We propose a numerical technique for modeling quantum multimodal light scattering by a perfectly conducting body. Using the special quantization technique, we develop the quantum adaptation of the characteristic mode approach widely used in classical electrodynamics. The method is universal with respect to the body's configuration, as well as its dimensions relative to the wavelength. Using this method and calculating the first- and second-order field correlation functions, we demonstrate how scattering affects quantum-statistical features of the field. As an example, we consider the scattering of two single-photon incident Gaussian beams on a cylinder with a circular cross section. We show that the scattering is accompanied by two-photon interference and demonstrates the Hong-Ou-Mandel effect. It is shown that the scattered two-photon field and its correlations manifest directive propagation, which is controllable by various means (angles of incidence, configuration of the body, relations between its dimensions and the wavelength). We expect that this method will be useful for designing quantum-optical devices.
We propose a numerical technique for modeling quantum multimodal light scattering by a perfectly conducting body. Using the special quantization technique, we develop the quantum adaptation of the characteristic mode approach widely used in classical electrodynamics. The method is universal with respect to the body's configuration, as well as its dimensions relative to the wavelength. Using this method and calculating the first- and second-order field correlation functions, we demonstrate how scattering affects quantum-statistical features of the field. As an example, we consider the scattering of two single-photon incident Gaussian beams on a cylinder with a circular cross section. We show that the scattering is accompanied by two-photon interference and demonstrates the Hong-Ou-Mandel effect. It is shown that the scattered two-photon field and its correlations manifest directive propagation, which is controllable by various means (angles of incidence, configuration of the body, relations between its dimensions and the wavelength). We expect that this method will be useful for designing quantum-optical devices.
We consider the scattering of multimodal quantum light by the perfectly conducting cylinder and its emission by quantum two-element phased array antenna. For the scattering description, we use the well-known classical numerical technique based on the characteristic modes adapted to the quantum light. The method is applicable to cylinders of arbitrary cross-section and size relative to the wavelength. It is shown that the antenna emission and scattering are accompanied by the transformation of the quantum-statistical properties of light (the second-order far field correlation function becomes directional and the multimodal entanglement is created. The obtained results are promising for applications in various branches of quantum technologies.
Understanding the complex interactions of the quantum light with different media provides valuable insights into potential applications in quantum tomography, microscopy, circuit and network design, and imaging. This thesis investigates quantum light interaction with two types of media: I. Random media entailing multiple scattering (Chapters 2-5), and II. Structured media, specifically designed to control quantum interferences (Chapters 6 and 7). In the first part of the thesis, and through solving the Lippmann-Schwinger equation for collections of small scatterers, a first principle scalar model for multiple scattering in finite-sized random media is developed. This efficient numerical model serves as the basis for investigating the coherent backscattering, a manifestation of weak localization in random media, for several bounded random media and various illuminations. Through employing mode expansion, next, the developed model is adapted to a general class of quantum-optical studies and quantum correlations are successfully derived and analyzed in scattering from finite disordered structures as well as systems of few scatterers. In multiple scattering of two-photon states in weak localization regime, the emergence of coherent two-photon backscattering is presented for the first time in coincidence detection, and it is demonstrated that quantum correlations can be used as a probe of entanglement dimensionality. Multiple scattering of two-photon states results in granular patterns known as speckle patterns. The statistical properties of single- and two-photon speckle patterns in scattering of different states are numerically calculated and the speckle visibilities and relevant parameters are derived. Specifically, the deviation of the probability density functions from negative exponential distributions, traditionally recognized as Rayleigh statistics in classical scattering, is identified, and shown to significantly depend on the presence of entanglement. Lastly, a different numerical implementation (based on COMSOL Multiphysics package) is used to consolidate our findings by incorporating the polarization effects. Coherent backscattering and coherent two-photon backscattering are observed for co-polarized fields in scattering from synthesized disordered media. It is demonstrated that depending on the particle exchange symmetry in polarization entangled excitation, the photons can exhibit statistical tendency to bunch together in the same mode, appear in separate modes (antibunching), or show a mixed response after multiple scattering. These bosonic-, fermionic-, and anyonic-like behaviors are studied in connection with coherent backscattering phenomenon, and it is demonstrated that the degree of enhancement in backscattering depends on the exchange symmetries. The simplicity and effectiveness of the implemented scattering analysis and the significance of the consequent conclusions suggest our approach as a promising platform for ‘numerical experiments’ without the limitations of analytical or semi-analytical models, and a practical tool prior to experiments. In the second part of the thesis, the random media operating as multimode platforms are replaced with engineered surfaces, i.e., metasurfaces, to realize targeted quantum interferences. First, a design roadmap for general lossy, asymmetric, and unbalanced coupling networks is presented, allowing to achieve maximum programmability in two-photon interferences. Next, two switchable metasurface-based coupling networks are designed to control nonclassical two-photon interferences via thermally driven crystallographic phase transitions. Numerical simulations confirm smooth transition between coalescence and anti-coalescence, aiming to address the current need in quantum optics for free-space compact devices creating tunable quantum interferences and acting as fast modulators for the second order quantum correlations. Our proposed compact and rapidly controllable devices pave the way towards new quantum applications as well as improving the current free-space quantum systems.
Wavefront shaping allows for ultimate control of light propagation in multiple-scattering media by adaptive manipulation of incident waves. We have demonstrated a method to program general multiport linear optical circuits in multiple-scattering materials by phase modulation of incident wavefronts. Applying this method to quantum light makes it possible to use these optical circuits for adaptive quantum optical experiments, with high flexibility in the control of quantum interference between multiple optical modes. To this end we have constructed a bright single-photon source, producing heralded single-photon states with a measured production rate of > 106 s−1. We have demonstrated that we are able to control the propagation of these single-photon states in random-scattering media, and we are currently investigating Hong-Ou-Mandel interference in these circuits.
We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as well as plane-wave modes. We specify two useful alternative bases of normalized eigenmodes: spherical eigenmodes and scattering eigenmodes. A canonical transformation between plane-wave modes and normalized eigenmodes is derived. This formalism is employed to study the scattering of a single photon, coherent squeezed light, and two-photon states off a dielectric sphere. In the latter case, we calculate the second-order correlation function of the scattered field, thereby unveiling the angular distribution of the Hong–Ou–Mandel interference for a dielectric sphere acting as a three-dimensional beam splitter. Our results are analytically derived for a dielectric sphere of arbitrary refractive index and size with a particular emphasis on the small-particle limit. As shown in Phys. Rev. A 108 , 033714 ( 2023 ) PLRAAN 1050-2947 10.1103/PhysRevA.108.033714 , this work sets the theoretical foundation for describing the quantum interaction between light and the motional, rotational, and vibrational degrees of freedom of a dielectric sphere.
Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. We also give several additional examples of how the theory works, for various quantum input states, which may be easily tested in the laboratory, including two single-mode squeezed vacuums, single- and two-photon inputs, where we show that the diffraction process produces a two-mode squeezed vacuum, number-path entanglement, and a Hong-Ou-Mandel-like effect analogous to that of a beam splitter.