Lindbladians with multiple steady states: theory and applications

TL;DR

This paper explores Lindbladians with multiple steady states, providing a theoretical framework and applications for engineered quantum environments that can stabilize exotic phases or protected subspaces.

Contribution

It introduces a comprehensive theory for Lindbladians with multiple steady states and demonstrates their relevance in quantum system engineering.

Findings

Lindbladians can have multiple steady states similar to degenerate Hamiltonians.

Engineered environments can stabilize exotic quantum phases.

Applications include noise-resistant quantum subspaces.

Abstract

Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum properties, an engineered environment can drive the system toward exotic phases of matter or toward subspaces protected from noise. These cases often require the Lindbladian to have more than one steady state, and such Lindbladians are dissipative analogues of Hamiltonians with multiple ground states. This thesis studies Lindbladian extensions of topics commonplace in degenerate Hamiltonian systems, providing examples and historical context along the way.