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Latin America Optics and Photonics Conference

Revealing hidden entanglement in the covariance matrix

F. A. S. Barbosa, A. S. Coelho, K. N. Cassemiro, P. Nussenzveig, M. Martinelli, Claude Fabre, Alessandro S. Villar

Published Jan 1, 2012• 0 citations
Publisher

Abstract

Interferometric techniques, combined with electronic signal processing, have provided powerful tools for the precise reconstruction of quantum states of the field. Nevertheless, in most cases the completeness of the measurement relies in strong assumptions about its symmetry. In the present work, I will show how the use of optical cavities as a tool for state reconstruction can provide a complete description of the state, relaxing a priori assumptions and revealing a broad distribution of entanglement among sidebands of different optical beams, as in the case of those generated by an optical parametric oscillator.

DOI
10.1364/laop.2012.ls2b.1

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Interferometric techniques, combined with electronic signal processing, have provided powerful tools for the precise reconstruction of quantum states of the field. Nevertheless, in most cases the completeness of the measurement relies in strong assumptions about its symmetry. In the present work, I will show how the use of optical cavities as a tool for state reconstruction can provide a complete description of the state, relaxing a priori assumptions and revealing a broad distribution of entanglement among sidebands of different optical beams, as in the case of those generated by an optical parametric oscillator.
Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we describe in detail and experimentally demonstrate a robust and reliable method to fully characterize bipartite optical Gaussian states by means of a single homodyne detector. We have successfully applied our method to the bipartite states generated by a sub-threshold type-II optical parametric oscillator which produces a pair of thermal cross-polarized entangled cw frequency degenerate beams. The method provides a reliable reconstruction of the covariance matrix and allows us to retrieve all the physical information about the state under investigation. These include observable quantities, such as energy and squeezing, as well as nonobservable ones such as purity, entropy, and entanglement. Our procedure also includes advanced tests for the Gaussianity of the state and, overall, represents a powerful tool to study the bipartite Gaussian state from the generation stage to the detection one.
The quantum noise in photocurrent fluctuations usually gives incomplete information about the quantum state of spectral sideband modes of bright light beams involved in the detection. Each frequency component of the noise spectrum corresponds to two sideband modes symmetrically located around the bright optical field. In the case of the usual homodyne detection, it limits the ability to recover discriminated information of each mode involved. We theoretically show that complete reconstruction of the two-mode quantum state can be obtained by using phase-locked (coherent) resonator detection, even for non-Gaussian states. We experimentally demonstrate the technique by measuring a two-mode displaced coherent state.
We use a versatile model to evaluate the multipartite entanglement and the nonclassical light generation in optical parametric oscillators, exploring the differences between doubly and triply resonant cavity configurations. We demonstrate the entanglement of the pump mode with converted fields in both situations, and the fundamental differences of oscillators using parametric down conversion and four wave mixing processes as the intracavity amplification technique. The strong correlations involving the sidebands of the pump and converted fields give the signatures of a rich dynamic of multipartite entanglement.
Proper characterization of quantum correlations in multimode optical quantum states is critical for applications in quantum information science. However, standard entanglement measurements can lead to incomplete state reconstruction and characterization. Here, we implement a resonator-based detection system that reveals entanglement between sideband modes of twin beams, achieving full tomography and retrieving often ignored quantum correlations. Unlike standard spectral measurements such as homodyne detection, resonator detection can independently address the sidebands of each beam, thereby accessing these hidden correlations. Additionally, we show how phase shifts between the carrier and the sideband modes of the involved fields redistribute information and modify the observation of entanglement for different witnesses. The ability of the resonant detection to independently address sideband modes of entangled states can contribute to enhancing the capacity for secure communication and quantum networking protocols.