The thesis is devoted to the theoretical studies of coherent control and manipulation of classical or quantum light via nonlocal effects. At the classical level, controllable light propagation dynamics in the paraxial regime is investigated. The specific type of nonlocal linear effects induced in thermal atomic vapor is explored to achieve diffractionless and lossless propagation, uniform phase modulation, and frequency conversion with diffractionless image duplication for laser beams with arbitrarily encoded spatial profiles. Next, the study is extended to investigate propagation dynamics in the presence of nonlocal nonlinear effects generated in thermal interacting Rydberg atoms, which mainly reveals simultaneous competition between the nonlocal nonlinear absorption and the modulational instability for each wave component. Moreover, parity-time (PT) symmetric dynamics in cold Rydberg atoms are exploited, and it is shown that a phase transition from unbroken to broken PT symmetry can be induced by nonlocal nonlinear effects. At the quantum level, it is further proposed to test the quantum nonlocality of single x-ray photons in a system where very weak x-ray pulses interact with 57Fe nuclei in a thin cavity, such that a Bell-like inequality in the single-photon version is violated. All these proposals are feasible in current experimental settings.
The thesis is devoted to the theoretical studies of coherent control and manipulation of classical or quantum light via nonlocal effects. At the classical level, controllable light propagation dynamics in the paraxial regime is investigated. The specific type of nonlocal linear effects induced in thermal atomic vapor is explored to achieve diffractionless and lossless propagation, uniform phase modulation, and frequency conversion with diffractionless image duplication for laser beams with arbitrarily encoded spatial profiles. Next, the study is extended to investigate propagation dynamics in the presence of nonlocal nonlinear effects generated in thermal interacting Rydberg atoms, which mainly reveals simultaneous competition between the nonlocal nonlinear absorption and the modulational instability for each wave component. Moreover, parity-time (PT) symmetric dynamics in cold Rydberg atoms are exploited, and it is shown that a phase transition from unbroken to broken PT symmetry can be induced by nonlocal nonlinear effects. At the quantum level, it is further proposed to test the quantum nonlocality of single x-ray photons in a system where very weak x-ray pulses interact with 57Fe nuclei in a thin cavity, such that a Bell-like inequality in the single-photon version is violated. All these proposals are feasible in current experimental settings.
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.
In modern physics, coherent manipulation of photons and electrons has been intensively studied, and may have important applications in classical and quantum information processing. In this dissertation, we consider some interesting schemes to realize photonic and electronic coherent manipulation. ^ In order to coherently manipulate photons, electromagnetically induced transparency (EIT) systems have been widely adopted because the optical response of EIT systems can be controlled by the laser-induced atomic coherence. ^ In the second chapter, we theoretically investigate image storage in hot-vapor EIT media. A so-called 4f system is adopted for imaging, and an atomic vapor cell is placed over the transform plane. The Fraunhofer diffraction pattern of an object in the object plane can thus be transformed into atomic Raman coherence according to the idea of "light storage". We investigate how the stored diffraction pattern evolves under diffusion and discuss the essence of the stability of its dark spots. Our result indicates under appropriate conditions that an image can be reconstructed with high fidelity. The main reason for this procedure is the fact that diffusion of opposite-phase components of the diffraction pattern interfere destructively. ^ In the third chapter, we show theoretical evidence that EIT systems can function as optically addressed spatial light modulators with megahertz modulation rates. The transverse spatial properties of continuous-wave probe fields can be modulated rapidly using two-dimensional optical patterns. To exemplify our proposal, we study real-time generation and manipulation of Laguerre-Gaussian beams by means of phase or amplitude modulation using flat-top image-bearing pulse trains as coupling fields in low-cost hot-vapor EIT systems. ^ In order to coherently manipulate electrons, we consider graphene systems, including single-layer graphene and bilayer graphene, which have recently attracted considerable attention. Due to the long coherence length and electrically tunable Fermi levels, electrons in graphene systems have some photon-like behaviors, and could be coherently manipulated. ^ Therefore, in the fourth chapter, we theorize that at a sharp electrostatic step potential in graphene massless Dirac fermions can obtain Goos-Hänchen-like shifts under total internal reflection. Also, we study coherent propagation of the quasiparticles along a sharp graphene p-n-p waveguide, and derive novel dispersion relations for the guided modes. Consequently, coherent graphene-based devices, e.g., movable mirrors, buffers and memories, induced only by the electric field effects may be proposed. ^ Finally, we theoretically investigate the coherent propagation of massive chiral fermions along a sharp bilayer graphene p-n-p waveguide, and indicate that the guided quasiparticles can be coherently slowed, stored and retrieved based on tunable electric field effects. Controlling group velocity in the bilayer graphene p-n-p waveguide is accomplished via interband tunneling through the p-n interfaces, and does not depend on the bandgap opening. ^
Photons are good candidates for carrying quantum information because they are very stable particles: they interact weakly with the medium and barely with each other. However, this has drawbacks when you want to process the information because, in this case, it is preferable to have photon-photon interactions. For example, for applications in quantum repeaters, such interactions would allow deterministic Bell state measurements, increasing the entanglement distribution rate between two remote nodes. Getting two photons to interact with each other efficiently requires mapping them into a nonlinear medium at the single-photon level, that is, a medium that reacts differently when it interacts with a single photon than when it does with two. Such strong nonlinearity has been demonstrated with Rydberg atoms, which are atoms excited to a state with a high principal quantum number.
In this thesis we have performed nonlinear quantum optics experiments using an ensemble of cold Rydberg atoms, where we have studied the properties of the quantum light emitted by these atoms. First, we demonstrated nonlinearities at the single-photon level. To reach this stage, we made several improvements to the previous experimental setup available in the group, of which the implementation of a dipole trap was especially relevant. We evidence quantum nonlinearity by measuring photon antibunching for the transmitted light after interacting with the Rydberg state under electromagnetically induced transparency (EIT). We also showed the generation of single photons on-demand after storing weak coherent states of light pulses as collective Rydberg excitations.
Then, we studied the variation of the light statistic throughout the output pulse after propagating through the medium as Rydberg polaritons, which are superposition states of light and Rydberg excitations. We showed that the properties at the beginning and the end of the pulse were different from those of the steady state. In particular, the light detected after the input pulse was abruptly turned off gave much stronger suppression of two-photon events. Then, we investigated how to exploit this effect to generate single photons on demand. To do this, we analyzed the quality of the single photons detected at the end of the pulse as a function of the detection probability and compared the results with those obtained by storing the input pulse as collective Rydberg excitations. We showed that the photons were generated more efficiently when increasing the detection window at the cost of deteriorating the single photons statistics.
Finally, we investigated the indistinguishability of the photons emitted by our Rydberg atomic ensemble, a crucial property for using Rydberg atoms as nodes in quantum networks. We also compared the single photons generated after storage under EIT conditions with those obtained using a two-photon Raman excitation to the Rydberg state. We measured the indistinguishability by making them interfere with weak coherent states of light in a Hong-Ou-Mandel experiment. And we showed that, although we obtained better photon statistics under EIT conditions, the indistinguishability from those obtained with Raman excitation was significantly higher.
In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting interaction entangles the light and the system, and the light continues its course. Within the framework of open quantum systems, the light is eventually traced out, leaving the reduced quantum state of the system as the primary mathematical subject. Two major results are presented. The first is a master equation approach for a quantum system interacting with a traveling wave packet prepared with a definite number of photons. In contrast to quasi-classical states, such as coherent or thermal fields, these N-photon states possess temporal mode entanglement, and local interactions in time have nonlocal consequences. The second is a model for a three-dimensional light-matter interface for an atomic ensemble interacting with a paraxial laser beam and its application to the generation of QND spin squeezing. Both coherent and incoherent dynamics due to spatially inhomogeneous atom-light coupling across the ensemble are accounted for. Measurement of paraxially scattered light can generate squeezing of an atomic spin wave, while diffusely scattered photons lead to spatially local decoherence.
Most phenomena around us can be explained by classical optics since photons interact weakly with atoms. When the interaction is strong enough where one photon affects the properties of other photons, we go to the regime of quantum photon-photon nonlinear optics. The work in this thesis explores this regime of physics. This paves the path to exploring strongly interacting many-body physics with photons which is still a largely unexplored domain. The ability to control strongly interacting photons is also of central importance in quantum science and engineering. We use the approach of Electromagnetically Induced Transparency (EIT) in atomic ensembles to create strong interactions and demonstrate coherent control between single photons. Using EIT, we coherently map single photons onto the atoms which travel as coupled excitations of light and matter called dark-state polaritons. When the medium is optically dense, the polariton propagates as a massive particle with a velocity that is much smaller than the speed of light. These polaritons interact with each other via their atomic component. In this thesis, we show robust symmetry-protected collisions between photons that imprint a large phase of π/2 with little loss and extend the nature of photon-photon interactions to the repulsive regime, which are essential for quantum communication and metrology. We use the technique of photon blockade to make a fast optical detector of Rydberg states, directly demonstrating the use of quantum nonlinear optics for quantum computation. We also study the extensions of the attractive and repulsive photons for three particles shedding light into the formation of bound states and crystals of photons and paving the way to studying many-body physics of photons.
Integrated optical quantum circuits based on photonic waveguiding structures are increasingly gaining attention as a possible solution for scalable quantum technologies with important applications to quantum simulations. Quantum communication provides secure information transmission, but the distance over which quantum states of light can be distributed without significant disturbance is limited due to inescapable losses and noise in optical elements. Loss is the greatest challenge facing the implementation of integrated photonic technologies, and it is inescapable in experimental reality. In recent years there is a rise of interest in structures with spatially inhomogeneous losses. Light propagation in waveguiding structures with spatially distributed sections of loss can be used for implementation of quantum plasmonic circuits, which are able to strongly confine light to sub-wavelength dimensions, as well as for parity-time (PT) symmetric structures, with phase transition associated with PT-symmetry breaking, which opens new possibilities for light manipulation. The PhD thesis contains research on the controllable classical and quantum dynamics of optical frequency conversion processes in quadratically nonlinear photonic integrated circuites in the presence of losses. Namely, I discuss spontaneous parametric down-conversion (SPDC), sum-frequency generation (SFG) and optical parametric amplification (OPA) in nonlinear structures governed by non-Hermition Hamiltonians. I explore the fundamental features of multi-photon generation in integrated nonlinear waveguides. I have been shown that arrays of coupled nonlinear waveguides can serve as a robust integrated platform for the generation of entangled photon states with nonclassical spatial correlations through spontaneous parametric down-conversion (SPDC), and that the operation of such quantum circuit is tolerant even to relatively high losses. Furthermore, I have studied the bi-photon multimode quantum emission tomography in waveguide structures with spatially inhomegeneous losses. The PhD thesis also covers the research on the effect of these losses in waveguide couplers possessing parity-time (PT) symmetry. I have identified an anti-PT spectral symmetry of a parametric amplifier based on those couplers. Finally, I describe the single-photon conversion to a photon pair, and identify opportunities for the efficient enhancement of this process.