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This research introduces a rigorous computational framework combining the BBGKY hierarchy and HEOM to model open quantum many-body systems within structured environments like photonic cavities. By effectively handling strong system-environment coupling and non-Markovian effects, this method bridges condensed matter physics with quantum optics for applications ranging from spin-squeezing to molecular electronics. The approach offers a scalable solution for analyzing complex interactions where traditional methods in either field face significant barriers due to large Hilbert spaces or many-body correlations.
Hierarchical approach to quantum many-body systems in non-Markovian environments
arXiv:2405.05093v3 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:2405.05093v3 [quant-ph] for this version)
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