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arXiv:1901.11421 · Physical Review A

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

Ievgen I. Arkhipov, Adam Miranowicz, Omar Di Stefano, Roberto Stassi, Salvatore Savasta, Franco Nori, Şahin Kaya Özdemir

Published May 6, 2019• 66 citations
arXivHTMLPDF

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 nonreciprocity [Peng et al., Nat. Phys. 10, 394 (2014); Chang et al., Nat. Photon. 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.

DOI
10.1103/physreva.99.053806

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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 nonreciprocity [Peng et al., Nat. Phys. 10, 394 (2014); Chang et al., Nat. Photon. 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.
We propose a scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time ([Formula: see text]) symmetric system (i.e., coupled active-passive cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The increased optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability, and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.
We propose an alternative scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\textrm{PT}) system (i.e., active-passive coupled cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The giant optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.
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A two-mode optical parity-time (PT\mathcal{PT}PT) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and nonclassicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the nonclassicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.
We study the coupled even number of microcavities with the balanced gain and loss between any pair of their neighboring components. The effective non-Hermitian Hamiltonian for such a structure has the cyclic permutation-time symmetry with respect to the cavity modes, and this symmetry determines the patterns of the dynamical evolutions of the cavity modes. The systems also have multiple exceptional points for the degeneracy of the existing supermodes, exhibiting the ``phase transition'' of system dynamics across these exceptional points. We illustrate the quantum dynamical properties of the systems with the evolutions of cavity photon numbers and correlation functions. Moreover, we demonstrate the effects of the quantum noises accompanying the amplification and dissipation of the cavity modes. The reciprocal light transportation predicted with the effective non-Hermitian models for the similar couplers is violated by the unavoidable quantum noises.
Gain saturation is ubiquitous but has not been fully explored in the newly developed field of non-Hermitian optics. On the other hand, the nonclassical properties of light are highly relevant to the gain saturation that influences the quantum noise accompanying light amplification. In this paper, we systematically examine the gain saturation effects in a non-Hermitian system of coupled gain-loss waveguides. We explain the impact of gain saturation on a quantum light field dynamically evolving in the coupled system. In contrast to the ideal situation without gain saturation, one can achieve a quasisteady state under the gain saturation. Moreover, gain saturation reduces the influence of amplification noise and thereby better preserves such quantum features as entanglement. We illustrate the effects of gain saturation by examining the time evolution of the Wigner function, entanglement of the light fields, and the cross-correlation function between the two output modes. Significant differences exist between unsaturated and saturated situations, especially for low photon numbers.