We consider propagation of light pulses detuned from the atomic resonance in a dense two-level medium and the photonic structures with it. The large density of the medium is important for decreasing the spatial scale of nonlinear effects such as pulse compression, though it does not provide any fundamentally new phenomena as compared to dilute media. Frequency detuning decreases the effectivity of nonlinear phenomena such as pulse compression and dispersion-spreading compensation as well. We propose simple logic gates based on interaction between two pulses in one-dimensional nonlinear photonic crystal. We found that frequency detuning is necessary to obtain ultrafast AND gates, while OR and NOT gates can be realized in the system without detuning.
We consider propagation of light pulses detuned from the atomic resonance in a dense two-level medium and the photonic structures with it. The large density of the medium is important for decreasing the spatial scale of nonlinear effects such as pulse compression, though it does not provide any fundamentally new phenomena as compared to dilute media. Frequency detuning decreases the effectivity of nonlinear phenomena such as pulse compression and dispersion-spreading compensation as well. We propose simple logic gates based on interaction between two pulses in one-dimensional nonlinear photonic crystal. We found that frequency detuning is necessary to obtain ultrafast AND gates, while OR and NOT gates can be realized in the system without detuning.
Abstract : The mathematical algorithms and programs for the study of the resonant light-matter interactions in the multi-component and multilevel media and photonic bandgap structures have been developed. The optimal component distribution in the two-component media have been found to get a pulse of a superradiative emission of the highest intensity. The mathematical algorithms and programs for the study of the femtosecond pulse propagation in an extended medium of the two-level atoms have developed. The regime of the inversionless superradiance in the two-component superradiative medium has been investigated. The theory of the superradiance by an ensemble of the two-level atoms embedded in the dielectric host was developed. It was shown that the near dipole-dipole interaction of dense collection of two-level atoms is enhanced by the presence of the host material, decreasing the pulse temporal width and increasing the peak pulse intensity of superradiative emission. The theory of nonlinear light-matter interaction in multidimensional resonant photonic crystals under Bragg diffraction condition has been developed. It was obtained the analytical and numerical solutions describing the novel kinds of nonlinear solitary waves: the Laue soliton, O-field, propagating and standing gap solitary waves. It has been described the spatio-temporal nonlinear dynamics of coherent field in periodic resonant structures with arbitrary modulation of atomic density and gain gratings.
The present thesis is devoted to theoretical studies of pulse propagation of light through linear and nonlinear media, and of light-induced nuclear dynamics. The first part of the thesis addresses propagation of light pulses in linear periodical media - photonic crystals. The main accent was put on studies of the angular properties of two qualitatively different types of photonic crystals: holographic photonic crystals, and impurity band based photonic crystals. The anisotropy of band structure, group velocity and pulse delay with respect to the light polarization are analyzed. In the second part of the thesis a strict theory of nonlinear propagation of a few strong interacting light beams is presented. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material. This technique is applied to studies of dynamics of cavityless lasing generated by ultra-fast multi-photon excitation. It is shown that interaction of co- and counter-propagating pulses of amplified spontaneous emission (ASE) affects the dynamics and efficiency of nonlinear conversion. Our dynamical theory allows to explain the asymmetric spectral properties of the forward and backward ASE pulses, which were observed in recent experiment with different dye molecules. It is shown that the ASE spectral profile changes drastically when the pump intensity approaches the threshold level. The effect of the temporal self-pulsation of ASE is studied in detail. The third part of the thesis is devoted to light-induced nuclear dynamics. Time- and frequency-resolved X-ray spectroscopy of molecules driven by strong and coherent infrared (IR) pulses shows that the phase of the IR field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. Such a dependence arises due to the interference of one (X-ray) and two-photon (X-ray + IR) excitation channels. The phase of the light influences the dynamics also when the Rabi frequency approaches the vibrational frequency, breaking down the rotating-wave approximation. The probe X-ray spectra are also sensitive to the delay time, the duration, and the shape of the pulses. The evolution of the nuclear wave packets in the dissociative core-excited state affects the dynamics of resonant Auger scattering from fixed-in-space molecules. One of the important dynamical effects is the atomic-like resonance which experiences electronic Doppler shift. We predict that the scattering of the Auger electrons by nearby atoms leads to new Doppler shifted resonances. These extra resonances show sharp maxima in the bond directions, which makes them very promising as probes for local molecular structure using energy and angular resolved electron-ion coincidence techniques. Our theory provides prediction of several new effects, but also results that are in good agreement with the available experimental data.
Ultrashort light pulses propagating through a resonant photonic crystal can be reshaped to shorter duration output through self-induced transparency. The reshaping process is shown to result from the unique transmission behavior of light pulses through the photonic structure. Pulse compression and pulse merging, with which multipeak optical pulses can be evolved to give rise to a single-peak, high-quality transmitted pulse output, are obtained. The pulse propagation in a resonant photonic crystal is compared with that in a bulk atomic medium, which shows that the effect of pulse reshaping is much more powerful in the former than in the latter.
In this paper, we consider a method for implementing a quantum logic gate with photons whose wave function propagates in a one-dimensional Kerr-nonlinear photonic crystal. The photonic crystal causes the incident photons to undergo Bragg reflection by its periodic structure of dielectric materials and forms the photonic band structure, namely, the light dispersion relation. This dispersion relation reduces the group velocity of the wave function of the photons, so that it enhances nonlinear interaction of the photons. (Because variation of the group velocity against the wave vector is very steep, we have to tune up the wavelength of injected photons precisely, however.) If the photonic crystal includes layers of a Kerr medium, we can rotate the phase of the wave function of the incident photons by a large angle efficiently. We show that we can construct the nonlinear sign-shift (NS) gate proposed by Knill, Laflamme, and Milburn (KLM) by this method. Thus, we can construct the conditional sign-flip gate for two qubits, which is crucial for quantum computation. Our NS gate works with probability unity in principle while KLM's original one is a nondeterministic gate conditioned on the detection of an auxiliary photon.
In this paper, we consider a method for implementing a quantum logic gate with photons whose wave function propagates in a one-dimensional Kerr-nonlinear photonic crystal. The photonic crystal causes the incident photons to undergo Bragg reflection by its periodic structure of dielectric materials and forms the photonic band structure, namely, the light dispersion relation. This dispersion relation reduces the group velocity of the wave function of the photons, so that it enhances nonlinear interaction of the photons. (Because variation of the group velocity against the wave vector is very steep, we have to tune up the wavelength of injected photons precisely, however.) If the photonic crystal includes layers of a Kerr medium, we can rotate the phase of the wave function of the incident photons by a large angle efficiently. We show that we can construct the nonlinear sign-shift (NS) gate proposed by Knill, Laflamme and Milburn (KLM) by this method. Thus, we can construct the conditional sign-flip gate for two qubits, which is crucial for quantum computation. Our NS gate works with probability unity in principle while KLM's original one is a nondeterministic gate conditioned on the detection of an auxiliary photon.
The present thesis is devoted to theoretical studies of light pulse propagation through different linear and nonlinear media. One dimensional holographic photonic crystals and one dimensional impurity band based photonic crystals are investigated as linear media. The effects of angular dependence of the band structures and pulse delay with respect to the light polarization are analyzed. A strict theory of nonlinear propagation of a few strong interacting light beams is presented and applied in the field of nonlinear optics. The key idea of this approach is a self-consistent solution of the nonlinear wave equation and the density matrix equations of the material beyond the so-called rotating wave approximation. The results of numerical studies led to a successful interpretation of recent experimental data [Nature, 415:767, 2002]. A theoretical study of the NO molecule by means of two-color infrared -- X-ray pump probe spectroscopy is presented. It was found that the phase of the infrared field strongly influences the trajectory of the nuclear wave packet, and hence, the X-ray spectrum. The dependence of the X-ray spectra on the delay time, the duration and the shape of the pulses are studied.