Gapless fluctuations and exceptional points in semiconductor lasers
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PhysRevB.109.045306.pdf
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Affiliation
Wyant College of Optical Sciences, The University of ArizonaDepartment of Physics, The University of Arizona
Issue Date
2024-01-23
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American Physical SocietyCitation
Kwong, N. H., Spotnitz, M. E., & Binder, R. (2024). Gapless fluctuations and exceptional points in semiconductor lasers. Physical Review B, 109(4), 045306.Journal
Physical Review BRights
© 2024 American Physical Society.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We analyze the spectrum of spatially uniform, single-particle fluctuation modes in the linear electromagnetic response of a semiconductor laser. We show that if the decay rate of the interband polarization, γp, and the relaxation rate of the occupation distribution, γf, are different, a gapless regime exists in which the order parameter Δ(0)(k) (linear in the coherent photon field amplitude and the interband polarization) is finite but there is no gap in the real part of the single-particle fluctuation spectrum. As the laser is an open, pumped, and dissipative system, this regime may be considered a nonequilibrium analog of gapless superconductivity. We analyze the fluctuation spectrum in both the photon laser limit, where the interactions among the charged particles are ignored, and the more general model with interacting particles. In the photon laser model, the order parameter is reduced to a momentum-independent quantity, which we denote by Δ. We find that, immediately above the lasing threshold, the real part of the fluctuation spectrum remains gapless when 0<|Δ|<2/27|γf-γp| and becomes gapped when |Δ| exceeds the upper bound of this range. Viewed as a complex function of |Δ| and the electron-hole energy, the eigenvalue set displays some interesting exceptional point (EP) structure around the gapless-gapped transition. The transition point is a third-order EP, where three eigenvalues (and eigenvectors) coincide. Switching on the particle interactions in the full model modifies the spectrum of the photon laser model and, in particular, leads to a more elaborate EP structure. However, the overall spectral behavior of the continuous (noncollective) modes of the full model can be understood on the basis of the relevant results of the photon laser model. © 2024 American Physical Society.Note
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2469-9950Version
Final Published Versionae974a485f413a2113503eed53cd6c53
10.1103/PhysRevB.109.045306