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Conference on Lasers and Electro-Optics

Quantum Interference of Multiple Beams Induced by Multiple Scattering

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

Published Jan 1, 2011• 1 citation
Publisher

Abstract

We report on quantum interference induced by the transmission of quantized light through a multiple-scattering medium. We show that entangled states can be created by multiple-scattering and that quantum interference survives disorder averaging.
DOI
10.1364/qels.2011.qthf5

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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.
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.
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.
Multiple-scattering has become an exciting platform for quantum optical experiments [1-5]. In wavefront shaping one uses spatial light modulation in combination with strongly scattering materials to achieve control over light in space and time [6]. Recent wavefront-shaping experiments have transformed opaque media in equivalents of waveguides, lenses, waveplates and optical pulse compressors that are inherently robust against disorder and imaging errors. In quantum optics, interference of quantum states is studied in often complicated optical circuits. This requires a close-to-perfect implementation of the setup and provides little flexibility or programmability of the interference. We implement the radically different approach to apply wavefront shaping on quantum light to obtain ample flexibility in optimization and manipulation of the quantum interference. This offers unique opportunities for sample characterization, quantum patterning, secure key generation, or quantum transport through disordered media.