Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
arxiv(2024)
摘要
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
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, that cancels the final non-adiabatic
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.
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