Fast optimal transition between two equilibrium states

TL;DR

This paper introduces a Hamiltonian invariants-based technique for rapid state transitions in quantum systems, demonstrated by fast decompression of ultracold atoms with minimal excitations, outperforming traditional methods in speed.

Contribution

The paper presents a novel invariant-based approach enabling fast, adiabatic-like transitions in quantum systems, significantly reducing transition times compared to standard linear methods.

Findings

Achieved a 15-fold decompression in 35 ms

Suppressed sloshing and breathing modes effectively

Reduced transition time by a factor of 37 compared to linear decompression

Abstract

We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of Rubidium 87 atoms held in a harmonic magnetic trap, in the presence of gravity. We are able to decompress the trap by a factor of 15 within 35 ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of 37 on the transition time.