\\hat{H} =~\\omega_1\\hat a^\\dagger_1\\hat a_1~+~E_{C_{22}}(\\hat{n}_2-n_{g_{2}})^2~~-~E_{J_{1}}\\cos(-\\hat{\\varphi}_1+\\hat{\\varphi}_2+0.5\\varphi_{\\text{ext}_{1}})~-~E_{J_{2}}\\cos(-\\hat{\\varphi}_1-\\hat{\\varphi}_2+0.5\\varphi_{\\text{ext}_{1}})\n------------------------------------------------------------\n\\text{mode}~1:~~~~~~~~~~~\\text{harmonic}~~~~~~~~~~~\\hat{\\varphi}_1~=~\\varphi_{zp_{1}}(\\hat a_1+\\hat a^\\dagger_1)~~~~~~~~~~~\\omega_1/2\\pi~=~3.22489~~~~~~~~~~~\\varphi_{zp_{1}}~=~2.49e+00\n\\text{mode}~2:~~~~~~~~~~~\\text{charge}~~~~~~~~~~~~~~~~n_{g_{2}}~=~0\n------------------------------------------------------------\n\\text{parameters}:~~~~~~~~~~~E_{C_{22}}~=~0.296~~~~~~~~~~~E_{J_{1}}~=~5.0~~~~~~~~~~~E_{J_{2}}~=~5.0~~~~~~~~~~~\n\\text{loops}:~~~~~~~~~~~~~~~~~~~~\\varphi_{\\text{ext}_{1}}/2\\pi~=~0.5~~~~~~~~~~~