Figure 2

\(\Delta \Phi _0\) dependence of theoretical \((\lambda _+,\lambda _-)\) Floquet eigenenergies and \(\Omega _L\) dressed frequency, and of measured \(f_L\) frequencies. In (a) \((\lambda _+,\lambda _-)\) with the x axis larger than the first Floquet zone to evidence the eigenenergy periodicity. \(\Omega _L\) is derived from the \(|\lambda _+-\lambda _-|\) difference. Parameters: \(p=1\), \(\Omega _x=1.3, \Omega _y=0.64\), \(\omega _{0z}=0.3375\) and \(\omega _{0y}=0\). Black line for \(\omega _{0x}=0\), and red dots for \(\omega _{0x}=0.03\). In (b) \(\Omega _L\) theory (continuous lines) and \(f_L\) experiment (markers) dressed Larmor frequencies within the Floquet zone. Blue line and squares for \(\Omega _{x}=2.60(1)\) and \(\Omega _{y}=3.15(2)\), red line and circles for \(\Omega _{x}=2.60(1)\) and \(\Omega _{y}=1.90(1)\). Other parameters: \(p=1\), \(\omega _{0x}=\omega _{0y}=0\), \(f=40.00\,\) kHz, \(\omega _{0z}=0.3375(3)\) corresponding to \(f_0=13.50(5)\,\) kHz. In (c) \(\Omega _L\) and \(f_L\) within a limited Floquet zone. The transition from a Dirac-like crossing into an anti-crossing is explored by tuning the \(\omega _{0x}\) field. Parameters: \(p=1\), \(\Omega _{x}=1.670(5)\), \(\Omega _{y}=1.20(1)\), \(f=135.00\,\) kHz \(\omega _{0y}=0\), \(\omega _{0z}=0.100(3)\), corresponding to \(f_0=13.50(5)\,\) kHz. In both experimental plots the error bar is smaller than the dot size, and the red dashed horizontal lines denote the \(f_0=13.50(5)\,\) kHz undressed Larmor frequency value. All experimental data are acquired in the RPP mode. The number in brackets represents, according to the standard notation, the error in the last digit.