Shortcuts to adiabaticity, unexciting backgrounds, and reflectionless potentials

TL;DR

This paper explores shortcuts to adiabaticity in quantum systems, revealing their connection to reflectionless potentials and transmission resonances, and extends the analysis from quantum harmonic oscillators to quantum field theory in dynamic backgrounds.

Contribution

It establishes a novel analogy between STA protocols and scattering theory, linking quantum control techniques to reflectionless potentials and transmission resonances in both QHO and QFT.

Findings

STA protocols correspond to transmission resonances in QHO.

In QFT, STA relate to reflectionless potentials in non-stationary backgrounds.

STA completions can be interpreted via anti-squeezing operators.

Abstract

We analyze shortcuts to adiabaticity (STA) and their completions for the quantum harmonic oscillator (QHO) with time-dependent frequency, as well as for quantum field theory (QFT) in non-stationary backgrounds. We exploit the analogy with one-dimensional quantum mechanics, and the well known correspondence between Bogoliubov coefficients in the QHO and transmission/reflection amplitudes in scattering theory. Within this framework, STA protocols for the QHO are equivalent to transmission resonances, while STA in QFT with homogeneous backgrounds correspond to reflectionless potentials. Moreover, using the connection between particle creation and squeezed states, we show how STA completions can be understood in terms of the anti-squeezing operator.