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In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
We study the self interference effect of a resonator coupled with a bent waveguide at two separated ports. Such interference effects are shown to be similar for the cases of standing-wave and traveling-wave resonators, while in the system…
We study a fermionic atom optics counterpart of parametric down-conversion with photons. This can be realized through dissociation of a Bose-Einstein condensate of molecular dimers consisting of fermionic atoms. We present a theoretical…
We study CPT- and Lorentz-odd electrodynamics described by the Standard Model Extension. Its radiation is confined to the geometry of hollow conductor waveguide, open along $z$. In a special class of reference frames, with vanishing both…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We study the light transmission in two-dimensional photonic crystal waveguides with embedded nonlinear defects. First, we derive the effective discrete equations with long-range interaction for describing the waveguide modes, and…
We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the…
Quantum imaging enhances imaging systems performance, potentially surpassing fundamental limits such as noise and resolution. However, these schemes have limitations and are still a long way from replacing classical techniques. Therefore,…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
A novel approach to study transmission through waveguides in terms of optical streamlines is presented. This theoretical framework combines the computational performance of beam propagation methods with the possibility to monitor the…
Parametric down-conversion is a widely used source of nonclassical light in quantum optics and photonic quantum technologies. While stimulated parametric down-conversion with strong classical seeds is well studied, the regime in which…
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the…
Recent advances in quantum optics have highlighted the critical role of spatial propagation in controlling the quantum coherence of light beams. However, the evolution of quantum coherence for light beams undergoing fundamental optical…
We propose a numerical technique for modeling the quantum multimode light scattering by a perfectly conducting body. Using the novel quantization technique, we give the quantum adaptation of the characteristic mode approach widely used in…
This Habilitation manuscript describes the work done at JQI-NIST and LKB-ENS-Sorbonne University since 2010. After a brief introduction of the needed concepts for non-linear and quantum optics in optically dense atomic medium, I review…
We study the fundamental limits of the precision of estimating parameters of a quantum matter system when it is probed by a travelling pulse of quantum light. In particular, we focus on the estimation of the interaction strength between the…
Nanophotonics focuses on the control of light and the interaction with matter by the aid of intricate nanostructures. Typically, a photonic nanostructure is carefully designed for a specific application and any imperfections may reduce its…
Development of artificial materials exhibiting unusual optical properties is one of the major strands of current photonics research. Of particular interest are soft-matter systems reconfigurable by external stimuli that play an important…
This thesis is devoted to the study of the coupling of single-photon emitters with photonic nanostructures by using the properties of the near field of a photonic structure in view of the realization of a compact integrated single-photon…
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical…