Quantum to classical transition induced by gravitational time dilation

We study the loss of quantumness caused by time dilation [I. Pikovski, M. Zych, F. Costa, and Č. Brukner, Nat. Phys. 11, 668 (2015)] for a Schrödinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion, and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely, on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decoherence times due to classical noise originating from the unavoidable statistical fluctuations in the characteristic parameters of the system [J. Trapani, M. Bina, S. Maniscalco, and M. G. A. Paris, Phys. Rev. A 91, 022113 (2015)]. We show that the experimental observation of decoherence due to time dilation imposes severe limitations on the allowed levels of classical noise in the experiments.

Figure 1

Behavior of different nonclassicality indicators plotted as a function of (dimensionless) $\alpha$ in units of ${\tau }_W$ (s). ${\tau }_{\mathrm{dec}}$ represents the peak of the interference fringe.

Figure 2

Ratio between the decoherence times for different nonclassicality indicators due to classical noise and those due to time dilation induced decoherence, as a function of $\gamma$ and $\lambda$ for $\alpha =\sqrt{2}$. The shaded areas represent the region of parameters in which decoherence due to classical noise dominates over time dilation induced decoherence. $\gamma$ and $\lambda$ are given in units of ${\omega }_0$ (Hz).