We study the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit. We derive a general, basis-independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well-controlled fluctuations in the potential, making the atom-lattice system attractive for the study of decoherence and the connection between classical and quantum physics.

We present analytical and numerical results for the microwave excitation of nonhydrogenic atoms in a static electric field when up to 1000 photons are required to ionize an atom. For small microwave fields, dynamical localization in photon number leads to exponentially small ionization while above quantum delocalization border ionization goes in a diffusive way. For alkali-metal atoms in a static field the ionization border is much lower than in hydrogen due to internal chaos.

The dissociation of a diatomic molecule by a chirped infrared laser pulse is modeled by a Morse oscillator interacting with a classical electric field with a time-dependent frequency. Our previous classical analysis in terms of bucket dynamics, in which systems within the single-node separatrices (buckets) in phase space are trapped and undergo convection to highly excited states, is found to be applicable to the more general cases of nonlinear chirping and using a realistic dipole moment function for the molecule. This route of excitation leads to a much lower dissociation threshold laser intensity when compared to the chaotic diffusion route for monochromatic excitation. Time-dependent quantum mechanical calculations of the dissociation probability based on the split-operator method are performed. It is found that the classical and quantum results agree well, and the classical resonances appear also in the quantum probabilities. Hence the classical method can be used to investigate various characteristics of the chirped pulse excitation and dissociation processes.

Analytic expressions for the peak positions and pump frequency shift of equal intensity weak probe Autler-Townes transitions to a third level in the presence of a linearly polarized pump field are given. It is found that the presence of the third level affects the pump field dressing of the strongly excited two levels. A comparison of the Bloch-Siegert shift estimated by this weak probe technique with earlier methods suggests this condition provides a practical method for obtaining the Bloch-Siegert shift for three level systems where the pump field does not directly excite the probe transition. If the pump field off-resonantly drives the probe transition, additional light shifts occur which may dominate the Bloch-Siegert shift.

We investigate the Rydberg wave packet dynamics of core-driven two-electron atoms with the density matrix formalism. The spontaneous emission of the core transition is included. We show how it modifies the dynamics of radial Rydberg wave packets, which are nondispersing, but slowly decaying in the absence of spontaneous emission. Although our considerations apply to all two-electron atoms, we focus on the experimentally convenient element calcium.

Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He${}_2$ dimer, this might no longer hold true due to the possibility of breakup processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system, we recover the usual optics results. For smaller widths, however, deviations therefrom occur. We find that the location of possible diffraction peaks is indeed still governed by the usual grating function from optics, but the peaks may have a lower intensity. This is not unexpected when breakup processes are allowed. More unusually though, diffraction peaks that would be absent for de Broglie waves may reappear. The results are illustrated for diffraction of He${}_2$.

We investigate the possibility of obtaining Bose-Einstein condensation (BEC) in a steady state by continuously loading atoms into a magnetic trap while keeping the frequency of the radio frequency field fixed. A steady state is obtained when the gain of atoms due to loading is balanced with the three dominant loss mechanisms due to elastic collisions with hot atoms from the background gas, inelastic three-body collisions, and evaporation. We describe our model of this system and present results of calculations of the peak phase-space density ${\rho }_0$ in order to investigate the conditions under which one can reach the regime ${\rho }_0>~2.612$ and attain BEC in steady state.

The degenerate and nondegenerate nonlinear Kerr coefficients $n_2$ of disordered media composed of submicrometer dioxide titania particles embedded in a dye solution were measured using an interferometric technique. The influence of the scattering particles on the value of $n_2$ are discussed in the light of stimulated emission in these systems. The results obtained can be useful for applications in nonlinear ultrashort pulse propagation in disordered media.

The lasing threshold of a multimode chaotic cavity (linear size $D$ $\gg$ wavelength $\lambda )$ coupled to the outside through a small hole (linear size $d\ll \lambda )$ is studied. For sufficiently weak absorption by the boundaries, the statistical distribution of the threshold is wide, its mean value being much less than the pumping rate needed to compensate the average loss. The average number $〈N_{\mathrm{nc}}〉\gg 1$ of noncompeting excited modes is proportional to the square root of the pumping rate. We use the classical model of spatial hole burning to account for mode competition and find a reduction in the average number of excited modes to $〈N〉{=3\mathrm{}}^{1/3}〈N_{\mathrm{nc}}{〉}^{2/3}$.

A sub-Poissonian distribution of photon numbers (photon-number squeezing) within a microcavity is theoretically shown to be possible using a realistic model of nonlinear photon dissipation. By deriving and solving a stochastic Schrödinger equation for a system with photons and atoms in a microcavity, we have obtained strong antibunching and a sub-Poissonian distribution of the number of emitted photons from the microcavity. The relationship among the above three statistical quantities, which describe the nonclassical nature of the quantum radiation field, are also discussed.

Transverse effects in the laser threshold, originated by electronic-vibrational coupling in the active centers, are analyzed theoretically by means of the semiclassical two-level Maxwell-Bloch equations. A single longitudinal mode is considered. It is found that the first laser threshold suffers modifications depending on the electronic-vibrational coupling strength. This coupling imposes certain conditions for the selection of a particular transverse spatial state and provides the minimum wavelength that can appear in the transverse pattern. The nature of the bifurcation and the stability of the homogeneous and critical traveling waves are analyzed.

We show that, for a pure state, the quantum state of the radiation field can be directly determined from the resonance fluorescence spectrum when the quantized field serves as the driving field for the two-level atoms. This happens when the vacuum Rabi frequency is much larger than the atomic decay rate. The proposed method is insensitive to the detector efficiency.

The modification of the statistical properties of vacuum fluctuations, via quadrature squeezing, can dramatically reduce the absorptive and dispersive properties of two-level atoms. We show that for some range of parameter values the system exhibits zero absorption accompanied by zero dispersion of the probe field. This complete transparency is attributed to the coherent population oscillations induced by the squeezed vacuum.

Evaluation of the Greenberger-Horne-Zeilinger (GHZ) theory requires an entangled $n$-particle state with $n>~3$. To date, experimental achievement of a suitable GHZ state has proved elusive. This paper presents an approach to generate a three-photon entangled state and presents the theory of its space-time structure. Since an accurate picture of the space-time structure is important in understanding the two-photon state, an accurate picture of the three-photon state should be equally important.

The polarization properties of semiconductor vertical-cavity lasers (VCSELs) are generally described with a model introduced by San Miguel, Feng, and Moloney (SFM) in Phys. Rev. A 52, 1728 (1995). We have analyzed this SFM model from an experimentalist’s point of view, using the idea that under certain conditions, which are satisfied by most practical VCSELs, the complicated spin dynamics can be adiabatically eliminated, leading to a managable analytical description. We hereby obtain new physical insight and intuitive pictures. One of the key results is the prediction that, via the spin dynamics, the presence of a strong lasing mode with a certain polarization will effectively lead to a broadening and frequency shift of the weak nonlasing mode with orthogonal polarization. This result gives a simple physical explanation for a polarization switch predicted by the model, and leads to further predictions that can be experimentally verified. The analysis also shows how the relaxation oscillations are related to the polarization dynamics and how they might be of crucial importance to experimentally determine the various parameters in the SFM model. We then discuss how the spin elimination reduces the SFM model to existing models for the polarization dynamics of class A (gas) lasers, with intuitive pictures of the polarization evolution on the Poincaré sphere. Finally we will show how, within the context of adiabatic elimination, the cubic crystalline symmetry plays a special role in possible generalizations of the SFM model.

The photon correlation phenomenon and photon count statistics in the resonance fluorescence of a two-level atom interacting with a strong bichromatic field are investigated. An analytical result is obtained for the second-order correlation function. Unusual quantum-statistical properties of the fluorescent radiation are obtained, and effects on the photon correlation influenced by electromagnetic reservoirs is shown.

We present a scheme that deterministically generates an arbitrary prescribed quantum entangled state of a trapped ion. The quantum entanglement is between the external (center-of-mass motion in one dimension) and the internal (electronic) state of the trapped ion. We examine the influence of technical errors in our scheme. Further we show how to entangle the center-of-mass motion of the confined ion in two dimensions.

Squeezing properties of a quantized photon field interacting with cascade four-wave-mixing materials (phase conjugators) are investigated theoretically by the transfer-matrix method. The controllability of the quantum fluctuation of the photon field is improved with the use of modulation pumping, in which phases of pumping beams of the phase conjugators are individually controlled even when their optical nonlinearity and/or the pumping power are fixed. By choosing appropriate numbers of phase conjugators and phase differences of the pump beams, incident coherent light is transformed to quadrature-phase-amplitude (QPA) squeezed states and photon-number-squeezed states. Optimal squeezing of both the QPA and photon number can be realized with this cascade system by modulation pumping. Partial (normal) reflection of light at surfaces of the phase conjugators is shown quantitatively to suppress the squeezing. Comparison with an ordinary method using a single-phase conjugator is also made.

In this paper we study the one-dimensional dynamical Casimir effect. We consider a one-dimensional cavity formed by two mirrors, one of which performs an oscillatory motion with a frequency resonant with the cavity. The naive solution, perturbative in powers of the amplitude, contains secular terms. Therefore it is valid only in the short time limit. Using a renormalization-group technique to resum these terms, we obtain an improved analytical solution which is valid for longer times. We discuss the generation of peaks in the density energy profile and show that the total energy inside the cavity increases exponentially.

First-order multiple-scale perturbation theory is used to derive a set of coupled-mode equations valid for electromagnetic-wave propagation in a weakly periodic, nonlinear medium with periodicity on the order of a wavelength. We apply this to a problem where the medium has a ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ response and find that the second-harmonic signal generated is enhanced when the fundamental is tuned near the band edge. Results are given for a possible experiment with optical fibers.