Decoherence of multicomponent symmetrical superpositions of displaced quantum states
V. V. Dodonov, L A de Souza
We study the decoherence of superpositions of displaced quantum states of the form (where | g ⟩ is an arbitrary 'fiducial' state and is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 'mesoscopic' components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the 'initial decoherence time' and 'final decoherence time' and study their dependence on the parameters α k and N . We obtain approximate formulae for an arbitrary state | g ⟩ and explicit exact expressions in the special case of | g ⟩ = | m ⟩, i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m . We show that the superposition with a large number of components N and rich 'internal structure' ( m ∼ |α| 2 ) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.
Journal of Physics A Mathematical and Theoretical•Oct 31, 2007•4 citations