Implementation of STIRAP in degenerate systems by dimensionality reduction

TL;DR

This paper presents a method to implement STIRAP in degenerate multi-level systems by reducing the problem to an effective three-level system, enabling arbitrary superposition transfer with minimal computational effort.

Contribution

It introduces a dimensionality reduction technique that simplifies the implementation of STIRAP in complex degenerate systems, allowing arbitrary superposition control.

Findings

Effective three-level reduction for degenerate systems

Minimal computational complexity in pulse design

Universal applicability to initial and target superpositions

Abstract

We consider the problem of the implementation of Stimulated Raman Adiabatic Passage (STIRAP) processes in degenerate systems, with a view to be able to steer the system wave function from an arbitrary initial superposition to an arbitrary target superposition. We examine the case a $N$-level atomic system consisting of $ N-1$ ground states coupled to a common excited state by laser pulses. We analyze the general case of initial and final superpositions belonging to the same manifold of states, and we cover also the case in which they are non-orthogonal. We demonstrate that, for a given initial and target superposition, it is always possible to choose the laser pulses so that in a transformed basis the system is reduced to an effective three-level $\Lambda$ system, and standard STIRAP processes can be implemented. Our treatment leads to a simple strategy, with minimal computational complexity, which allows us to determine the laser pulses shape required for the wanted adiabatic steering.