Exact dynamics of the Tomonaga-Luttinger liquid and shortcuts to adiabaticity

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mtext>SU</a:mtext><a:mo>(</a:mo><a:mn>1</a:mn><a:mo>,</a:mo><a:mn>1</a:mn><a:mo>)</a:mo></a:mrow></a:math> 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