$~~~~$Quantum correlations are the central features characterizing many-body physics, which become one of the most important observables in many experiments. Here we present an alternate scheme both theoretically and experimentally, probing the equilibrium correlations by ramping dynamics which can tell a strong correlated system has well-defined quasi-particle descriptions or not. By ramping a physical parameter non-adiabatically with finite speeds, we find the leading deviation of any measured observable to the adiabatic value is linearly proportional to the ramping speed, path-independent and only depending on the final states' equilibrium correlations. The slope of linearity reflects the equilibrium correlations and is significant while the system does not have a well-defined quasi-particle description. We demonstrate and experimentally prove our theory in Bose-Hubbard models with degenerate cold gas.
$~~~~$Experimentally, we first ramp our system from four different initial lattice depths to the same final one at 15Er (recoil energy). After each ramp, we extract our observable, the central quasi-momentum distribution in 1D by means of our developed band-mapping method. Through the four sets of measurements, we find that the strength of our observable is only linearly dependent on the ramping speed and we obtain the same slope of linearity reflecting the same equilibrium correlations for the same final state. Then we change the final lattice depths to 11, 13, 17, 19, 21Er to obtain the slopes of linearity for different final states. We find the slopes of linearity are apparently larger in quantum critical region, reflecting the significant equilibrium correlations.
$~~~~$Ideally, by comparing our measurements with theoretical results, we can determine the critical exponent by studying the temperature dependence of this correlation. Our scheme can be directly applied to probe correlations in other ultra-cold atomic gases systems, such as unitary Fermi gas and quantum simulation of various spin models. Our method can also be applied to other systems beyond ultra-cold atomic gases, such as trapped ions, NV centers, and condensed matter systems. As shown in the example of studying the Bose-Hubbard model, our method accesses a different aspect of quantum many-body correlation compared with many existing measurement tools. Thus, our protocol provides a new direction to study correlations in quantum matters.
|Presenter name||Libo Liang|
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