Figure 6

WRSEs as dephasing-noise filters. \(\mathrm{WRSE}_{3}\) dephasing noise filter characteristics. (a) Taylor expansion coefficients \(C^{(z)}_{2,4,6}(\Omega_{0};3)\) for \(F_{z} (\omega)\). The inset shows typical behaviour: \(\Omega_{0}=8\pi\) is a concurrent zero of \(C^{(z)}_{2,4}(\Omega_{0};3)\), but not of \(C^{(z)}_{6}(\Omega_{0};3)\). Hence \(\mathrm{WRSE}_{3}\) can only filter up to second-order. (b) Dephasing filter-transfer functions for \(\mathrm{WRSE}_{3}\) corresponding to \(\Omega_{0} = 2\pi q\), \(q\in\{1,\ldots,8\}\). When \(\Omega_{0}\) is a multiple of 8π we achieve second-order filters, that is \((p-1) = 2\).