aiqbench analysis
This research introduces a rigorous computational framework combining BBGKY and HEOM hierarchies to model quantum many-body systems interacting with structured electromagnetic environments. The method effectively bridges condensed matter physics and quantum optics, offering a scalable solution for analyzing spin-squeezing and superradiance in complex open systems. By addressing the challenges of large Hilbert spaces and strong system-environment coupling, this work advances the theoretical tools necessary for developing practical quantum devices.
A Hierarchical Approach to Quantum Many-Body Systems in Non-Markovian Environments
arXiv:2405.05093v4 Announce Type: replace Abstract: Quantum many-body systems in cavities combine the rich physics of condensed matter systems or quantum chemistry with strong coupling to the surrounding electromagnetic field. In these systems, large Hilbert spaces, many-body interactions and strong system-environment coupling are all fundamental, posing a significant barrier for established methods in quantum optics and condensed matter physics. Here we propose a novel method based on a combination of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and the Hierarchical Equations of Motion (HEOM) to achieve a rigorous description of open many-body systems in contact with structured photonic and phononic baths. We rationalize that this stacked hierarchy accounts for spin-squeezing and superradiant emission despite its applicability to arbitrarily many emitters. The potential of BBGKY-HEOM is then demonstrated for many-body electronic systems embedded in host materials (e.g. molecules in organic crystals). We show that the impact of phononic coupling and charge noise can be as relevant as electronic correlation. Our work establishes an accessible, yet rigorous, route between condensed matter and quantum optics, fostering the growth of a new domain at their interface.
Abstract:Quantum many-body systems in cavities combine the rich physics of condensed matter systems or quantum chemistry with strong coupling to the surrounding electromagnetic field. In these systems, large Hilbert spaces, many-body interactions and strong system-environment coupling are all fundamental, posing a significant barrier for established methods in quantum optics and condensed matter physics. Here we propose a novel method based on a combination of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and the Hierarchical Equations of Motion (HEOM) to achieve a rigorous description of open many-body systems in contact with structured photonic and phononic baths. We rationalize that this stacked hierarchy accounts for spin-squeezing and superradiant emission despite its applicability to arbitrarily many emitters. The potential of BBGKY-HEOM is then demonstrated for many-body electronic systems embedded in host materials (e.g. molecules in organic crystals). We show that the impact of phononic coupling and charge noise can be as relevant as electronic correlation. Our work establishes an accessible, yet rigorous, route between condensed matter and quantum optics, fostering the growth of a new domain at their interface.
Quantum Physics (quant-ph); Materials Science (cond-mat.mtrl-sci); Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph); Optics (physics.optics)
arXiv:2405.05093 [quant-ph]
(or arXiv:2405.05093v4 [quant-ph] for this version)
Full text under the publisher's open licence · 196 words
Related coverage
Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model
Quantum Journal · Sep 2, 2026
Hierarchical approach to quantum many-body systems in non-Markovian environments
arXiv · Jul 20, 2026
University of Waterloo Simulates Non-Markovian Dissipation in Trapped Ion
Quantum Zeitgeist · Aug 6, 2026
A Tensor Network Framework for Lindbladian Spectra and Steady States
arXiv · Jun 9, 2026