Quantum geometry and bounds on dissipation in slowly driven quantum systems

TL;DR

This paper reveals that energy dissipation in slowly-driven quantum systems is fundamentally connected to the geometry of the driving protocol, establishing bounds influenced by topology and system-bath coupling.

Contribution

It introduces a geometric framework linking dissipation to the quantum metric and derives bounds based on topology and system-bath coupling quality factors.

Findings

Dissipation bounds depend on the quantum metric and protocol topology.

Lower bounds on dissipation are established for two-tone protocols.

Results provide design principles for minimizing energy loss in quantum control.

Abstract

We show that energy dissipation in slowly-driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower bounds on dissipation rates in two-tone protocols, such as those employed for topological frequency conversion. Notably, in appropriate limits these bounds are only determined by the topology of the protocol and an effective quality factor of the system-bath coupling. Our results bridge topological and geometric phenomena with energy dissipation in open quantum systems, and further provide design principles for optimal driving protocols.