  The measurement of topological number is crucial in the research of
topological systems. Recently, the relations between the topological number and
the dynamics are built. But a direct method to read out the topological number
via the dynamics is still lacking. In this work, we propose a new dynamical
protocol to directly measure the topological number of an unknown system.
Different from common quench operations, we change the Hamiltonian of the
unknown system to another one with known topological properties. After the
quench, different initial states result in different particle number
distributions on the post-quench final Bloch bands. Such distributions depend
on the wavefunction overlap between the initial Bloch state and the final Bloch
state, which is a complex number depending on the momentum. We prove a theorem
that when the momentum varies by $2\pi$, the phase of the wavefunction overlap
change by $\Delta n\pi$ where $\Delta n$ is the topological number difference
between the initial Bloch band and the final Bloch band. Based on this and the
known topological number of the final Bloch band, we can directly deduce the
topological number of the initial state from the particle number distribution
and need not track the evolution of the system nor measure the spin texture.
Two experimental schemes are also proposed as well. These schemes provide a
convenient and robust measurement method and also deepens the understanding of
the relation between topology and dynamics.
