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AIP conference proceedings

Scattering Induced Quantum Interference of Multiple Quantum Optical States

J. R. Ott, Martijn Wubs, N. Asger Mortensen, Peter Lodahl, Dmitry N. Chigrin

Published Jan 1, 2011• 1 citation
Publisher

Abstract

Using a discrete mode theory for propagation of quantum optical states, we investigate the consequences of multiple scattering on the degree of quadrature entanglement and quantum interference. We report that entangled states can be created by multiple‐scattering. We furthermore show that quantum interference induced by the transmission of quantized light through a multiple‐scattering medium will persist even after averaging over an ensemble of scattering samples.

DOI
10.1063/1.3644219

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Using a discrete mode theory for propagation of quantum optical states, we investigate the consequences of multiple scattering on the degree of quadrature entanglement and quantum interference. We report that entangled states can be created by multiple‐scattering. We furthermore show that quantum interference induced by the transmission of quantized light through a multiple‐scattering medium will persist even after averaging over an ensemble of scattering samples.
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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.
The authors demonstrates that spatial quantum correlations are induced by multiple scattering of quadrature squeezed light through a random medium. As a consequence, light scattered along two different directions by the random medium will not be independent, but be correlated to an extent that can only be described by a quantum mechanical theory for multiple scattering. The spatial quantum correlation is revealed in the fluctuations of the total intensity transmission or reflection through the multiple scattering medium.
Propagating quadrature squeezed light through a multiple scattering random medium is found to induce pronounced spatial quantum correlations that have no classical analogue. The correlations are revealed in the number of photons transported through the sample that can be measured from the intensity fluctuations of the total transmission or reflection. In contrast, no pronounced spatial quantum correlations appear in the quadrature amplitudes where excess noise above the shot noise level is found.