Dynamics of fluctuations in a quantum system

‘‘The noise is the signal” [R. Landauer, Nature (London) 392, 658 (1998)] emphasizes the rich information content encoded in fluctuations. This paper assesses the dynamical role of fluctuations of a quantum system driven far from equilibrium, with laser-aligned molecules as a physical realization. Time evolutions of the expectation value and the uncertainty of a standard observable are computed quantum mechanically and classically. We demonstrate the intricate dynamics of the uncertainty that are strikingly independent of those of the expectation value, and their exceptional sensitivity to quantum properties of the system. In general, detecting the time evolution of the fluctuations of a given observable provides information on the dynamics of correlations in a quantum system.

Figure 1

Laser-induced alignment dynamics of ${\text{Br}}_2$ molecules under adiabatic conditions: (a) mean $\langle {cos}^2\theta \rangle \left(t\right)$ and (b) fluctuation $\Delta {cos}^2\theta \left(t\right)$. Red solid curves for quantum results; blue dot-dashed curves for classical ones. See text for parameters used.

Figure 2

Laser-induced alignment dynamics of ${\text{Br}}_2$ molecules under impulsive conditions: (a) mean $\langle {cos}^2\theta \rangle \left(t\right)$ and (b) fluctuation $\Delta {cos}^2\theta \left(t\right)$. In above-mentioned panels, red solid curves show quantum results and blue dot-dashed curves show classical ones. For comparison, time evolutions of total angular probability distributions $\rho \left(\theta \right)$ computed quantum mechanically and classically are plotted in (c) and (d), respectively. See text for parameters used.