }=2\mathrm{}$ vibrational level of $A{}^2{\Sigma }^{+}$ NO is excited by two-photon absorption at frequencies above and below the weak-field $A{}^2{\Sigma }^{+}\leftarrow X{}^2{\Pi }_r+2\mathrm{}ħ\omega$ resonance and its time-dependent population monitored by fluorescence detection at different incident laser intensities. Dispersed $A{}^2{\Sigma }^{+}\to X{}^2{\Pi }_r$ spectra recorded at $I>~{10}^{13}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2}$ exhibit prominent features due to fluorescence from the $n^{\prime }=2,$ 1, and 0 levels of the $A{}^2{\Sigma }^{+}$ state. These results can be quantitatively described by a kinetic treatment of multiphoton absorption and ionization that takes into account ac Stark shifting of the vibrational levels of the $A{}^2{\Sigma }^{+}$ state at different coordinates in space time mapped out by the laser pulse. An analysis of the experimental data within the terms of this model leads to the deduction that the ac Stark shift is 0.4 times the ponderomotive energy of a free electron at the laser fields used, corresponding to a shift of 0.36 eV at an intensity of $I=6\mathrm{}\times {10}^{13}{\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{-}2}$ at $\lambda =400\mathrm{}\mathrm{nm}.$

The moment of inertia Θ of a trapped superfluid gas of atomic fermions ${(}^6\mathrm{Li})$ is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to $T_c$ is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.

We report the study of lasing modes in broad-area, equilateral-triangular laser cavities. An alternative approach is proposed to study optical modes in equilateral triangular cavities in an analytical form. The modes were obtained by examining the simplest optical paths inside the cavity, which yields the final solution with the boundary conditions. The cavities can be fabricated from semiconductor heterostructures grown on (111)-oriented substrates, which can be easily cleaved into equilateral triangular shapes. Such a design takes advantage of total internal reflection at the cleaved facets of the cavity for circulating modes. Experimental results are obtained from cavities fabricated from a superlattice structure of ${\mathrm{In}}_{0.13}{\mathrm{Ga}}_{0.87}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ grown on a (111) GaAs substrate.

Transmissivity of up to 200% has been observed in an absorption imaging study of electromagnetically induced transparency in cold sodium atoms, when a focused coupling beam is applied near the edge of the atom cloud. The signal behavior strongly depends on the frequency difference between the probe beam and the coupling beam. Such high transmissivity can be attributed to the strong focusing effect of the probe beam, when it propagates in a medium with spatially inhomogeneous refractive index induced by the coupling beam. A detailed numerical analysis based upon the Maxwell propagation equations is presented.

It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. 77, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifest in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory that explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as well as numerically the steady-state fluorescence, and find that the number of peaks depends on the excitation process. If the molecule is driven to the upper levels by a two-photon process, the fluorescent intensity consists of two peaks regardless of the mutual polarization of the transition dipole moments. If the excitation process is composed of both a two-step, one-photon process and a one-step, two-photon process, then there are two peaks on transitions with parallel dipole moments and three peaks on transitions with antiparallel dipole moments. This latter case is in excellent agreement with the experiment.

We construct generally applicable small-loss rate expansions for the density operator of an open system. Successive terms of those expansions yield characteristic loss rates for dissipation processes. Three applications are presented in order to give further insight into the context of those expansions. The first application, of a two-level atom coupling to a bosonic environment, shows the procedure and the advantage of the expansion, whereas the second application that consists of a single mode field in a cavity with linewidth $\kappa$ due to partial transmission through one mirror illustrates a practical use of those expansions in quantum measurements, and the third one, for an atom coupled to modes of a lossy cavity shows another use of the perturbative expansion.

Spontaneous emission of photons by an atom placed near a dielectric cylindrical waveguide at an arbitrary position is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (travelling) and the modes trapped to a waveguide (waveguided). To describe angular properties of the spontaneous emission, a parametrization of the travelling modes by the outgoing waves has been proposed. Angular characteristics of the travelling photon emission, distributions of the trapped photon emission, as well as the global decay rates have been calculated using the quantum approach and the standard perturbation theory. Difficulties due to the presence of sharp resonances (whispering gallery modes) among the travelling photons are pointed out.

A theory of the dispersion in the Moiré gratings is developed and it is shown that the group velocity of light in them can be reduced by up to three orders of magnitude. A conceptual similarity between Moiré grating and the electro-magnetic-induced transparency medium is demonstrated, and it is argued that for some applications the Moiré gratings present a simple viable alternative to electromagnetically induced transparency.

We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.

We present a calculation of the fidelity of a cavity-field state teleported by means of a scheme that requires only two high-$Q$ cavities. Based on current experimental capabilities, we demonstrate the feasibility of our scheme if the mean photon number of the cavity field is on the order of unity, allowing a reasonably accurate teleportation.

We simulate in the mean-field limit the effects of rotationally stirring a three-dimensional trapped Bose-Einstein condensate with a Gaussian laser beam. A single vortex cycling regime is found for a range of trap geometries, and is well described as coherent cycling between the ground and the first excited vortex states. The critical angular speed of stirring for vortex formation is quantitatively predicted by a simple model. We report preliminary results for the collisions of vortex lines, in which sections may be exchanged.

A detailed presentation is given of the analytic calculation of the single-photon annihilation contributions to the positronium ground-state hyperfine splitting, to order $m_e{\alpha }^6$ in the framework of nonrelativistic effective theories. The current status of the theoretical description of the positronium ground-state hyperfine splitting is reviewed.

We calculate the Casimir force and free energy for plane metallic mirrors at nonzero temperature. Numerical evaluations are given with temperature and conductivity effects treated simultaneously. The results are compared with the approximation where both effects are treated independently and the corrections simply multiplied. The deviation between the exact and approximated results takes the form of a temperature dependent function for which an analytical expression is given. The knowledge of this function allows simple estimations that are accurate below the 1% level.

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including, for example, a dynamics governed by a nonlinear Schrödinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.

We present two optimal methods of teleporting an unknown qubit using any pure entangled state. We also discuss how such methods can also have successful application in quantum secret sharing with pure multipartite entangled states.

We describe a protocol which can be used to generate any N-partite pure quantum state using Einstein-Podolsky-Rosen pairs. This protocol employs only local operations and classical communication between the N parties $(N$-LOCC). In particular, we rely on quantum data compression and teleportation to create the desired state. The protocol can be used to obtain upper bounds for the bipartite entanglement of formation of an arbitrary N-partite pure state, in the asymptotic limit of many copies. We apply it to a few multipartite states of interest, showing that in some cases it is not optimal. Generalizations of the protocol are developed which are optimal for some of the examples we consider, but which may still be inefficient for arbitrary states.

Nuclear-magnetic-resonance (NMR) quantum computation is a fruitful arena in which to develop and demonstrate an enhanced capability for quantum control over molecular systems, regardless of the prospects, which may be limited, for building a quantum computer superior to a conventional computer for any computing task. We demonstrate a five-bit NMR quantum computer that distinguishes among various functions on four bits, making use of quantum parallelism, an example of the Deutsch-Jozsa problem. Its construction draws on the recognition of the sufficiency of linear coupling along a chain of nuclear spins, the synthesis of a suitably coupled molecule containing four distinct nuclear species, and the use of a multichannel spectrometer. Radio-frequency pulse sequences are described to execute controlled-NOT gates on two adjoining spins while leaving the other three spins essentially unaffected.

The fine-structure intervals separating the highest-L, $n=9\mathrm{}$ and 10 Rydberg states of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ bound to the $\nu =0,$ $R=0\mathrm{}$ ground states of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ have been measured precisely with microwave spectroscopy and used to deduce the isotropic dipole polarizabilities of the ground states of both these ions. The results, ${\alpha }_S{(\mathrm{H}}_2^{+})=3.167\mathrm{}{96\left(15\right)a}_0^3$ and ${\alpha }_S{(\mathrm{D}}_2^{+})=3.071\mathrm{}{87\left(54\right)a}_0^3,$ agree with a priori theory to within about 0.02%, but the ${\mathrm{H}}_2^{+}$ result indicates that the theory is incomplete at this level.

Using a frequency-doubled diode laser system, we have measured the hyperfine splitting in the ${(6s}^2{7s)7S}_{1/2}$ excited state of the two naturally occurring thallium isotopes. For ${}^{205}\mathrm{Tl}$ and ${}^{203}\mathrm{Tl}$ we find frequency intervals of 12294.5(1.5) and 12180.5(1.8) MHz, respectively. This measurement addresses an earlier discrepancy in measured values for these intervals. At the same time, we have measured, with a factor of 50 improved precision, the ${}^{205}\mathrm{Tl}{-}^{203}\mathrm{Tl}$ isotope shift within the 378-nm ${6P}_{1/2}-{7S}_{1/2}$ transition.

We report theoretical cross sections for capture and detachment in collisions between ${}^3{\mathrm{He}}^{2+}$ ions and negative hydrogen ions ${\mathrm{H}}^{-}$ calculated in a range of laboratory collision energies extending from 150 eV to 2 MeV for the incident ${}^3{\mathrm{He}}^{2+}$ projectile. Calculations have been carried out within the semiclassical impact parameter method using a 30-state two-center atomic orbital expansion. Additional estimates of the same cross sections have also been obtained with the help of the classical trajectory Monte Carlo model. These results are compared with available experimental and theoretical cross sections.