Shortcuts to Adiabaticity Using Time-dependent Harmonic Oscillators

Jonas F. G. Santos

Kiran Thengil, M. Ponmurugan

We investigate the shortcuts to adiabaticity (STA) of a quantum harmonic oscillator under time-dependent frictional force, using an invariant-based inverse-engineering method with a class of invariants characterized by a time-dependent frictional coefficient. We discuss the implementation of a shortcut protocol in a generalized framework for any arbitrary time-dependent frictional interaction and study a class of such interaction from which the STA for the quantum harmonic oscillator can be obtained. We also discuss the application of the above protocol for the harmonic oscillator with time-varying mass. For an illustration, we consider the coupled photonic lattice as a harmonic oscillator with time-varying mass and frequency and discuss implementing the above protocol.

Fernando C. Lombardo, Francisco D. Mazzitelli

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.

Anthony Kiely

Xi Chen, Juan Gonzalo Muga

We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes (``shortcuts to adiabaticity'') designed to reproduce the initial populations at some predetermined final frequency and time. We provide lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.

Yanan Zhang, Yang Liu, H. D. Liu