A harmonic oscillator in superposition of coherent states |α⟩+|-α⟩. Visualise the Wigner quasi-probability distribution and decoherence.
Cat states |cat⟩ = N(|α⟩+e^{iφ}|-α⟩) are superpositions of two macroscopically distinct coherent states |α⟩ (cat alive) and |-α⟩ (cat dead). Their Wigner function W(x,p) shows two Gaussian blobs plus interference fringes between them — the signature of quantum coherence. Coupling to an environment causes decoherence: the fringes decay exponentially at rate γ|2α|² while the blobs survive, turning a quantum superposition into a classical mixture.