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arXiv:quant-ph/0312137 · Physical Review A

Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation

Zehui Zhai, Yongming Li, Jiangrui Gao

Published Apr 7, 2004• 6 citations
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Abstract

Quantum fluctuation and quantum entanglement of the pump fields reflected from an optical cavity for type-II second-harmonic generation are theoretically analyzed. The correlation spectra of quadrature components between the reflected subharmonic fields are interpreted in terms of pump parameter, intracavity losses, and normalized frequency. High correlation of both amplitude and phase quadratures can be accessed in a triple resonant cavity before the pitchfork bifurcation occurs. The two reflected subharmonic fields are in an entangled state with quantum correlation of phase quadratures and anticorrelation of amplitude quadratures. The proposed system can be exploited as a source for generating entangled states of continuous variables.

DOI
10.1103/physreva.69.044301

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Quantum fluctuation and quantum entanglement of the pump fields reflected from an optical cavity for type-II second-harmonic generation are theoretically analyzed. The correlation spectra of quadrature components between the reflected subharmonic fields are interpreted in terms of pump parameter, intracavity losses, and normalized frequency. High correlation of both amplitude and phase quadratures can be accessed in a triple resonant cavity before the pitchfork bifurcation occurs. The two reflected subharmonic fields are in an entangled state with quantum correlation of phase quadratures and anticorrelation of amplitude quadratures. The proposed system can be exploited as a source for generating entangled states of continuous variables.
Quantum fluctuation and quantum entanglement in competing nonlinear processes of type II second-harmonic generation in a triple-resonant cavity is analyzed. Operating above threshold with intracavity loss, the mean amplitude and the entanglement of reflected subharmonic field as a function of pump and loss parameters are calculated. It is found that the two eigenmodes become unbalanced when internal loss intervenes. The dependence of the entanglement characteristics of two reflected subharmonic modes on output coupling efficiency µ_b/µ, pump parameter sigma, and normalized frequency Omega are discussed. Under appropriate conditions, this system can be exploited as a bright entanglement resource.
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.
A generation system of continuous-variable (CV) quadripartite entangled state based on two cascaded second-harmonic generation (SHG) cavities below the threshold is investigated. Two reflected fundamental beams of the first cavity, the reflected second-harmonic beam and the output fourth-harmonic beam of the second cavity are proved to be entangled, and the dependence of the entanglement degree on the normalized frequency, pump parameter, fourth-harmonic loss parameter, and second-harmonic loss parameter is also analyzed. Due to the fact that the cavity parameters and the nonlinear crystals of the two SHG cavities can be freely chosen, the practicality of the proposed protocol is relatively perfect and the system can also be extended to the preparation of multicolor entangled states for a quantum network.
For the process of intracavity generation of the second harmonic, the dynamics of correlation of quadrature amplitudes fluctuations of the fundamental and the second harmonic modes is studied depending on the nonlinear coupling coefficient between the modes. It was shown that in this system the entangled states of field related to variables of quadrature amplitudes may be obtained depending on the nonlinear coupling coefficient. It was also shown that the entanglement of the states of field modes related to one quadrature amplitude may vanish depending on the value of nonlinear coupling coefficient, whereas the states of field modes related to the other quadrature amplitude stay entangled.
Classical and quantum fluctuations are analyzed in the system of type-II harmonic generation where two frequency-degenerate subharmonic fields with orthogonal polarizations are required for the generation of a harmonic field. The two subharmonic fields as well as the harmonic fields are on resonance in a cavity. It is found that there is no self-pulsing behavior as predicted for the type-I case where the intensities of both the subharmonic and the harmonic fields undergo fast oscillation. Instead there exists a threshold that is identified as the onset of an optical parametric oscillator (OPO) formed by a subharmonic mode with its polarization orthogonal to the input polarization (not the original modes). When the loss for the harmonic field is small, most of the input power is converted to the output power of the OPO. Under this circumstance, quantum-nondemolition measurements of the input can be performed at certain frequencies. The spectra of squeezing are calculated for the two subharmonic modes and it is found that both modes are squeezed for a certain range of frequency. The output of the OPO is found to exhibit phase squeezing.
The classical behavior and the quantum fluctuations are analyzed for the system of nondegenerate second-harmonic generation inside a cavity, where two frequency degenerate but orthogonally polarized harmonic modes are coupled to a second-harmonic mode via a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium. We consider the consequences of asymmetrically pumping the two harmonic modes. Asymmetric pumping causes large changes in the classical dynamical behavior of the system; the pitchfork bifurcation, predicted by Ou [Phys. Rev. A 49, 4902 (1994)] and Eschmann and Reid [Phys. Rev. A 49, 2881 (1994)] for symmetric pumping, is transformed into a saddle node for any antisymmetric pumping. This new dynamics brings about the possibility of the system reaching a Hopf and a saddle-node--Hopf bifurcation point. Squeezed-state production is investigated at the critical points of the system. Large squeezing is predicted at the saddle-node and Hopf bifurcation points. The wealth of squeezing predicted by this model at the pitchfork bifurcation point is interpreted in terms of the dynamics of the system. For symmetric pumping, this system is shown to be able to produce two coherent amplitude and phase correlated beams both above and below the pitchfork bifurcation point and so is a candidate for an Einstein-Podolsky-Rosen experiment. \textcopyright{} 1996 The American Physical Society.