Interaction-free evolution in the presence of time-dependent Hamiltonians

TL;DR

This paper extends the concept of interaction-free evolutions to time-dependent Hamiltonians, revealing richer structures and conditions for their occurrence, supported by specific examples and analyses.

Contribution

It generalizes IFE to time-dependent Hamiltonians, uncovering new structures and providing a comprehensive condition for their existence.

Findings

More complex interaction-free states are possible with time-dependent Hamiltonians

Derived a general condition for interaction-free evolutions in time-dependent systems

Presented specific examples illustrating the new structures and conditions

Abstract

The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows for much more rich structures of interaction-free states and interaction-free subspaces. The general condition for the occurrence of IFE is found and exploited to analyze specific situations. Several examples are presented, each one associated to a class of Hamiltonians with specific features.