Motivated by atom optics experiments, we investigate a new class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{ \mathrm{ Da}}(t) = | <\psi | e^{ i H_2 t / 2} e^{ i H_1 t / 2} e^{ -i H_2 t / 2} e^{ -i H_1 t / 2} | \psi >|^2$. We show that the decay of $M_{ \mathrm{ Da}}$ is quartic in time at short times, and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{ \mathrm{ Da}}$ contains easily extractable information on the strength of decoherence in these systems.
Categories: quant-ph cond-mat.other nlin.CD physics.atom-ph