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Collapse and revival of a coherent state in an oscillator linearly coupled to a qubit. The Wigner function is plotted as a function of time. The model parameters in the Hamiltonian of Eq. (1) are Ω = ω = 0.48, g 1 = 0.05, and g 2 = g 3 = 0. The qubit is initially in a symmetric superposition of up and down states; the initial coherent state of the oscillator contains ⟨a † a⟩ = 16 photons (Eq. (25) ).
Collapse and revival for varying linear coupling strength. The initial state is the same as in Fig. 1 . The Wigner function is plotted for g 2 = g 3 = 0 and (a) Ω = ω = 1, g 1 = 0.1; (b) Ω = ω = 0.5, g 1 = 0.5; (c) Ω = ω = 0.1, g 1 = 0.2.
Effect of quadratic coupling on collapse and revivals of the initial state Eq. (25) . For weak coupling (Ω = ω = 1; g 1 = g 2 = g 3 = 0.1) the collapse and revival of the diagonal components, (a) and (b) are almost identical to the linear case (g 3 = 0, Fig. 2 ). Relatively strong linear coupling (Ω = ω = 0.1; g 1 = g 2 = 0.1; g 3 = 0.01) changes the trajectories of the cat state components and disrupts the revivals (c).
Evolution of the initial oscillator Fock state with strong linear and weak quadratic qubit-oscillator coupling (Ω = ω = 0.1; g 1 = g 2 = 0.1; g 3 = 0.01). The qubit is initially in a symmetric superposition of states. The components , , and are shown in panels (a), (b), and (c), respectively.
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