We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\epsilon \left(\mathbf{r}\right)$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system-and-bath Hamiltonian of quantum optics. The field dynamics is investigated using the input-output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

The temporal evolution of electromagnetically induced transparency (EIT) and absorption (EIA) coherence resonances in pump-probe spectroscopy of degenerate two-level atomic transition is studied for light intensities below saturation. Analytical expressions for the transient absorption spectra are given for simple model systems and a model for the calculation of the time-dependent response of realistic atomic transitions, where the Zeeman degeneracy is fully accounted for, is presented. EIT and EIA resonances have a similar (opposite sign) time-dependent line shape, however, the EIA evolution is slower and thus narrower lines are observed for long interaction time. Qualitative agreement with the theoretical predictions is obtained for the transient probe absorption on the ${}^{85}\mathrm{Rb}$ $D_2$ line in an atomic beam experiment.

The Casimir interaction between two perfectly conducting, infinite, concentric cylinders is computed using a semiclassical approximation that takes into account families of classical periodic orbits that reflect off both cylinders. It is then compared with the exact result obtained by the mode-by-mode summation technique. We analyze the validity of the semiclassical approximation and show that it improves the results obtained through the proximity theorem.

The properties of all-optical phase-coherent frequency division by 3, based on a self-phase-locked continuous-wave (cw) optical parametric oscillator (OPO), are investigated theoretically and experimentally. The frequency to be divided is provided by a diode laser master-oscillator power-amplifier system operated at a wavelength of 812 nm and used as the pump source of the OPO. Optical self-phase-locking of the OPO signal and idler waves is achieved by mutual injection locking of the signal wave and the intracavity frequency-doubled idler wave. The OPO process and the second-harmonic generation of the idler wave are simultaneously phase matched through quasi-phase-matching using two periodically poled sections of different period manufactured within the same ${\mathrm{LiNbO}}_3$ crystal. An optical self-phase-locking range of up to 1 MHz is experimentally observed. The phase coherence of frequency division by three is measured via the phase stability of an interference pattern formed by the input and output waves of the OPO. The fractional frequency instability of the divider is measured to be smaller than $7.6\times {10}^{-14}$ for a measurement time of 10 s (resolution limited). The self-phase-locking characteristics of the cw OPO are theoretically investigated by analytically solving the coupled field equations in the steady-state regime. For the experimental parameters of the OPO, the calculations predict a locking range of 1.3 MHz and a fractional frequency instability of $1.6\times {10}^{-15},$ in good agreement with the experimental results.

By applying a multiple time scale perturbation method, we simplify the spin-flip model equations [San Miguel et al., Phys. Rev. A $52,$ 1728 (1995)] describing the polarization behavior of vertical-cavity surface-emitting lasers. The reduced problem consists of three rate equations for a two-mode semiconductor laser. The asymptotic theory is based on the natural values of the laser parameters and considers the case of large values of the spin-flip rate and birefringence with respect to the relaxation oscillation frequency. Our analysis corrects and complements previous derivations of rate equations from the spin-flip model equations. We find that the cross-gain saturation coefficients due to spin-flip processes are not symmetric and may become negative. As a result, a new physical interpretation of polarization switching from the high-frequency mode to the low-frequency mode and for high values of the birefringence is possible.

We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These preparations can be seen as the outcomes of certain minimal positive operator valued measures. The connection of our results with these generalized measurements is briefly discussed.

Optically controlled exciton dynamics in coupled quantum dots is studied. We show that the maximally entangled Bell states and Greenberger-Horne-Zeilinger (GHZ) states can be robustly generated by manipulating the system parameters to be at the avoided crossings in the eigenenergy spectrum. The analysis of population transfer is systematically carried out by using a dressed-state picture. In addition to the quantum dot configuration that has been discussed by Quiroga and Johnson [Phys. Rev. Lett. 83, 2270 (1999)], we show that the GHZ states also may be produced in a ray of three quantum dots with a shorter generation time.

Consider a system consisting of n d-dimensional quantum particles and an arbitrary pure state $|\Psi 〉$ of the whole system. Suppose we simultaneously perform complete von Neumann measurements on each particle. The Shannon entropy of the outcomes’ joint probability distribution is a functional of the state $|\Psi 〉$ and of n measurements chosen for each particle. Denote $S\left[\Psi \right]$ the minimum of this entropy over all choices of the measurements. We show that $S\left[\Psi \right]$ coincides with the entropy of entanglement for bipartite states. We compute $S\left[\Psi \right]$ for some special multipartite states: the hexacode state $|H〉$ $(n=6,$ $d=2)$ and the determinant states $|{\mathrm{Det}}_n〉$ $\mathrm{}(d=n).$ The computation yields $S\left[H\right]=4\mathrm{}\log 2$ and $S\left[{\mathrm{Det}}_n\right]=\log \mathrm{}(n!).$ Counterparts of the determinant state defined for $d<n$ are also considered.

Accurate QED evaluations of the one- and two-photon interelectron interaction for low-lying two- and three-electron configurations for ions with nuclear charge numbers $60<~Z<~93$ are performed. The three-photon interaction is also partly taken into account. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations. A detailed investigation of the behavior of the energy levels of the configurations ${1s}_{1/2}{2s}_{1/2}^1{S}_0,$ ${1s}_{1/2}{2p}_{1/2}^3{P}_0$ near $Z=64\mathrm{}$ and $Z=92\mathrm{}$ is carried out. The knowledge of the exact energy difference near these regions is important for the future experimental search for parity nonconserving effects in highly charged ions.

Forbidden transitions such as intercombination ones, appear due to relativistic effects. In light atoms these effects are usually incorporated through the use of Breit-Pauli Hamiltonian. We show that for some transitions such as $E2\mathrm{}$ or $M1\mathrm{}$ this treatment is incomplete. There exist additional corrections to the transition amplitude which can be equally significant. We analyze also the role of the anomalous magnetic moment of the electron in some forbidden transitions.

We present a general lattice model for a multicomponent atomic Bose-Einstein system in an optical lattice. Using the model, we analytically study the quantum phase transition between the Mott insulator and a superfluid. A mean-field theory is developed from the Mott-insulator ground state. When the interspecies interactions are strong enough, the Mott insulator demonstrates the phase separation behavior. For weak interspecies interactions, the multispecies system is miscible. Finally, the phase diagram is discussed with emphasis on the role of interspecies interactions. The tip and the shape of the Mott insulator lobes do not depend on the interspecies interactions, but the latter indeed modify the position of the phase boundaries.

The decay of superfluid turbulence in the limit of low temperature is studied by numerical simulations of vortex ring collisions. In particular we excite Kelvin waves and study the loss of vortex line length due to Kelvin-wave radiation. Although the effect is small, the decay constant is not inconsistent with recent experiments on vortex lattices in dilute Bose-Einstein condensates, and on superfluid turbulence in helium at very low temperature. We also consider the character of the decay when both vortex reconnections and Kelvin-wave radiation are present.

We present a cryptographic protocol based upon entangled qutrit pairs. We analyze the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.

The study of quantum cryptography and quantum entanglement have traditionally been based on two-level quantum systems (qubits). In this paper, we consider a generalization of Ekert’s entanglement-based quantum cryptographic protocol where qubits are replaced by three-level systems (qutrits). In order to investigate the security against the optimal individual attack, we derive the information gained by a potential eavesdropper applying a cloning-based attack. We exhibit the explicit form of this cloner, which is distinct from the previously known cloners, and conclude that the protocol is more robust than those based on entangled qubits as well as unentangled qutrits.

The linear dichroism in the $4f$ photoelectron spectra of atomic Eu excited at photon energies in the range of the giant $4d-4f$ resonance have been determined. Dramatic changes of the dichroism have been observed when tuning the photon energy through the giant resonance. The dichroism patterns are compared to the predictions of a model based on LS coupling which takes the interaction of the discrete resonances with the ionization continua into account.

Detailed results of numerical one-dimensional wave-packet simulations are reported for the dynamics of a ${\mathrm{D}}_2^{+}$ molecule subjected to separated and combined 400-nm and 800-nm intense laser pulses with their polarization vectors lying either parallel or perpendicular to the internuclear axis of the molecule. Depending on the laser excitation conditions, the model employed involves from four to a maximum of eight electronic channels, comprising molecular states correlating, in the dissociative limit, with the $n=1\mathrm{}$ shell of atomic hydrogen and those correlating with the $n=2\mathrm{}$ shell. Preliminary results of calculations including molecular rotations within a two-dimensional model are also reported. Overall, calculated fragment kinetic-energy spectra, the main results of the present work, are in accord with the findings of recent experimental works [Talebpour et al., Phys. Rev. A 62, 042708 (2000); Vijayalakshmi et al., ibid. 053408 (2000)], which reported evidences of perpendicular dissociation induced by intense 400-nm and 800-nm laser pulses. These results are thus supportive of the hypothesis made therein of perpendicular transitions to upper molecular excited states, through a ${\pi }_u$ doorway. Deviations from the predictions of the Floquet schemes proposed in these works are discussed in terms of the laser-driven rotational dynamics of the molecular ion and in terms of bond-softening versus bond-hardening effects.

We discuss an approach to quantum control based on initial adiabatic tuning of the field-free Hamiltonian by a strong laser field to optimize the system for the desired transitions induced by the control laser pulse. As an illustration, we describe single-qubit, two-qubit, and some qudit logical gates within rotational and vibrational states of a diatomic molecule. Gate operations use resonant Raman transitions, and the prior adjustment of the Hamiltonian is done by a strong nonresonant aligning field.

The index of refraction for sodium matter waves traveling in a cold noble-gas medium is calculated as a function of temperature and beam velocity. Resonances and glory oscillations are present in the center-of-mass scattering amplitude and may be seen in the refractive index at very low temperatures. The sensitivity of the calculations to the molecular potential is investigated for the case of argon, and results at 300 K are compared to a recent experiment. Effective range parameters are computed and the attenuation and phase of the matter waves are analyzed as a function of temperature and beam velocity.

We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of two-dimensional (2D) and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.

Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that $U^m$ is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most ${O(mK+m}^2\ln m)$ elementary gates. The functions of U are realized by a generic quantum circuit, which has a particularly simple structure. Among other results, we obtain efficient circuits for the fractional Fourier transform.