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arXiv · 2306.17722

Impact of the phonon environment on the nonlinear quantum-dot-cavity QED. I. Path-integral approach

L. S. Sirkina·E. A. Muljarov
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Abstract

We demonstrate a strong influence of the phonon environment on the coherent dynamics of the quantum dot (QD)-cavity system in the quantum strong coupling regime. This regime is implemented in the nonlinear QD-cavity QED and can be reliably measured by heterodyne spectral interferometry. We present a semi-analytic asymptotically exact path integral-based approach to the nonlinear optical response of this system, which includes two key ingredients: Trotter's decomposition and linked-cluster expansion. Applied to the four-wave-mixing optical polarization, this approach provides access to different excitation and measurement channels, as well as to higher-order optical nonlinearities and quantum correlators. Furthermore, it allows us to extract useful analytic approximations and analyze the nonlinear optical response in terms of quantum transitions between phonon-dressed states of the anharmonic Jaynes-Cummings (JC) ladder. Being well described by these approximations at low temperatures and small exciton-cavity coupling, the exact solution deviates from them for stronger couplings and higher temperatures, demonstrating remarkable non-Markovian effects, spectral asymmetry, and strong phonon renormalization of the JC ladder.

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L. S. Sirkina, E. A. Muljarov. 2023-06-30. Impact of the phonon environment on the nonlinear quantum-dot-cavity QED. I. Path-integral approach. https://doi.org/10.1103/physrevb.108.115312

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