Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an arbitrary interaction quench, making use of the SU(1,1) dynamical symmetry group and the Schrödinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, which cancels the final nonadiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols.
Published by the American Physical Society
2024