Classification of Dark States in Multi-level Dissipative Systems

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.

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Cited by in corpus (14)

• Dissipation-engineered family of nearly dark states in many-body cavity-atom systems
• Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
• Lyapunov equation in open quantum systems and non-Hermitian physics
• Collective dynamics of the unbalanced three-level Dicke model
• Avoiding leakage and errors caused by unwanted transitions in Lambda systems
• Non-equilibrium diagrammatic approach to strongly interacting photons
• Morris-Shore transformation for non-degenerate systems
• Loading and Cooling in an Optical Trap via Hyperfine Dark States
• Dark-state and loss-induced phenomena in the quantum-optical regime of $\Lambda$-type three-level systems
• Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems
• Entanglement versus Bell nonlocality of quantum nonequilibrium steady states
• Coherent interaction of multistate quantum systems possessing the Majorana and Morris-Shore dynamic symmetries with pulse trains
• Multilevel Electromagnetically Induced Transparency Cooling
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection