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Sideband four-mode entanglement in a Four-wave mixing process

Raul Leonardo Rincon Celis

Published Oct 25, 2022• 0 citations
Publisher

Abstract

We present a detailed characterization of the entanglement in a stimulated Fourwave mixing process.This process is widely studied by the homodyne detection, a technique insensitive to the details of the sideband modes of the involved beams.The emission profile of the FWM process in atomic media shows an imbalance in the amplification of the sidebands, which suggest an asymmetry in the entanglement of the generated states, that can not be observed by the homodyne detection.The stimulated FWM consists on a single frequency pump and a seed beam interacting with the hot rubidium atoms, generating a pair of entangled states, the probe and the conjugated.By the implementation of the resonantor detection, we revealed the hidden entanglement structure of the generated beams.We found that the usual characterization of the state through the homodyne detection is incomplete.On the contrary, the reconstruction of the covariance matrix from the resonant detection allows the full characterization of the quantum correlations and a more complete entanglement structure between the sideband frequency modes.Therefore, with the measurement using resonant detection over a Four-wave mixing process, we can demonstrate the advantage of the detection to reveal entanglement that would be hidden if the usual two-mode description is used.

DOI
10.11606/t.43.2022.tde-08122022-220746

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We present a detailed characterization of the entanglement in a stimulated Fourwave mixing process.This process is widely studied by the homodyne detection, a technique insensitive to the details of the sideband modes of the involved beams.The emission profile of the FWM process in atomic media shows an imbalance in the amplification of the sidebands, which suggest an asymmetry in the entanglement of the generated states, that can not be observed by the homodyne detection.The stimulated FWM consists on a single frequency pump and a seed beam interacting with the hot rubidium atoms, generating a pair of entangled states, the probe and the conjugated.By the implementation of the resonantor detection, we revealed the hidden entanglement structure of the generated beams.We found that the usual characterization of the state through the homodyne detection is incomplete.On the contrary, the reconstruction of the covariance matrix from the resonant detection allows the full characterization of the quantum correlations and a more complete entanglement structure between the sideband frequency modes.Therefore, with the measurement using resonant detection over a Four-wave mixing process, we can demonstrate the advantage of the detection to reveal entanglement that would be hidden if the usual two-mode description is used.
Proper characterization of quantum correlations in a multimode optical state is critical for applications in quantum information science; however, the most common entanglement measurements can lead to an incomplete state reconstruction. This is the case for the ubiquitous spectral measurement of field quadratures for which a full characterization of the quantum correlations between optical beams is not possible. We demonstrate this effect in twin beams generated through parametric amplification by four-wave mixing in hot rubidium vapor, showing the role of a frequency dependent gain response. We implement a resonator-based measurement that reveals entanglement between beams that is otherwise hidden by usual spectral measurements. Additionally, this system shows how the phase shifts between the carrier and the sidebands on the involved fields affect the observation of entanglement for different entanglement witnesses, demonstrating the relevance of making a complete state tomography.
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.
Multimode entanglement is essential for the generation of quantum networks, which plays a central role in quantum information processing and quantum metrology. Here, we study the spatial multimode entanglement characteristics of the large scale quantum states via a dual-pumped four-wave-mixing (FWM) process of Rubidium atomics vapors. A linear mode transform approach is applied to solve the four- and six-mode Gaussian states and the analytical input-output relations are presented. Moreover, via reconstructing the full covariance matrix of the produced states, versatile entanglement with from two up to six modes is analyzed. The results show that most of the 1 versus n-mode and m versus n-mode states are entangled, and the amount of entanglement can be regulated due to the competitions of mode components caused by different interaction strengths of co-existing FWMs. Our study could be applied for any multimode Gaussian states with a quadratic Hamiltonian.
We present the measurement of entanglement between twin beams generated with a doubly resonant optical parameter oscillator (OPO) based on four-wave mixing in hot ^{85}Rb vapor above threshold. This is the first measurement of entanglement in an OPO with a χ^{(3)} media above threshold. We reconstruct the covariance matrix for several configurations and based on a full picture of the four side band mode state, we study entanglement between all possible bipartitions. We show a robust generation of entanglement with stronger generation for a specific pair of modes. For this system, we show that atomic density is a determinant factor for the generation and loss of quantum correlations. The generation of entangled fields with an atomic OPO operating close to atomic resonance of alkali atoms enables a natural integration into quantum networks.