Many-Body Spin Echo

We report the prediction of a coherent many body echo in systems of interacting fermions with spin-orbit coupling. The signal is given by the time evolution of the transition probability between an initial many-body state and its time-reversed version, after flipping of the spins at some intermediate time $t$. Around the time $2t$ (and only then) the signal, which contrary to its single-particle counterpart is not suppressed by interactions, differs from its otherwise flat background, a hallmark signature of echo phenomena. In the non-perturbative regime where interactions, spin-orbit coupling and kinetic energy compete, the echo signal has a universal form, with a width which is independent of the interaction strength, and with its amplitude and sign depending on combinatorial relations between the total number of particles and the number of spins that are flipped. As an interference effect, the many-body spin echo is thus a universal signature of many-body coherence.