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Advanced Quantum Technologies

Tunable Continuous‐Variable Tripartite Entanglement via Simultaneous and Ordinal Cascaded Nonlinear Processes

Muhua Zhai, Feng Wen, Shaowei Zhang, Huapeng Ye, Sijia Hui, Yuesong Liang, Jia Zeng, Ting Yang, Dong Zhong, Yanpeng Zhang, Hongxing Wang

Published Apr 11, 2024• 0 citations
Publisher

Abstract

Abstract Multipartite quantum entanglement plays a vital role in both fundamental science and quantum applications. The cascaded four‐wave mixing (FWM) process is an effective method to prepare multipartite entanglement, however, the physical nature of entanglement based on different cascading paths, i.e., simultaneous cascaded FWM (SC‐FWM) and ordinal cascaded FWM (OC‐FWM), has not yet been conclusively determined. In this article, tunable continuous‐variable (CV) triple‐mode entanglement is proposed to be generated by using both the SC‐FWM and OC‐FWM schemes. The simulation results reveal that the absorption/dispersion properties of the two nonlinear processes can be efficiently tuned by varying the optical parameters (i.e., the photon detuning and the nonlinear susceptibility), resulting in triple‐mode CV entanglement with tunable properties. Compared with the OC‐FWM scheme, the SC‐FWM scheme has a broader entanglement bandwidth and a higher degree of entanglement, where the tripartite entanglement region is 4.38% larger than that of the OC‐FWM scheme. Furthermore, these results indicate that the SC‐FWM scheme has a more compact and stable mode structure with better entanglement performance. Such tunable optical triple‐mode entanglement may find applications in specific quantum communication protocols and pave the way for implementing and manipulating multichannel quantum networks.

DOI
10.1002/qute.202300457

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Abstract Multipartite quantum entanglement plays a vital role in both fundamental science and quantum applications. The cascaded four‐wave mixing (FWM) process is an effective method to prepare multipartite entanglement, however, the physical nature of entanglement based on different cascading paths, i.e., simultaneous cascaded FWM (SC‐FWM) and ordinal cascaded FWM (OC‐FWM), has not yet been conclusively determined. In this article, tunable continuous‐variable (CV) triple‐mode entanglement is proposed to be generated by using both the SC‐FWM and OC‐FWM schemes. The simulation results reveal that the absorption/dispersion properties of the two nonlinear processes can be efficiently tuned by varying the optical parameters (i.e., the photon detuning and the nonlinear susceptibility), resulting in triple‐mode CV entanglement with tunable properties. Compared with the OC‐FWM scheme, the SC‐FWM scheme has a broader entanglement bandwidth and a higher degree of entanglement, where the tripartite entanglement region is 4.38% larger than that of the OC‐FWM scheme. Furthermore, these results indicate that the SC‐FWM scheme has a more compact and stable mode structure with better entanglement performance. Such tunable optical triple‐mode entanglement may find applications in specific quantum communication protocols and pave the way for implementing and manipulating multichannel quantum networks.
Abstract In this study, a tunable continuous‐variable (CV) triple‐mode entanglement scheme generated by cascading a spontaneous parametric four‐wave and a sum‐frequency four‐wave mixing process is proposed. The entanglement feature of the triple‐mode is demonstrated by using a sufficient inseparability criterion. It is confirmed that the triple‐mode CV entanglement property, including the degree of violation of the sufficient inseparability criterion and the entanglement range in the frequency domain, can be modulated dynamically by modifying the nonlinear susceptibility and optical parameters. In particular, the intensity of the pumping field affects the modulation of the degree of entanglement, and the splitting of the entanglement spectrum comes from electromagnetically induced transparency. Although changing the relative detuning between the Stokes and anti‐Stokes fields can increase the entanglement degree of the triple‐mode, it results in the expansion of the entanglement range in frequency as well. Furthermore, although nonlinear susceptibility directly improves the degree of triple‐mode CV entanglement, optical detuning related nonlinear dispersion has an indirect effect as well. Such an optical triple‐mode CV entanglement with tunable properties can find applications in all‐optical quantum communication and pave the way for the generation and manipulation of multichannel quantum networks.
Quantum entanglement shared by different parties enhances their capabilities to communicate, which is the core content of continuous-variable quantum optics and quantum information science. Here, we study an experimentally feasible scheme for generating quantum entanglement of bipartite and tripartite cases based on phase-sensitive cascaded four-wave mixing processes in rubidium vapor. Quantum entanglement of bipartite and tripartite cases in our system, which can be manipulated by the phases and the intensity gains of the input beams, is predicted. We also find a sufficient optimal single-condition criterion to give a valid description for genuine tripartite quantum entanglement in our system. The sufficient optimal single-condition criterion is convenient and can be extended to genuine multipartite entanglement.
Abstract Multipartite entanglement is the crucial requirement for quantum information processing, quantum computation, quantum communication and quantum sensing. Therefore, the generation and characterization of such entanglement are primary goals in quantum technologies. Here we theoretically study the multipartite continuous-variable quadrature entanglement generated by three symmetric cascaded nonlinear optical systems. Such cascaded systems allow us to study the bipartite, tripartite and quadripartite entanglement. We use different continuous-variable entanglement criteria to characterize the entanglement. We observe that only a few bipartite combinations show the entanglement out of all possible combinations, while most tripartite combinations are entangled. Interestingly such a system depicts a full quadripartite entanglement. Moreover, we show that, unlike the quadrature sum-variance entanglement criterion, the negative partial transpose criterion can show the entanglement in most cases. The present comprehensive analysis of the generation and characterization of the continuous-variable entanglement with cascaded systems would pave the way to realizing a complex quantum network.
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 correlations and entanglement shared among multiple modes are fundamental ingredients of most continuous-variable quantum technologies. Recently, a method used to generate multiple quantum correlated beams using cascaded four-wave mixing (FWM) processes was theoretically proposed and experimentally realized by our group [Z. Qin et al., Phys. Rev. Lett. 113, 023602 (2014)]. Our study of triple-beam quantum correlation paves the way to showing the tripartite entanglement in our system. Our system also promises to find applications in quantum information and precision measurement such as the controlled quantum communications, the generation of multiple quantum correlated images, and the realization of a multiport nonlinear interferometer. For its applications, the degree of quantum correlation is a crucial figure of merit. In this letter, we experimentally study how various parameters, such as the cell temperatures, one-photon, and two-photon detunings, influence the degree of quantum correlation between the triple beams generated from the cascaded two-FWM configuration.
A maximal joint quadrature squeezing of -6.8±0.4 dB is experimentally obtained by a scheme of cascaded four-wave mixing (FWM) processes, which gives strong proof about the inseparability or entanglement between output of the twin beams from the system. Here joint quadrature is the difference between the two quadratures of the twin beam output from the cascaded FWM processes. This result is enhanced by about 3.1 dB, compared with the one of the single FWM process. We also study the gain dependence of the entanglement enhancement in this cascaded system. Theoretical predictions with the considerations of the losses in the experiment are also studied, and a similar trend in the low-gain regime can be found between the experimental results and the theoretical predictions. The scheme of cascaded FWM processes, which can be used to improve or even manipulate the degree of the entanglement between the output fields from the single FWM process, may find its applications in the continuous-variable quantum communication protocols.