Shortcuts to adiabaticity in harmonic traps: a quantum-classical analog

TL;DR

This paper introduces a novel quantum control technique based on classical stochastic processes, enabling rapid state transitions in harmonic traps while minimizing energy and phase costs, surpassing traditional adiabatic methods.

Contribution

It develops a new quantum-classical analogy using Nelson's stochastic quantization to design optimal, fast quantum protocols for harmonic oscillators, minimizing specific cost functions.

Findings

Successfully applied to time-dependent harmonic oscillators.

Achieved protocols that minimize energy and phase costs.

Demonstrated the method's ability to produce adiabatically optimal solutions.

Abstract

We present a new technique for efficiently transitioning a quantum system from an initial to a final stationary state in less time than is required by an adiabatic (quasi-static) process. Our approach makes use of Nelson's stochastic quantization, which represents the quantum system as a classical Brownian process. Thanks to this mathematical analogy, known protocols for classical overdamped systems can be translated into quantum protocols. In particular, one can use classical methods to find optimal quantum protocols that minimize both the time duration and some other cost function to be freely specified. We have applied this method to the time-dependent harmonic oscillator and tested it on two different cost functions: (i) the cumulative energy of the system over time and (ii) the dynamical phase of the wavefunction. In the latter case, it is possible to construct protocols that are "adiabatically optimal", i.e., they minimize their distance from an adiabatic process for a given duration.