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arXiv:quant-ph/0603079 · Physical Review A

Intensity correlations and entanglement by frequency doubling in a two-port resonator

Oo-Kaw Lim, Mark E. Saffman

Published Aug 23, 2006• 10 citations
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Abstract

We show that nonclassical intensity correlations and quadrature entanglement can be generated by frequency doubling in a resonator with two output ports. We predict twin-beam intensity correlations $6\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ below the coherent-state limit, and that the product of the inference variances of the quadrature fluctuations gives an Einstein-Podolsky-Rosen correlation coefficient of ${V}_{\mathrm{EPR}}=0.64<1$, using the criterion of Reid [Phys. Rev. A 40, 913 (1989)]. Comparison with an entanglement source based on combining two frequency doublers with a beam splitter shows that the dual-ported resonator provides stronger entanglement at lower levels of individual beam squeezing. Calculations are performed using a self-consistent propagation method that does not invoke a mean-field approximation. Results are given for physically realistic parameters that account for the Gaussian shape of the intracavity beams, as well as intracavity losses.

DOI
10.1103/physreva.74.023816

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We show that nonclassical intensity correlations and quadrature entanglement can be generated by frequency doubling in a resonator with two output ports. We predict twin-beam intensity correlations 6dB6\phantom{\rule{0.3em}{0ex}}\mathrm{dB}6dB below the coherent-state limit, and that the product of the inference variances of the quadrature fluctuations gives an Einstein-Podolsky-Rosen correlation coefficient of VEPR=0.64<1{V}_{\mathrm{EPR}}=0.64<1VEPR​=0.64<1, using the criterion of Reid [Phys. Rev. A 40, 913 (1989)]. Comparison with an entanglement source based on combining two frequency doublers with a beam splitter shows that the dual-ported resonator provides stronger entanglement at lower levels of individual beam squeezing. Calculations are performed using a self-consistent propagation method that does not invoke a mean-field approximation. Results are given for physically realistic parameters that account for the Gaussian shape of the intracavity beams, as well as intracavity losses.
We demonstrate production of short wavelength beams with nonclassical intensity correlations and quadrature entanglement using second harmonic generation in a nonlinear resonator with two output ports. The two output beams at the harmonic frequency have no direct interaction but are both nonlinearly coupled to a common pump beam. The nonlinear coupling produces amplitude and phase correlations between the beams which results in quadrature entanglement. The output beams at λ = 428.5 nm are shown to exhibit 0.6 dB of amplitude quadrature squeezing, 0.9 dB of nonclassical intensity correlations, and 0.3 dB of entanglement using about 30 mW of pump power.
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.