Quantum response of dephasing open systems

TL;DR

This paper develops a geometric theory of adiabatic response for open quantum systems with dephasing, linking dissipative effects to Hilbert space structures like the Fubini-Study metric and adiabatic curvature.

Contribution

It introduces a geometric framework for understanding quantum response in open systems, incorporating dephasing effects and residual dissipation.

Findings

Response coefficients depend on dephasing rates.

Non-dissipative response can be immune to dephasing under certain geometric conditions.

Examples include qubits, coherent states, and quantum Hall systems.

Abstract

We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap. We give quantum response a geometric interpretation in terms of Hilbert space projections: For a two level system and, more generally, for systems with suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini-Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing. We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: The qubit, coherent states and a model of the integer quantum Hall effect.