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Photonics

Multi-Mode Correlation in a Concurrent Parametric Amplifier

Hailong Wang, Yunpeng Shi

Published Jun 23, 2022• 0 citations
Publisher

Abstract

A concurrent parametric amplifier consisting of two pump beams is used to investigate the possibility of generating multi-mode correlation and entanglement. The existence of three-mode entanglement is demonstrated by analyzing the violation degree of three-mode entanglement criteria, including the sufficient criterion, i.e., two-condition and optimal single-condition criterion, and necessary and sufficient criterion, i.e., positivity under partial transposition (PPT) criterion. Besides, two-mode entanglement generated from any pair is also studied by using the Duan criterion and PPT criterion. We find that three-mode entanglement and two-mode entanglement of the two pairs are present in the whole parameter region. Our results pave the way for the realization and application of multi-mode correlation and entanglement based on the concurrent parametric amplifiers.

DOI
10.3390/photonics9070443

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We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.
Quantum entanglement swapping is one of the most promising quantum techniques to create or manipulate large-scale multi-mode entanglement between two distant quantum entangled systems. In this work, a scheme for the generation of three-mode entanglement based on parametric amplifiers using quantum entanglement swapping has been proposed. The newly generated three-mode entanglement is always present in the whole power gain region from parametric amplifiers and its dependence on transmission loss and feedforward gain is also investigated. In addition, the effects of power gain, transmission loss, and feedforward gain on the two-mode entanglement of the three pairs in the newly generated three-mode entanglement have also been analysed in detail. The results presented here may find some practical applications in quantum secure communication.
Continuous-variable multipartite entanglement is a key resource for quantum technologies. This paper considers the multipartite entanglement generated in separated spatial modes of the same light beam by three different parametric sources: a standard ${\ensuremath{\chi}}^{(2)}$ medium pumped by two pumps, a single-pump nonlinear photonic crystal, and a doubly pumped nonlinear photonic crystal. These sources have in common the coexistence of several concurrent nonlinear processes in the same medium, which allows the generation of nonstandard three- and four-mode couplings. We test the genuine nature of the multipartite entangled states thereby generated in a common framework, using criteria based both on proper bounds for the variances of nonlocal observables and on the positive partial transpose criterion. The relative simplicity of these states allows a (hopefully) useful comparison of the different inseparability tests.
The tripartite entanglement generated from a cascaded parametric amplifier is always present in the whole gain region in the ideal condition. However, in practical applications, the quantum entanglement is very fragile and easily deteriorated by quantum noise from interactions with external environments, e.g., the avoidable attenuation and amplification operations may lead to some degradation effects on the quantum entanglement. Therefore, in this work, bipartite entanglement for the three pairs and tripartite entanglement in this cascaded parametric amplifier under the circumstances of attenuation and amplification operations are analyzed by using positivity under partial transposition criterion. The results show that tripartite entanglement is robust to the deterioration effects from the attenuation and amplification operations rather than bipartite entanglement. Our results may find some practical applications of multipartite quantum entanglement in quantum secure communications.
In this paper, the detailed inseparability criteria of entanglement quantification of correlated two-mode light generated by a three-level laser with a coherently driven parametric amplifier and coupled to a two-mode vacuum reservoir is thoroughly analyzed. Using the master equation, we obtain the stochastic differential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the squeezing and the photon entanglement by considering different inseparability criteria. The various criteria of entanglement used in this paper show that the light generated by the quantum optical system is entangled and the amount of entanglement is amplified by introducing the parametric amplifier into the laser cavity and manipulating the linear gain coefficient.
In recent years, multi-mode quantum entanglement and quantum squeezing have gained significant research interest. This paper successfully realizes quantitative control over the characteristic of quantum entanglement produced by cascaded parametrically amplified four-wave mixing (PA-FWM) through adjusting the Rabi frequency and dephasing rate of dressing fields, in which PT and anti-PT symmetry breaking, respectively, induce distinct energy-level quantization and generate coherent multi-channels in the atomic transition of the natural non-Hermitian system. Further simulations of the Duan criterion, the PPT criterion, and quantum steering have been implemented to investigate the properties of generated multi-mode entanglement when employing schemes featuring EPR injection and degenerate FWM. The comparison reveals that EPR injection enhances the entanglement of the injected EPR mode while suppressing the entanglement of other modes. Distinctive schemes of degenerate FWM and two pairs of EPR injections would successfully transform two originally separate modes into a pair of entangled modes, exhibiting significant research value in quantum metrology and relevant applications.