Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity

Abstract

We use a non-Lindbladian master equation of the Scully-Lamb laser model for the analysis of light propagation in a parity-time symmetric photonic system composed of coupled active and passive whispering-gallery microresonators. Performing the semiclassical approximation, we obtain a set of two nonlinear coupled differential equations describing the time evolution of intracavity fields. These coupled equations are able to explain the experimentally-observed light non-reciprocity [Peng {\em et al.}, Nature Physics {\bf 10}, 394 (2014), Chang {\em et al.}, Nature Photonics {\bf 8}, 524 (2014)]. We show that this effect arises from the interplay between gain saturation in the active microcavity, intercavity coupling, and losses in the cavities. Additionally, using this approach, we study the effect of the gain saturation on exceptional points, i.e., exotic degeneracies in non-Hermitian systems. Namely, we demonstrate that the inclusion of gain saturation leads to a modification of the exceptional points in the presence of intense intracavity fields. The Scully-Lamb master equation for systems of coupled optical structures, as proposed and applied here, constitutes a promising tool for the study of quantum optical effects in coupled systems with losses, gain, and gain saturation.

arXiv comment16 pages, 14 figures

References in corpus (22)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Loss-induced suppression and revival of lasing
• Topological energy transfer in an optomechanical system with exceptional points
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Unidirectional Nonlinear PT-symmetric Optical Structures
• PT-Symmetric Phonon Laser
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Second-Order Topological Phases in Non-Hermitian Systems
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Must a Hamiltonian be Hermitian?
• Parity-time-symmetric quantum critical phenomena
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Perfectly absorbing exceptional points and chiral absorbers
• High-order exceptional points in optomechanics
• General Theory of Spontaneous Emission Near Exceptional Points
• Effective spontaneous PT-symmetry breaking in hybridized metamaterials
• Exceptional Points in Random-Defect Phonon Lasers
• $\mathcal{P}\mathcal{T}$-symmetric circuit-QED
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators

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