Extended Data Fig. 4: Generality of asymmetric echo.
From: Signal amplification in a solid-state sensor through asymmetric many-body echo
a, Time-reversed mirror symmetry of the considered Hamiltonians (see Supplement for their explicit expressions), where the flow directions are reversed under the mirror reflections. The gray dots at -Y axis indicate the initial states, which are preserved under the symmetries. b, Simulated amplification for these Hamiltonians, under the assumption that the coupling is all-to-all. In these plots, each trace indicates a different t−, and darker traces correspond to smaller t− values. c, d, Same as (b), but for 1/r3 coupling on a 2D lattice and positionally-disordered 2D ensemble. e, f, Heuristic argument for why t+ = t−/2 gives a maximum amplification in most cases: Asymmetric echo allows doubling the amplifying time t− without encountering the highly over-twisted regime (shaded zones). Note that this heuristic argument is not a rigorous statement, as amplification is not necessarily degraded in the highly over-twisted regime (see our complementary work by N.T.L. et al., in preparation).
