We propose a method of determining quantum evolution equations for dissipative systems. Our approach is based on the observations that (1) the equations of quantum mechanics for a Hamiltonian system correspond to the classical equations describing the evolution of a special statistical ensemble of copies of the system, and (2) the quantum equations can be determined if the corresponding classical equations are known and the satisfaction of the uncertainty principle for particle position and momentum is postulated. Namely, if these statements are required to remain valid for a dissipative system, the quantum evolution equations for that system can be obtained.

A theory for laser-assisted resonant x-ray Raman scattering (RXS) is presented. The conditions for nonlinearity due to strong x-ray fields but without a laser field are first investigated, followed by studies of the consqeunces for the RXS cross section of having a weak x-ray field but strong laser fields resonant with different levels involved in the x-ray scattering. These levels are either connected with excitations of the ground state, with excitations between core excited states, or between unoccupied final states. When the final states are discrete, the RXS line is split by the applied laser field; when they are continuous the laser field induces autoionizationlike resonances in the RXS spectrum.

X-ray yields of M-shell emission from Xe clusters excited by Ti:sapphire (800 nm) and KrF (248 nm) laser pulses were compared under the same irradiation condition that was experimentally well characterized. Xe clusters were irradiated by 350-fs laser pulses of 20-mJ energy. For the KrF laser irradiation, the absolute x-ray yield in the wavelength region from 8 Å to 16 Å was estimated to be 38 $\mu \mathrm{J}$ per pulse. The x-ray yield was 20 times higher than that for the Ti:sapphire laser irradiation. It was found that the x-ray yield from clusters in the keV region depends on the pump laser wavelength.

The realization of a paradigm chaotic system, namely, the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.

We consider the process of electron-ion recombination in a powerful laser field and investigate the spectrum of emitted x-ray radiation. This process is of interest in the interaction of laser radiation with gaseous or solid targets in connection with harmonic and coherent x-ray production. The process is treated in the framework of the inverse Keldysh-Faisal-Reiss model describing the ingoing electron either by a Gordon-Volkov wave or by a Coulomb-Volkov solution. Even for higher energies of the impinging electrons, considerable Coulomb effects are recognized. We evaluate the rates of the generated x-ray field and determine the energy range of its spectrum. The maximum photon energy achieved by this process is estimated by $ħ{\omega }_X{=E}_{\mathit{p}}{+U}_p+|E_B|+2\mathrm{}\sqrt{{2U}_p{E}_{\mathit{p}}},$ with $E_{\mathit{p}}$ being the kinetic energy of the ingoing electron, $U_p$ the ponderomotive energy, and $E_B$ the binding energy. The equivalence of the two models for the zero-range interaction is also shown.

A single ${}^{40}{\mathrm{Ca}}^{+}$ ion is confined in a linear Paul trap and Doppler-cooled on the $S_{1/2}$ to $P_{1/2}$ dipole transition. Then the narrow quadrupole $S_{1/2}$ to $D_{5/2}$ transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion’s temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.

In an earlier work [P. J. Bardroff and S. Stenholm, Phys. Rev. A 60, 2529 (1999)], we have derived a fully quantum-mechanical description of excess noise in strongly damped lasers. This theory is used here to derive the corresponding quantum Langevin equations. Taking the semiclassical limit of these we are able to regain the starting point of Siegman’s treatment of excess noise [Phys. Rev. A 39, 1253 (1989)]. Our results essentially constitute a quantum derivation of his theory and allow some generalizations.

We present an analysis of absorptive optical bistability in a system of cold atoms enclosed in a bidirectional ring cavity. This analysis is carried out using a system of equations that extends the so-called Maxwell-Bloch model to self-consistently include atomic center-of-mass motion. The analysis predicts an instability resulting in the simultaneous generation of an atomic density grating and a coherently backscattered radiation field. The formation of the density grating arises from a modulation of the radiation pressure forces exerted on the atoms. A consequence of this instability is that the lower transmission branch of the usual bistability curve, where atomic motion is neglected, can become unstable and the system switches to the upper transmission branch destroying the bistability.

We present an exact analytic solution for the Jaynes-Cummings model in a leaky optical cavity without using the Markov master equation. In our approach we solve directly the whole quantum state associated with the atom and the continuous field modes—modes-of-universe. Our solution exhibits a hierarchy structure and it is applicable to cases with arbitrary number of photons. The solution can be used to study decoherence effects and the quantum state of the transmitted field.

The security of the previous quantum key distribution protocols, which is guaranteed by the laws of quantum physics, is based on legitimate users. However, impersonation of the legitimate communicators by eavesdroppers, in practice, will be inevitable. In this paper, we proposed a quantum key verification scheme, which can simultaneously distribute the quantum secret key and verify the communicators’ identity. Investigation shows that this proposed identity verification scheme is secure.

The main objective of this paper is to investigate the applicability of the subspace density-functional theory (SDFT) for the calculation of excited-state energies. The exchange and correlation energy density functionals, $E_{\mathrm{xc}}\left(\rho \right),$ used in the present calculation are local and depend on the polarizability parameter $\zeta =2S/N.\mathrm{}$ The deviations of the calculated excited-state energies from their corresponding experimental values range from 0.1% to 0.8% for systems with more than two electrons, while for the helium isoelectronic series the corresponding range is from 0.1% to 1.9%. Thus the SDFT accuracy compares well in most cases with that of the ground-state local-density approximation calculations. Virial theorem and other relations concerning atoms are verified in the context of SDFT calculations. In this paper we also present a new formulation of the SDFT. Our new formulation alleviates the initial Kohn and Sham (KS) theory from the constraint of densities representable by single Slater determinants. This is an essential development as there are eigenstates of spin and other quantum operators, not representable by single Slater determinants.

Universal properties of the spectra of certain matrices describing multiple elastic scattering of scalar waves from a collection of randomly distributed point-like objects are discovered. The elements of these matrices are equal to the free-space Green’s function calculated for the differences between positions of any pair of scatterers. A striking physical interpretation within Breit-Wigner’s model of the single scatterer is elaborated. Proximity resonances and Anderson localization are considered as two illustrative examples.

Dielectronic recombination cross sections for $\Delta n=0\mathrm{}$ transitions in Pb${}^{79+}$ are calculated in a fully relativistic distorted-wave approximation. We present detailed $\mathrm{nlj}$ results for the first resonances associated with the $2\overrightarrow{s}2\overline{p}(j=\frac{1}{2})$ core excitation, which opens up at $n=20,$ and for the first resonances associated with the $2\overrightarrow{s}2p(j=\frac{3}{2})$ core excitation, which overlap the ${1s}^{2}2\overline{p}\mathrm{nl}$ resonances series. An accurate identification of these peaks is of importance in the ongoing dielectronic recombination experiments for the determination of the $2s-2p$ threshold energies. Careful examinations of Breit interaction and QED effects are performed in order to calculate the resonance energies with a resolution comparable with present experimental resolution. Fully relativistic calculations for Auger and radiative rates are performed for an accurate determination of the peak heights.

Emerging charge states of He and Li ions impinging with grazing incidence on a SnTe surface are calculated at high impact velocities. The charge state distribution is obtained as result of the interplay of two atomic processes: electron capture from bound states of the topmost surface atoms and electron loss from the bound states of the projectile due to collisions with the surface atoms. At high energies we find that the projectile leaves the surface with a charge state larger than the quasiequilibrium charge state reached in the vicinity of the surface. We explain this behavior in terms of the different ranges of capture and loss mechanisms. As the projectile escapes from the surface, the balance between these two processes is broken: capture is no longer effective, and loss survives ionizing the projectile. Comparisons with the experiments are presented and discussed.

Atomic Talbot interferometry is shown to be potentially useful both for the experimental determination of arbitrary electromagnetic cavity photon number distributions and for the demonstration of the quantum nature of nearly classical light fields.

Modulational instability with sideband generation is experimentally observed in a passively mode-locked fiber soliton ring laser. We show numerically that this modulational instability is induced by the periodic dispersion variation experienced by light circulating in the laser cavity. Modulational instability caused by cross-phase-modulation is also observed in the laser and confirmed numerically.

The behavior of a V-type system in which the phase of the pump field is periodically changed in an abrupt manner is studied. For specific values of the time between phase changes, enhancements in the oscillatory responses of the imaginary parts of both the pump-and-probe coherences are observed. These Rabi resonances are well known for the pump coherence; their persistence into the coherence of the probe field is shown here. Under these conditions, the coherences reach dynamical steady states characterized by repetitive patterns of oscillation. Over approximately one-half of its pattern, the probe-induced coherence supports gain for the probe field. The maximum amplitude of this gain is more than an order of magnitude larger than would be found under steady-state conditions in the absence of phase changes. Additionally, the range of probe detunings supporting gain is much larger than that observed in the steady-state system. These findings suggest that using a Rabi-resonance approach has the potential to increase the gain that may be obtained in amplification-without-inversion (AWI) systems as well as establishing gain in systems unable to support AWI under steady-state conditions.

We present an ab initio three-dimensional quantum study of high-order harmonic generation (HHG) of atomic H in intense pulsed laser fields. Accurate time-dependent wave functions are obtained by means of the time-dependent generalized pseudospectral method recently developed and wavelet transform is used to perform time-frequency analysis of the resulting HHG power spectra. The results reveal striking details of the spectral and temporal fine structures of HHG, providing insights regarding HHG mechanisms in different energy regimes and benchmark data for testing the validity of existing HHG models.