Superradiant Quantum Phase Transition in Open Systems: System-Bath Interaction at the Critical Point
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AbstractThe occurrence of a second-order quantum phase transition in the Dicke model is a well-established feature. On the contrary, a comprehensive understanding of the corresponding open system, particularly in the proximity of the critical point, remains elusive. When approaching the critical point, the system inevitably enters first the system-bath ultrastrong coupling regime and finally the deepstrong coupling regime, causing the failure of usual approximations adopted to describe open quantum systems. We study the interaction of the Dicke model with bosonic bath fields in the absence of additional approximations, which usually relies on the weakness of the system-bath coupling. We find that the critical point is not affected by the interaction with the environment. Moreover, the interaction with the environment is not able to affect the system ground-state condensates in the superradiant phase, whereas the bath fields are $infected$ by the system and acquire macroscopic occupations. The obtained reflection spectra display lineshapes which become increasingly asymmetric, both in the normal and superradiant phases, when approaching the critical point.Popular summaryQuantum Phase Transitions are among the most fundamental collective phenomena in quantum physics, marking abrupt changes in the ground state of a system as an external parameter is varied. One of the most paradigmatic examples is the Superradiant Phase Transition, predicted by the Dicke model, in which many two-level systems coupled to a common electromagnetic field collectively reorganize and generate macroscopic, coherent excitations. While this transition is well understood for ideal, isolated systems, real physical implementations are inevitably influenced by their surrounding environment. The impact of such environments becomes especially subtle near the critical point of the transition, where the coupling between the system and its surroundings can become extremely strong, rendering standard theoretical approximations inadequate. In this work, we investigate the Dicke model coupled to environmental fields without relying on weak-coupling assumptions. We show that the critical point of the superradiant transition remains remarkably robust, when in the presence of environments with metastable minima. Moreover, in the superradiant phase, the fundamental condensates of the system are unaffected by the environmental interaction, while the environment itself is strongly modified and develops macroscopic occupations. These effects manifest in distinctive spectroscopic signatures, with increasingly asymmetric reflection spectra as the system approaches criticality, offering new insights into critical phenomena in open quantum systems.► BibTeX data@article{Lamberto2026superradiantquantum, doi = {10.22331/q-2026-01-19-1970}, url = {https://doi.org/10.22331/q-2026-01-19-1970}, title = {Superradiant {Q}uantum {P}hase {T}ransition in {O}pen {S}ystems: {S}ystem-{B}ath {I}nteraction at the {C}ritical {P}oint}, author = {Lamberto, Daniele and Orlando, Gabriele and Savasta, Salvatore}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1970}, month = jan, year = {2026} }► References [1] R. H. Dicke, Phys. Rev. 93, 99 (1954). https://doi.org/10.1103/PhysRev.93.99 [2] K. Hepp and E. H. Lieb, Ann. Phys. 76, 360 (1973). https://doi.org/10.1016/0003-4916(73)90039-0 [3] Y. K. Wang and F. T. 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Lett. 98, 103602 (2007). https://doi.org/10.1103/PhysRevLett.98.103602 [95] A. Zappalà, A. Mercurio, D. Lamberto, S. Napoli, O. Di Stefano, and S. Savasta, Phys. Rev. A 112, 063718 (2025). https://doi.org/10.1103/rgz2-4m69Cited byCould not fetch Crossref cited-by data during last attempt 2026-01-19 15:54:03: Could not fetch cited-by data for 10.22331/q-2026-01-19-1970 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-01-19 15:54:04: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThe occurrence of a second-order quantum phase transition in the Dicke model is a well-established feature. On the contrary, a comprehensive understanding of the corresponding open system, particularly in the proximity of the critical point, remains elusive. When approaching the critical point, the system inevitably enters first the system-bath ultrastrong coupling regime and finally the deepstrong coupling regime, causing the failure of usual approximations adopted to describe open quantum systems. We study the interaction of the Dicke model with bosonic bath fields in the absence of additional approximations, which usually relies on the weakness of the system-bath coupling. We find that the critical point is not affected by the interaction with the environment. Moreover, the interaction with the environment is not able to affect the system ground-state condensates in the superradiant phase, whereas the bath fields are $infected$ by the system and acquire macroscopic occupations. The obtained reflection spectra display lineshapes which become increasingly asymmetric, both in the normal and superradiant phases, when approaching the critical point.Popular summaryQuantum Phase Transitions are among the most fundamental collective phenomena in quantum physics, marking abrupt changes in the ground state of a system as an external parameter is varied. One of the most paradigmatic examples is the Superradiant Phase Transition, predicted by the Dicke model, in which many two-level systems coupled to a common electromagnetic field collectively reorganize and generate macroscopic, coherent excitations. While this transition is well understood for ideal, isolated systems, real physical implementations are inevitably influenced by their surrounding environment. The impact of such environments becomes especially subtle near the critical point of the transition, where the coupling between the system and its surroundings can become extremely strong, rendering standard theoretical approximations inadequate. In this work, we investigate the Dicke model coupled to environmental fields without relying on weak-coupling assumptions. We show that the critical point of the superradiant transition remains remarkably robust, when in the presence of environments with metastable minima. Moreover, in the superradiant phase, the fundamental condensates of the system are unaffected by the environmental interaction, while the environment itself is strongly modified and develops macroscopic occupations. These effects manifest in distinctive spectroscopic signatures, with increasingly asymmetric reflection spectra as the system approaches criticality, offering new insights into critical phenomena in open quantum systems.► BibTeX data@article{Lamberto2026superradiantquantum, doi = {10.22331/q-2026-01-19-1970}, url = {https://doi.org/10.22331/q-2026-01-19-1970}, title = {Superradiant {Q}uantum {P}hase {T}ransition in {O}pen {S}ystems: {S}ystem-{B}ath {I}nteraction at the {C}ritical {P}oint}, author = {Lamberto, Daniele and Orlando, Gabriele and Savasta, Salvatore}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1970}, month = jan, year = {2026} }► References [1] R. H. Dicke, Phys. Rev. 93, 99 (1954). https://doi.org/10.1103/PhysRev.93.99 [2] K. Hepp and E. H. Lieb, Ann. Phys. 76, 360 (1973). https://doi.org/10.1016/0003-4916(73)90039-0 [3] Y. K. Wang and F. T. 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