Generation of high harmonics by the interaction of intense laser fields with periodic crystal structures is investigated theoretically. A nonperturbative Floquet-Bloch theory of the interacting system (crystal plus laser field) is developed and applied to obtain the field-modified band structure of the system. The mean energy spectrum, the dispersion and the fluctuation of the band energy in the photon space, and the associated standard deviation and spectral entropy are calculated. The harmonic generation spectra in a thin crystal, for the neodymium-doped yttrium aluminum garnet laser frequency $\omega =1.169\mathrm{}$ eV, are obtained, both in the perturbative and nonperturbative intensity domains. The calculated emission spectra for an insulator, a semiconductor, and a metal film are compared. The semiconductor medium is found to be somewhat more efficient than the metal or the insulator. A “transition intensity” for strong harmonic generation in crystalline media occurs at about an intensity I=${10}^{-4}$ a.u., i.e., $3.51\times {10}^{12}$ W/cm${}^2$.

We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the code words can be explicitly constructed. For an $n$-qubit code whose stabilizer has $d$ generators, the resulting gate array consists of $O\left(\mathrm{nd}\right)\mathrm{}$ operations, and converts $k$-qubit data (where $k=n-d)$ into $n$-qubit code words.

Radiation conditions are introduced as an exact method to truncate numerical solutions of the time-dependent Schrödinger-equation at the boundaries of the numerical grid. A rigorous derivation of radiation conditions is given by the Green-function method for one- and three-dimensional regions. An accurate finite-difference representation is obtained for a one-dimensional region. The method is applied to calculations of strong-field photoionization. The calculation of ionization probabilities and energy spectra by the truncated solution is illustrated.

Molecular nonadiabatic response to the sudden switching on (rise times of few femtoseconds) of intense (tens of TW/cm${}^2)$ laser pulses may lead to some unexpected enhancements of dissociation rates. These effects are accounted for by the spreading of the molecule-plus-field wave packet over several resonances (instead of a single one predicted when the laser is adiabatically switched on) interfering during the excitation process. Typical time-resolved signatures of such highly nonlinear responses are thoroughly investigated in terms of the evolution of vibrational survival probabilities and fragment kinetic energy spectra of ${\mathrm{H}}_2^{+}$ molecular ion taken as an illustrative example. A plausible 532-nm wavelength single-photon dissociation scenario bringing into the system less energy than the minimum required for the fragmentation to occur is examined. The suggested mechanism, which may be termed below-threshold dissociation, as opposed to above-threshold dissociation, refers to a very sharp rise of the laser pulse resulting into temporal excitation of some resonances lying above the single-photon dissociation energy, with efficient decay rates.

We consider a fibrillar medium with a continuous distribution of two-level atoms coupled to quantized electromagnetic fields. Perturbation theory is developed based on the current algebra satisfied by the atomic operators. The one-loop corrections to the dispersion relation for the polaritons and the dielectric constant are computed. Renormalization-group equations are derived that demonstrate a screening of the two-level splitting at higher energies. Our results are compared with known results in the slowly varying envelope and rotating-wave approximations. We also discuss the quantum sine-Gordon theory as an approximate theory.

This paper describes the influence of nonlinear interaction of a two-level atom with a single-mode field via one-photon interaction on the squeezing properties of the radiation and the fluctuations of the atomic dipole variables. The thermal Jaynes-Cummings model nonlinear in occupation number is used.

Starting from the Maxwell-Bloch equations for a three-dimensional (3D) ring-cavity laser, we analyze stability of the nonlasing state and demonstrate that, at the instability threshold, the wave vectors of the critical perturbations belong to a paraboloid in the 3D space. Then, we derive a system of nonlinear evolution equations above the threshold. The nonlinearity in these equations is cubic. For certain sets of four spatial modes whose vectors belong to the critical paraboloid, the cubic nonlinearity gives rise to a resonant coupling between them. This is a nontrivial example of a nonlinear dissipative system in which the cubic terms are resonant. The equations for the four coupled amplitudes have two different solutions that are simultaneously stable: the single-mode one and a solution in which all the amplitudes are equal, while a certain combination of the phases is $\pi$. The latter solution gives rise to a quasiperiodic pattern in the infinite 3D cavity. We also consider effects of the boundary conditions and demonstrate that if the cavity’s cross section is a trapezium it may support the quasiperiodic four-mode state rather than suppressing it. Using the Lyapunov function, we find that for the ring-laser configuration the four-mode state is metastable. However, we demonstrate that for a Fabry-Pérot cavity, where diffusion washes out the standing-wave grating, this state is absolutely stable. We also consider a number of more complicated patterns. We demonstrate that adding a pair of resonant vectors, or any number of nonresonant ones, always produces an unstable solution. A set containing several resonant quartets without resonant coupling between them may be stable, but it is less energetically favorable than a single quartet.

Sum-frequency generation enhanced by electromagnetically induced transparency (EIT) has been extended to the production of extreme ultraviolet (XUV) radiation in the range 97.3–92.6 nm from $np-1s$ transitions $(n=4\mathrm{}–8)$ in atomic hydrogen. Pulsed radiation was generated by strong coupling of the $\mathrm{np}$ and $2s$ levels with laser radiation at Balmer wavelengths, and simultaneously (weaker) coupling of the $2s$ and $1s$ levels by two-photon resonance with 243-nm laser radiation. Investigations were carried out over a range of laser intensities and products of interaction length and atomic density $\mathrm{}\left(\mathrm{NL}\right).$ As the product $\mathrm{NL}$ increased, the XUV intensities were greatly enhanced by EIT, and at high $\mathrm{NL}$ values, the spectral distributions of some of the generated signals were found to be distorted by the presence of molecular hydrogen. Calculated profiles, modified to incorporate the effects of nearby molecular resonances, were shown to be in good agreement with the observed spectra.

The influence of laser fluctuations on the optical excitation of Rydberg and continuum states close to a photoionization threshold is investigated within the framework of the phase diffusion model. Theoretical methods are developed for solving the relevant master equation of the atomic density operator which is averaged over the laser fluctuations. In the long-time limit this laser-induced excitation process exhibits nonexponential decay. This nonexponential time dependence reflects the fluctuation-induced diffusion of the Rydberg electron toward the ionization threshold.

The hyperspherical harmonics which appear in the analysis of the planar three-body problem are explicitly expressed in terms of the harmonics of importance in the theory of magnetic monopoles. This connection is achieved by transforming the eigenvalue equations which define hyperspherical harmonics into the eigenvalue equations for monopole harmonics. This transformation requires the recognition of a gauge potential which arises in the three-body problem and which has the same form as that of a magnetic monopole. In this manner, explicit formulas for the two standard representations of the three-body harmonics are derived. The coupling coefficients between the two representations follow naturally from the derivation. Emphasis is placed on the gauge theoretical aspects of the derivations and the significance of gauge transformations is discussed.

A semiclassical model of the force and momentum diffusion on a point particle is used to describe the motion of a two-level atom strongly coupled to a single Gaussian cavity mode. The effects of the momentum diffusion on the motion of an atom in a cavity are investigated in a regime similar to that of the experiment performed by Mabuchi et al. [Opt. Lett. 21, 1393 (1996)]. It is found that a slow atom quickly develops significant velocities along the cavity axis. The limited bandwidth in the experiment of Mabuchi et al. means that the full intensity signal due to atomic motion in the standing wave is filtered leading to the apparently smaller velocities observed. It is shown that a negative detuning of the laser and cavity from the atomic resonance would lead to nonzero dipole forces and significantly reduced velocities along the standing wave. An analysis of the intensity signal with a larger bandwidth is proposed, which would track the velocity of the atom along the cavity axis. These results are compared with a Monte Carlo wave-function simulation similar to that used to treat Doppler cooling.

Semiconductor vertical-cavity surface-emitting lasers (VCSELs) are known to exhibit a small amount of birefringence. We present a model that enables us to estimate how much of this is due to the electro-optic effect produced by the inevitable internal electric field in working devices. Of vital importance for this model is the notion that the position-dependent changes in the refractive index should be weighted by the local optical intensity both in the spacer as well as in the distributed Bragg reflectors. Index variations in the optical nodes thus go unnoticed, whereas those in the antinodes can strongly affect the cavity resonance. This is related to the idea that the active quantum wells in a VCSEL should be positioned in optical antinodes to produce the highest modal gain. The results of our model calculation are compared with statistical data on the magnitude and orientation of the measured birefringence in planar proton-implanted VCSELs. These data show the presence of a systematic contribution to the birefringence, which can presumably be attributed to the electro-optic effect, and a random contribution, which we attribute to stress and strain.

The cone emission obtained from pumped two-level atoms is related, by a perturbation theory, to time-dependent terms in the macroscopic Bloch equations. It is described as a cooperative superfluorescence radiation from collections of spatially distributed atoms, including in the theory the far-zone dipole-dipole interactions, in the presence of the strong monochromatic field. The distribution of the cone emission as a function of frequencies and cone angles is analyzed. A phase-matching condition is obtained for the wave vectors of the pump and conical beams that is similar to the Cherenkov condition. The frequency shift for the maximum of the cone light is found to be equal to the generalized Rabi frequency. The broadening of the cone emission is related to inhomogeneity in Rabi frequencies and decoherence effects. An approximate result is obtained for the ratio of intensities of the blue-shifted cone relative to the red-shifted cone so that the blue-shifted cone can appear only for extremely strong laser intensities.

The amplified Stokes beam’s mode structure in the Raman amplifier, which comes from the interplay of gain guiding and index guiding, is studied both numerically and experimentally in this paper. Theoretical results predict that gain and index guiding will lead to a narrower amplified Stokes beam of higher output energy when the input Stokes signal is detuned to the blue side of the Raman resonance. In addition, the results show that the coupling strength of an input Stokes beam into the Raman amplifier is related to the spatial overlap of the input Stokes mode with the mode supported by the Raman amplifier. Overall there is a competition between diffraction and the nonlinear effects of gain and index guiding. Theoretical calculations predict that the coupling of the Gaussian input signal mode into the amplifier is optimized by shifting the focus of the input signal towards the entrance to the Raman amplifier, shortening the Rayleigh range on the input signal with respect to the pump beam, and detuning the input signal to the blue side of the Raman resonance, all of which are contrary to the common usage of the Raman amplifier. A discussion of these phenomena in terms of a nonorthogonal mode description of the amplifier is given.

We investigate the polarization fluctuations caused by quantum noise in quantum-well vertical-cavity surface-emitting lasers (VCSELs). Langevin equations are derived on the basis of a generalized rate equation model in which the influence of competing gain-loss and frequency anisotropies is included. This reveals how the anisotropies and the quantum-well confinement effects shape the correlations and the magnitude of fluctuations in ellipticity and in the polarization direction. According to our results, all parameters used in the rate equations may be obtained experimentally from precise time-resolved measurements of the intensity and polarization fluctuations in the emitted laser light. To clarify the effects of anisotropies and of quantum-well confinement on the laser process in VCSELs we therefore propose time-resolved measurements of the polarization fluctuations in the laser light. In particular, such measurements allow us to distinguish the effects of frequency anisotropy and of gain-loss anisotropy and would provide data on the spin relaxation rate in the quantum-well structure during cw operation as well as representing a different way of experimentally determining the linewidth enhancement factor $\alpha$.

A Langevin model is introduced to study quantum fluctuations below the threshold of pattern formation for optical parametric oscillators (OPO’s). In particular we compare analytical and numerical results for the OPO with one and two transverse spatial dimensions and in the presence of either plane or spherical cavity mirrors. The far-field structure and the correlation functions of the fluctuating signal field anticipate the onset of a transverse spatial pattern which arises classically even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field. Numerical simulations of the Langevin model describe the result of short time measurements and show that close to threshold the near-field signal is a noisy spot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experimentally accessible.

Quantum electrodynamics of two identical two-level atoms placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied within the framework of the dipole resonance (rotating-wave) approximation. For finite interatomic distances a polariton-atom bound state lying within the polaritonic gap is shown to be split into a doublet due to an effective atom-atom interaction. Evaluating the splitting as a function of the interatomic separation, we estimate a width of a polariton-impurity band when a system of spatially correlated atoms is present. The results obtained for the case of two atoms are then generalized to the case of an atomic chain (a one-dimensional atomic lattice). The equations describing a propagation of a band polariton are derived and the expressions for the band polariton spectrum and its effective mass are obtained. The model under consideration has quite a general structure and is applied to the case of photonic-band-gap materials as well. Numerical calculations are presented for SiC semiconductors.

We extend previous work on macroscopic canonical quantization leading to a multipolar Hamiltonian appropriate for application to quantum optics and cavity QED situations involving classical optical devices. In particular, we show that the electric displacement is the negative of the conjugate momentum field and that the Coulomb and polarization energies are equal to the sum of intra-atomic Coulomb and polarization energies and interatomic contact energies. The quantum Hamiltonian is now in a form in which the theory is manifestly gauge invariant.

Using a completely semiclassical approach we extend a previous theory of the collective atomic recoil laser to include propagation effects with and without a ring cavity, and to take into account the effects of Doppler broadening. For cold atoms, we determine a mean-field condition under which propagation effects are negligible, and find different dynamical regimes that we classify as “good” and “bad” cavity limits. We obtain the results of a previous single-mode theory only in the good cavity limit. In the bad cavity limit or in free space collective superradiant behavior dominates. For warm beams, where Doppler-broadening effects are important, a noncollective Raman gain mechanism dominates in general, as recently observed experimentally. The effects of particle trapping in the ponderomotive potential and radiation pressure have been described.

A simple approach is proposed for the quantization of the electromagnetic field in nonlinear and inhomogeneous media. Given the dielectric function and nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is determined completely by this quantization method. From Heisenberg’s equations we derive Maxwell’s equations for the field operators. When the nonlinearity goes to zero, this quantization method returns to the generalized canonical quantization procedure for linear inhomogeneous media [Phys. Rev. A 43, 467 (1991)]. The explicit Hamiltonians for the second-order and third-order nonlinear quasi-steady-state processes are obtained based on this quantization procedure.