  Ramping a physical parameter is one of the most common experimental protocols
in studying a quantum system, and ramping dynamics has been widely used in
preparing a quantum state and probing physical properties. Here, we present a
novel method of probing quantum many-body correlation by ramping dynamics. We
ramp a Hamiltonian parameter to the same target value from different initial
values and with different velocities, and we show that the first-order
correction on the finite ramping velocity is universal and path-independent,
revealing a novel quantum many-body correlation function of the equilibrium
phases at the target values. We term this method as the non-adiabatic linear
response since this is the leading order correction beyond the adiabatic limit.
We demonstrate this method experimentally by studying the Bose-Hubbard model
with ultracold atoms in three-dimensional optical lattices. Unlike the
conventional linear response that reveals whether the quasi-particle dispersion
of a quantum phase is gapped or gapless, this probe is more sensitive to
whether the quasi-particle lifetime is long enough such that the quantum phase
possesses a well-defined quasi-particle description. In the Bose-Hubbard model,
this non-adiabatic linear response is significant in the quantum critical
regime where well-defined quasi-particles are absent. And in contrast, this
response is vanishingly small in both superfluid and Mott insulators which
possess well-defined quasi-particles. Because our proposal uses the most common
experimental protocol, we envision that our method can find broad applications
in probing various quantum systems.
