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arXiv:1006.0107 · Physical Review Letters

Quantum Interference and Entanglement Induced by Multiple Scattering of Light

J. R. Ott, N. Asger Mortensen, Peter Lodahl

Published Aug 25, 2010• 46 citations
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Abstract

We report on the effects of quantum interference induced by the transmission of an arbitrary number of optical quantum states through a multiple-scattering medium. We identify the role of quantum interference on the photon correlations and the degree of continuous variable entanglement between two output modes. It is shown that quantum interference survives averaging over all ensembles of disorder and manifests itself as increased photon correlations due to photon antibunching. Furthermore, the existence of continuous variable entanglement correlations in a volume speckle pattern is predicted. Our results suggest that multiple scattering provides a promising way of coherently interfering many independent quantum states of light of potential use in quantum information processing.

DOI
10.1103/physrevlett.105.090501

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•Jan 1, 2021•0 citations
We report on the effects of quantum interference induced by the transmission of an arbitrary number of optical quantum states through a multiple-scattering medium. We identify the role of quantum interference on the photon correlations and the degree of continuous variable entanglement between two output modes. It is shown that quantum interference survives averaging over all ensembles of disorder and manifests itself as increased photon correlations due to photon antibunching. Furthermore, the existence of continuous variable entanglement correlations in a volume speckle pattern is predicted. Our results suggest that multiple scattering provides a promising way of coherently interfering many independent quantum states of light of potential use in quantum information processing.
Here we report on the predicted effects of quantum interference induced by combining an arbitrary number of quantum optical states in a random multiple scattering medium. We identify the role of quantum interference on the degree of photon correlations between two transmission paths through the medium and the degree of continuous variable entanglement. The investigation is performed using a scattering matrix formalism and based on random matrix theory. In this way the ensemble averaged 2-channel photon correlations Cοψ and the degree of entanglement εοψ between output modes a and β are related to the classical shortand long-range correlation functions, Cι and C2, and the average conductance g. The expressions are non-perturbative and valid in the entire mesoscopic regime.
This thesis concerns the theoretical investigation of interference phenomena related to elastic and inelastic scattering of quantized light. The presented work is naturally divided into two parts, the first is concerning elastic scattering while the second explores inelastic scattering. In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light to the photon correlations after ensemble averaging. This analysis enables us to describe an experimental observation of the quantum nature of light that survives the averaging over disorder. In the second part we investigate inelastic scattering. This we do by first treating the scattering of light on dipoles embedded in an arbitrary dielectric environment. By considering the two different models for dipole interaction known as the minimal-coupling and electric-dipole interaction Hamiltonians, we find exact relations between the electric field and the dipole operators in the Heisenberg picture, while keeping the model of the dipoles arbitrary. Due to the exact treatment of the electric-field operators, we obtain kernels known from classical scattering theory to describe the propagation of the field from the dipoles. Using the found electric field operators we derive the Heisenberg equations of motion for the dipoles while treating them as quantum two-level systems and using the Born–Markov and rotating-wave approximations. Postponing the rotating-wave approximation to the very end of the formal calculations allows us to identify the different physical parameters of the dipole evolution in terms of physical quantities known from optics. Finally, we use our Heisenberg picture formalism to treat a dilute cloud of two-level atoms, by simplifying the equations of motion using a single-scattering approximation for the interaction between the atoms. This enables us to derive expressions for the steady-state population and fluorescence spectrum, where we find cooperative effects in both the elastic and the inelastic spectra.
Abstract We present the emergence of coherent two-photon backscattering, a manifestation of weak localization, in multiple scattering of maximally entangled pure and fully mixed two-photon states and examine the effect of entanglement and classical correlations. Quantum correlations in backscattering are investigated for finite three-dimensional disordered structures in the weak localization regime, as well as systems of a small number of scatterers with specified spatial arrangements. No assumptions are made about the statistical behavior of the scattering matrix elements. Furthermore, we study the interplay between quantum correlations induced by multiple scattering and the correlations that may be present in the illumination fields, and how they are manifested in the output modes. We study the effect of the dimensionality of the entanglement and the angular distribution of the jointly measurable photon pairs on the emergence of enhancement and angular quantum correlations and show how quantum correlations can be used as a probe of the entanglement dimensionality. We show that by increasing the disordered material density, the width of the coherent two-photon backscattering cones increases, in accordance with the reduction of the mean free path length within the structure.
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.