Reply to “Comment on ‘Quantum measurement and decoherence’ ”

Abstract

While agreeing with our exact expression for the time dependence of the motion of a free particle in an initial superposition state, corresponding to two identical Gaussians separated by a distance $d$, at temperature $T$, Gobert et al., in the preceding Comment [Phys. Rev. A70, 026101 (2004)], dispute our conclusions on decoherence time scales. However, the parameters they used to generate their figures are outside the regime of validity of our interpretation of the results and, moreover, are not of physical interest in that they correspond to $T\ensuremath{\approx}0$. The point is that in their figures they have chosen the thermal de Broglie wavelength ${\ensuremath{\lambda}}_{th}=\ensuremath{\hbar}\sqrt{mkT}$ to be equal to slit spacing $d$, whereas we have clearly stated [in the paragraph preceding Eq. (21) of our paper] that decoherence occurs and that our expression for the decoherence time applies only in the limit where $d$ is large compared not only with the slit width $\ensuremath{\sigma}$ but also with the thermal de Broglie wavelength, $d⪢{\ensuremath{\lambda}}_{th},\ensuremath{\sigma}$.