Comment on “Quantum measurement and decoherence”
Dominique Gobert, Jan von Delft, Vinay Ambegaokar · Physical Review A · 2004
Ford, Lewis, and O'Connell [Phys. Rev. A 64, 032101 (2001)] have recently discussed a thought experiment in which a Brownian particle is subjected to a double-slit measurement . Analyzing the decay of the emerging interference pattern, they derive a decoherence rate that is much faster than previous results and even persists in the limit of vanishing dissipation. This result is based on the definition of a certain attenuation factor, which they analyze for short times. In this note, we point out that this attenuation factor captures the physics of decoherence only for times larger than a certain time ${t}_{\mathrm{mix}}$, which is the time it takes until the two emerging wave packets begin to overlap. Therefore, the strategy of Ford et al. of extracting the decoherence time from the regime $t{t}_{\mathrm{mix}}$, one recovers familiar behavior for the decoherence time; in particular, no decoherence is seen in the absence of dissipation. We confirm the latter conclusion by calculating the off-diagonal elements of the reduced density matrix.