Quantum Reversibility: Is there an Echo? Academic Article uri icon


  • We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology (``Loschmidt echo''), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief and demonstrate that the time ${t}_{r}$ for maximum return probability is in general shorter. We find that ${t}_{r}$ depends on $\ensuremath{\lambda}={\ensuremath{\epsilon}}_{\mathrm{e}\mathrm{v}\mathrm{o}\mathrm{l}}/{\ensuremath{\epsilon}}_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{p}}$, being the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

publication date

  • January 1, 2004