Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session K26: Open Quantum Systems I
8:00 AM–11:00 AM,
Wednesday, March 7, 2018
LACC Room: 404A
Sponsoring Unit: DAMOP DQI
Chair: Andrew Daley, University of Strathclyde
Abstract: K26.00007 : Perturbation theory of Lindbladians with multiple steady states
9:36 AM–9:48 AM
Lindbladians admitting multiple steady states are dissipative analogues of Hamiltonian systems with multiple ground states. As demonstrated with trapped-ion and circuit-QED quantum engineering, such systems can be used to store, protect, and process quantum information. We develop a perturbation expansion of a general Lindbladian whose unperturbed part can have multiple steady states. After making a few minor assumptions and dividing the expansion into terms that keep the initial state within the steady-state subspace and terms that take the state out, the expansion is solved exactly  and admits a diagrammatic interpretation. The number of diagrams in the expansion that are the same order in the perturbation is shown to be a Catalan number. With appropriate additional assumptions, the formalism reduces to open-system perturbation theory for a unique steady state , the effective operator formalism , and quantum Zeno dynamics .
 V. V. Albert, Ph.D. thesis, Yale University (2017).
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