Classification of Dark States in Multi-level Dissipative Systems

TL;DR

This paper provides a comprehensive analysis of dark states in dissipative multi-level systems, highlighting their dependence on system parameters and illustrating their relevance with hyperfine transitions in rubidium-87.

Contribution

It introduces a detailed framework for identifying stationary dark states in dissipative systems, including their dependence on laser detunings and intensities, and applies this to complex atomic systems.

Findings

Dark states depend on laser detunings and intensities.

A class of dark states is identified with specific parameter dependencies.

Knowledge of dark state manifolds aids in preparing pure quantum states.

Abstract

Dark states are eigenstates or steady-states of a system that are decoupled from the radiation. Their use, along with associated techniques such as Stimulated Raman Adiabatic Passage, has extended from atomic physics where it is an essential cooling mechanism, to more recent versions in condensed phase where it can increase the coherence times of qubits. These states are often discussed in the context of unitary evolution and found with elegant methods exploiting symmetries, or via the Bruce-Shore transformation. However, the link with dissipative systems is not always transparent, and distinctions between classes of CPT are not always clear. We present a detailed overview of the arguments to find stationary dark states in dissipative systems, and examine their dependence on the Hamiltonian parameters, their multiplicity and purity. We find a class of dark states that depends not only on the detunings of the lasers but also on their relative intensities. We illustrate the criteria with the more complex physical system of the hyperfine transitions of $^{87}$Rb and show how a knowledge of the dark state manifold can inform the preparation of pure states.