Stoliarov Y. Photon transport in one-dimensional waveguides and non-adiabatic molecular dynamics.

The thesis concerns the dynamics of scattering of photonic and nuclear wave packets on quantum emitters in one-dimensional waveguides and crossings of potential energy surfaces in molecular systems. The interaction of the coherent-state wave packet with a two-level atom (qubit) in a one-dimensional waveguide is studied. The evolution equation for the qubit excited state population is derived. It is demonstrated that the qubit excitation depends on the average photon number in the ingoing pulse. Statistics of the radiation scattered off the qubit is studied. It is found that for a large number of photons in the ingoing pulse, the transmitted radiation is described by the superpoissonian statistics, while the reflected radiation can feature either sub- or superpoissonian statistics depending on the coupling strength between the qubit and the waveguide. The photon density distribution function in phase (coordinate-momentum) space is used for the description of the scattering of single- and two-photon wave packets on a qubit. It is demonstrated that the average phase-space distribution function of the scattered single-photon wave packet acquires negative values in specific regions of phase space even in the case of the positive initial distribution. Analytical expressions for spatial and momentum-space (spectral) distributions of the scattered photons are derived. In the case of the two-photon ingoing wavepacket constituted by a pair of identical spatially-separated single-photon pulses, the equations of motion governing the evolution of the photon phase-space distribution function are derived and solved numerically. It is demonstrated that for the two-photon ingoing wave packet, the regions of negative values of the photon distribution function emerge only for specific values of the qubit-waveguide coupling and the distance between the single-photon components of the ingoing pulse. It is shown that the average number of scattered photons and its variance depends not only on the qubit-waveguide coupling strength and the distance between the single-photon ingoing pulses but also on the bandwidth of the latter. The time-dependent wavefunction of the system is employed for the description of the two-photon wave packet evolution in a one-dimensional waveguide coupled to a resonator-qubit system. The set of equations of motion governing the probability amplitudes, which describe the quantum state of the system, is derived and solved both analytically and numerically. This allows investigating a modification of the spectrum of the wave packet in the course of its interaction with the resonator-qubit system as well as the excitation dynamics of the latter. It is demonstrated that the probability of finding two excitations in the resonator-qubit system is significantly reduced compared to the case of the resonator uncoupled from the qubit, which indicates the photon blockade in this subsystem. It is shown that the spectrum of the scattered wave packet differs from the spectrum of the ingoing wave packet. Using the Schmidt decomposition, it is demonstrated that the scattered photons are entangled in contrast to the separable state of the ingoing photons. Dispersive readout of the qubit using the photodetector in the ultimate limit of the single-photon probe pulse is considered. Coupling between the qubit and the resonator is described by the Rabi Hamiltonian. Fast-oscillating terms in the qubit-resonator coupling Hamiltonian are treated as a perturbation and are eliminated using the unitary transformation resulting in the Bloch-Siegert shift in the resonator frequency. The advantages and limitations of the considered readout scheme is discussed in detail. The parameters of the system providing the maximal readout contrast are determined. Modeling the non-adiabatic processes in molecular systems is a requisite tool for the theoretical study of various photoinduced processes such as exciton localization, charge transfer in photosynthetic complexes and photovoltaic systems. The effective Hamiltonian, describing transitions between electronic adiabatic levels and quantum fluctuations along the classical nuclear trajectories, is introduced. The evolution equations governing the electronic occupation numbers and the nuclear degrees of freedom are derived using this Hamiltonian and the density operator formalism. It is shown that these equations become Markovian in the case of strong decoherence. Equations of motion for the electronic occupations are studied in the non-Markovian regime as well. The algorithm for modeling the non-adiabatic molecular dynamics is implemented using the proposed theoretical approach.