Quantum Geometry and Bounds on Dissipation in Slowly Driven Quantum Systems

Creators: Esin, Iliya^{1, 2}; Lantagne-Hurtubise, Étienne^{1, 3}; Nathan, Frederik^{1, 4}; Refael, Gil¹

1. California Institute of Technology
2. Bar-Ilan University
3. Université de Sherbrooke
4. University of Copenhagen

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.

Copyright and License

Acknowledgement

We thank Jason Alicea, Israel Klich, Nandagopal Manoj, Johannes Mitscherling, Valerio Peri, and Mark Rudner for insightful discussions. É. L.-H. was supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant No. GBMF8682. F. N. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019166, the Simons Foundation under Grant No. 623768, and the Carlsberg Foundation, Grant No. CF22-0727. G. R. and I. E. are grateful for support from the Simons Foundation and the Institute of Quantum Information and Matter. G. R. is grateful for support from the ARO MURI Grant No. FA9550-22-1-0339. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-221045.

Supplemental Material

The supplementary material includes an extended derivation of the heating rate in the steady state of the system, the derivation of the upper and lower bounds on the heating rate, symmetry conditions required from the drives for the mixed term to vanish, the derivation of the heating rate in the case of a multiband system, and the derivation of the master equation from a microscopic model of interacting spins.

Files

PhysRevLett.134.146603.pdf

Files (1.0 MB)

Name	Size	Download all
SupplementaryMaterial.pdf md5:4e6350328276261de47db63eb0a82e98	389.6 kB	Preview Download
PhysRevLett.134.146603.pdf md5:fa1c78ff55c6448e7be957c6ff64d283	650.8 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes