Figure 7
From: Hamiltonian of a flux qubit-LC oscillator circuit in the deep–strong-coupling regime
Expectation values of photon number, flux, and current operators for (a–d) \(\hat{\mathcal {H}}_{circ}\) and for (e,f) \(\hat{\mathcal {H}}_{circ}'\). (a,e) Expectation numbers of photons in the oscillator in the ground state as a function of \(L_c\). The solid curve corresponds to \(\left\langle 0 \left| \hat{\mathcal {H}}_1/\hbar \right| 0 \right\rangle /(1/\sqrt{L_{LC}C})-0.5\), while the dashed line in panel (a) indicates the simple expression \((g/\omega )^2\), which is valid in the limit \(\Delta _q \ll \omega\). (b,f) [d,h] Expectation values of fluxes \(2\pi \left\langle \hat{\Phi }_k\right\rangle /\Phi _0\) [Expectation values of currents \(\left\langle \hat{I}_k \right\rangle\)] as functions of the flux bias \(\Phi _x\) in the case \(L_c=350\) pH. Black and red colors respectively indicate \(k = 1\) and 2, and solid and dashed lines indicate the ground and the excited states, respectively. (c,g) Expectation value of flux \(2\pi \left\langle \hat{\Phi }_1\right\rangle /\Phi _0\) in the ground state as a function of \(L_c\) at \(\Phi _{x}/\Phi _{0} = 0.498\).
