Graduate Lunch Talk: Victor Albert, Yale University, “Geometry & response of Lindbladians”

Event time: 
Tuesday, June 7, 2016 - 12:00pm to 1:00pm
Sloane Physics Laboratory (SPL), 3rd Floor Lounge See map
217 Prospect St.
New Haven, CT 06511
(Location is wheelchair accessible)
Event description: 

Markovian reservoir engineering, in which time evolution of a quantum system is governed by a Lindblad master equation, is a powerful tool in studies of quantum matter and quantum information. This tool can be used to drive a quantum system to a desired (unique) steady state, which can be an exotic phase of matter difficult to stabilize in nature. This tool can also be used to drive a system to a unitarily-evolving subspace, which can be used to store, protect, and process quantum information. In this paper, we derive a formula for the map corresponding to infinitetime Lindbladian evolution and use it to study several important features of the unique state and subspace cases. We quantify how subspaces retain information about initial states and show how to use Lindbladians to simulate any quantum channels. We show that the quantum information in all subspaces can be successfully manipulated by small Hamiltonian perturbations, jump operator perturbations, or adiabatic deformations. We provide a Lindblad-induced notion of distance between adiabatically connected subspaces. We derive a Kubo formula governing linear response of subspaces to time-dependent Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the subspaces, resulting from either Hamiltonian/jump-operator perturbations or corrections to adiabatic evolution, is different from the conventional Lindbladian dissipative gap and, in certain cases, is equivalent to the excitation gap of a related Hamiltonian.