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Scaling Relations and Topological Quadruple Points in Light‐Matter Interactions with Anisotropy and Nonlinear Stark Coupling

Scaling Relations and Topological Quadruple Points in Light‐Matter Interactions with Anisotropy... Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological classification provides another type of universality essentially different from the critical universality. Both classes of universalities can be present in a single‐qubit system with light‐matter interactions, as exhibiting generally in the fundamental quantum Rabi model with anisotropy not only for linear coupling but also for nonlinear Stark coupling (NSC). In low frequencies different levels of scaling relations are extracted, holding for anisotropic or/and NSCs, locally or globally. At finite frequencies such a critical universality breaks down and diversity is dominant. However, common topological feature of the ground state can be extracted from the node number, which yields a topological class of universality amidst the critical diversity. Both conventional and unconventional topological transitions emerge, with their meeting, which never occurs in linear interaction, enabled by the nonlinear coupling to form topological quadruple points which are found to be spin‐invariant points. Sensitivity analysis indicates that the NSC can be another applicable approach to manipulate topological transitions in addition to coupling anisotropy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advanced Quantum Technologies Wiley

Scaling Relations and Topological Quadruple Points in Light‐Matter Interactions with Anisotropy and Nonlinear Stark Coupling

Ying, Zu‐Jian
Advanced Quantum Technologies , Volume 6 (1) – Jan 1, 2023
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18 pages

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Publisher
Wiley
Copyright
© 2023 Wiley‐VCH GmbH
eISSN
2511-9044
DOI
10.1002/qute.202200068
Publisher site
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Abstract

Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological classification provides another type of universality essentially different from the critical universality. Both classes of universalities can be present in a single‐qubit system with light‐matter interactions, as exhibiting generally in the fundamental quantum Rabi model with anisotropy not only for linear coupling but also for nonlinear Stark coupling (NSC). In low frequencies different levels of scaling relations are extracted, holding for anisotropic or/and NSCs, locally or globally. At finite frequencies such a critical universality breaks down and diversity is dominant. However, common topological feature of the ground state can be extracted from the node number, which yields a topological class of universality amidst the critical diversity. Both conventional and unconventional topological transitions emerge, with their meeting, which never occurs in linear interaction, enabled by the nonlinear coupling to form topological quadruple points which are found to be spin‐invariant points. Sensitivity analysis indicates that the NSC can be another applicable approach to manipulate topological transitions in addition to coupling anisotropy.

Journal

Advanced Quantum Technologies – Wiley

Published: Jan 1, 2023

Keywords: light‐matter interaction; nonlinear coupling; quantum phase transition; scaling relation; topological classification; topological quadruple point; universality class

References

  • Quantum Phase Transitions
    Sachdev, S.
  • The Jaynes‐Cummings Model and Its Descendants
    Larson, J.; Mavrogordatos, T.