Transitionless Quantum Driving of the Tomonaga-Luttinger Liquid

TL;DR

This paper introduces a shortcut-to-adiabaticity protocol for rapidly generating interacting states in a Tomonaga-Luttinger liquid using counter-diabatic driving, which suppresses excitations during fast state preparation.

Contribution

It develops a novel fast STA protocol for the Tomonaga-Luttinger liquid by deriving a closed-form counterdiabatic control based on its oscillator analogy.

Findings

Efficient suppression of excitations during rapid state preparation.

Closed-form expression for the counterdiabatic control field.

Demonstration of protocol's effectiveness in the model.

Abstract

Shortcuts to adiabaticity (STA) make the fast preparation of many-body states possible, circumventing the limitations of adiabatic strategies. We propose a fast STA protocol for generating interacting states in the Tomonaga-Luttinger liquid by counter-diabatic driving, stirring the dynamics with an auxiliary control field. To this end, we exploit the equivalence between the time-dependent Tomonaga-Luttinger liquid and an ensemble of quantum oscillators with driven mass and frequency. We specify the closed-form expression of the counterdiabatic control and demonstrate its efficiency in suppressing excitations.