  Memory effects can lead to history-dependent behavior of a system, and they
are ubiquitous in our daily life and have broad applications. Here we explore
possibilities of generating memory effects in simple isolated quantum systems.
By utilizing geometrical effects from a class of lattices supporting flat-bands
consisting of localized states, memory effects could be observed in ultracold
atoms in optical lattices. As the optical lattice continuously transforms from
a triangular lattice into a kagome lattice with a flat band, history-dependent
density distributions manifest quantum memory effects even in noninteracting
systems, including fermionic as well as bosonic systems in the proper ranges of
temperatures. Rapid growth in ultracold technology predicts a bright future for
quantum memory-effect systems, and here two prototypical applications of
geometry-induced quantum memory effects are proposed: An accelerometer
recording the mechanical change rate in a coupled system and a rate-controlled
memvalve where the rate of ramping the lattice potential acts as a control of
the remnant density in the lattice.
