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Journal of the Optical Society of America B

Generation of multicolored tripartite entanglement by frequency doubling in a two-port resonator

Rongguo Yang, Shuqin Zhai, Kui Liu, Junxiang Zhang, Jiangrui Gao

Published Nov 16, 2010• 6 citations
Publisher

Abstract

Multicolored multipartite entanglement is of great importance in quantum communication and quantum information networks. In this paper, we calculate the quantum fluctuations of the fundamental frequency pump beam and second-harmonic beams in a two-port frequency doubling resonator, and investigate the tripartite continuous-variable entanglement generated by this device for the first time, to our knowledge. The quantum correlation among fundamental frequency pump beam and two harmonic beams is studied using a necessary and sufficient criterion for Gaussian entanglement states, the positivity under partial transposition. It is found that two-color tripartite entanglement exists in a large range of pump intensities and analysis frequencies.

DOI
10.1364/josab.27.002721

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Multicolored multipartite entanglement is of great importance in quantum communication and quantum information networks. In this paper, we calculate the quantum fluctuations of the fundamental frequency pump beam and second-harmonic beams in a two-port frequency doubling resonator, and investigate the tripartite continuous-variable entanglement generated by this device for the first time, to our knowledge. The quantum correlation among fundamental frequency pump beam and two harmonic beams is studied using a necessary and sufficient criterion for Gaussian entanglement states, the positivity under partial transposition. It is found that two-color tripartite entanglement exists in a large range of pump intensities and analysis frequencies.
Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.
We analyze the entanglement characteristics of three harmonic modes, which are the output fields from three cavities with an input tripartite entangled state at fundamental frequency. The entanglement properties of the input beams can be maintained after their frequencies have been up-converted by the process of second harmonic generation. We have calculated the parametric dependences of the correlation spectrum on the initial squeezing factor, the pump power, the transmission coefficient, and the normalized analysis frequency of cavity. The numerical results provide references to choose proper experimental parameters for designing the experiment. The frequency conversion of the multipartite entangled state can also be applied to a quantum communication network.
In this paper, tripartite entanglement among the two pump fields and the second-order harmonic field is established in the process of type-II second-order harmonic generation (SHG) with a triply resonant optical cavity below threshold. A sufficient inseparability criterion for continuous-variable tripartite entanglement proposed by van Loock and Furusawa is used to evaluate the degree of the quadrature--phase-amplitude correlations between the three modes. The dependence of the entanglement on the pump parameter and analysis frequency is also discussed. It is shown that the best entanglement appears at the appropriate pump power and analysis frequency. These three entangled states with different frequencies generated directly from a simple SHG process make the scheme useful for the application in quantum communication and network.
We present a technique for generation of tripartite quantum-correlated amplitude-squeezed light beams, using frequency doubling in a singly resonant cavity with two output ports. The two-output second-harmonic (SH) beams are both nonlinearly coupled to the common fundamental beam even though they have no direct interaction. The nonlinear coupling produces noise reduction of amplitude for each beam and quantum correlations among three beams. In our first experiment, we measured amplitude squeezing of 0.5, 0.8, and 0.6 dB for the fundamental beam and two output SH beams, respectively. Meanwhile, quantum correlation of 0.6 dB between the two amplitude-squeezed SH beams and quantum anticorrelation of 0.6 and 0.8 dB between the squeezed fundamental beam and each of the SH beams were observed around the range of optimum conversion efficiency. This opens an alternate way to produce tripartite-quantum-correlated systems.
Bright three-color continuous-variable (CV) entanglement generated by a cascaded sum-frequency process in an optical cavity is investigated. The second- and fourth-harmonic beams can be generated by two quasi-phase-matched cascaded sum-frequency processes in a quasi-periodic optical superlattice. Quantum correlations among the fundamental and second- and fourth-harmonic beams are calculated and discussed by applying a sufficient and necessary inseparability criterion for CV three-mode entanglement. Strong three-color CV entanglement beams with a double frequency interval can be produced in this simple system. It is experimentally feasible and may be very useful for applications in quantum communication and computation networks.
We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant nondegenerate optical parametric oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.