Mirror-induced decoherence in hybrid quantum-classical theory

We reanalyze the optomechanical interferometer experiment proposed by Marshall et al. [Phys. Rev. Lett. 91, 130401 (2003)] with the help of a recently developed quantum-classical hybrid theory. This leads to an alternative evaluation of the mirror-induced decoherence. Surprisingly, we find that it behaves essentially in the same way for suitable initial conditions and experimentally relevant parameters, no matter whether the mirror is considered a classical or quantum-mechanical object. We discuss the parameter ranges where this result holds and possible implications for a test of spontaneous collapse models for which this experiment has been designed.

Figure 1

$|{\langle {\rho }_{AB}\left(t\right)\rangle }_f|$ as a function of $\tau :=\Omega t$ for $\kappa =1,\Omega =2\pi \times 500\mathrm{Hz}$. The dashed line (purple) is for $T={10}^{-3}\mathrm{K}$, and the full line (blue) is for $T={10}^{-4}\mathrm{K}$.

Figure 2

The probabilities $P_{1,2}(k=1)$ as a function of $\tau :=\Omega t$ for several values of the temperature. The upper full line (black) and lower full line (red) represent $P_1$ and $P_2$, respectively, for $T={10}^{-4}\mathrm{K}$; the dashed line (purple) and short-dashed line (blue) show $P_1$ and $P_2$, respectively, for $T={10}^{-3}\mathrm{K}$.