Bright quadripartite entanglement from competingχ(2)nonlinearities

Abstract

In this Brief Report, we investigate the generation of bright quadripartite entanglement of continuous variables in an experimentally realizable system involving second-order harmonic generation with competing nondegenerate optical parametric downconversion. By using the well-known van Loock-Furusawa criterion for continuous variable correlations, we find that the genuine quadripartite entanglement can be generated in the system over a wide range of controllable parameters. Besides this, it is shown that the bipartite entanglement between any two field modes can be achievable. In addition, the dependence of the quantum correlations on the pump parameter is also discussed.

Self-consistent renormalization group approach to continuous phase transitions in alloys: application to ordering in β-brass

“…Currently no universal theoretical techniques efficient at both stages exist partly because different alloys may exhibit qualitatively different behaviour and a technique efficient in alloys of one kind performs poorly in alloys of different kind. In particular, cluster methods of [1,9,10] that proved to be efficient in the description of the first order phase transitions fail to correctly describe continuous transitions because small clusters cannot properly account for the long range correlations in the critical region. The cluster sizes N c are restricted to small values because the number of terms in the equations grows as 2 N c so in practical calculations cluster radii have to be bounded by a few lattice constants [1,9,10].…”

“…In particular, cluster methods of [1,9,10] that proved to be efficient in the description of the first order phase transitions fail to correctly describe continuous transitions because small clusters cannot properly account for the long range correlations in the critical region. The cluster sizes N c are restricted to small values because the number of terms in the equations grows as 2 N c so in practical calculations cluster radii have to be bounded by a few lattice constants [1,9,10].…”

“…However, in some alloys the energy can be described with the use of only pair interactions, in particular, β-brass is considered to be such an alloy [6,15]. In this case the partition function can be represented in the form of a functional integral over a scalar lattice field with the field Hamiltonian formally of the Ginzburg-Landau type with conventional non-local quadratic ('free') part and a local interaction potential (see, e.g., [9,10,16]). The critical behaviour of the models of this type can be effectively treated within the functional renormalization group (RG) approach, in particular, within the local potential approximation (LPA) [17][18][19][20].…”

Optimal third-harmonic generation in an optical microcavity with χ(2) and χ(3) nonlinearities

“…Besides, people have also oberved DTHG accompanied by Raman scattering and four-wave mixing [25][26][27][28], which increases the potential for multiple applications. In addition to THG, some other cascaded nonlinear processes in cavities have also been applied for the realization of frequency combs, broadband wavelength conversion, quantum entanglement, etc [29][30][31][32].…”

Enhancement of second-harmonic generation based on the cascaded second- and third-order nonlinear processes in a multimode optical microcavity

“…This type of cascaded second-order (χ (2) ) nonlinear processes have been studied a lot in both classical and quantum fields [40,41]. By harnessing the cascaded effect of the χ (2) nonlinearity, it is feasible to achieve efficient higherorder harmonic light generation [32,37,39,42], multipartite entanglement [43] and frequency combs in different mode families [44][45][46]. However, for the analysis of those * clzou321@ustc.edu.cn † dxdai@zju.edu.cn nonlinear optical processes, previously people usually use a simple model, in which only the χ (2) nonlinearity is taken into consideration.…”