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Register a new userMicroscopic theory of phonon-induced effects on semiconductor quantum dot decay dynamics in cavity QED
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We investigate the influence of the electron-phonon interaction on the decay dynamics of a quantum dot coupled to an optical microcavity. We show that the electron-phonon interaction has important consequences on the dynamics, especially when the quantum dot and cavity are tuned out of resonance, in which case the phonons may add or remove energy leading to an effective non-resonant coupling between quantum dot and cavity. The system is investigated using two different theoretical approaches: (i) a second-order expansion in the bare phonon coupling constant, and (ii) an expansion in a polaron-photon coupling constant, arising from the polaron transformation which allows an accurate description at high temperatures. In the low temperature regime we find excellent agreement between the two approaches. An extensive study of the quantum dot decay dynamics is performed, where important parameter dependencies are covered. We find that in general the electron-phonon interaction gives rise to a greatly increased bandwidth of the coupling between quantum dot and cavity. At low temperature an asymmetry in the quantum dot decay rate is observed, leading to a faster decay when the quantum dot has a larger energy than to the cavity. We explain this as due to the absence of phonon absorption processes. Furthermore, we derive approximate analytical expressions for the quantum dot decay rate, applicable when the cavity can be adiabatically eliminated. The expressions lead to a clear interpretation of the physics and emphasizes the important role played by the effective phonon density, describing the availability of phonons for scattering, in quantum dot decay dynamics. Based on the analytical expressions we present the parameter regimes where phonon effects are expected to be important. Also, we include all technical developments in appendices.
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A semiconductor quantum dot (QD) embedded within an optical microcavity is a system of fundamental importance within quantum information processing. The optimization of quantum coherence is crucial in such applications, requiring an in-depth understanding of the relevant decoherence mechanisms. We provide herein a critical review of prevalent theoretical treatments of the QD-cavity system coupled to longitudinal acoustic phonons, comparing predictions against a recently obtained exact solution. Within this review we consider a range of temperatures and exciton-cavity coupling strengths. Predictions of the polaron Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equations, as well as a variation of the former adapted for adiabatic continuous wave excitation (CWE), are compared against an asymptotically exact solution based upon Trotters decomposition (TD) theorem. The NZ and TCL implementations, which apply a polaron transformation to the Hamiltonian and subsequently treat the exciton-cavity coupling to second order, do not offer a significant improvement accuracy relative to the polaron transformation alone. The CWE adaptation provides a marked improvement, capturing the broadband features of the absorption spectrum (not present in NZ and TCL implementations). We attribute this difference to the effect of the Markov approximation, and particularly its unsuitability in pulsed excitation regime. Even the CWE adaptation, however, breaks down in the regime of high temperature ($50K$) and strong exciton-cavity coupling ($g gtrsim 0.2$ meV). The TD solution is of comparable computational complexity to the above-mentioned master equation approaches, yet remains accurate at higher temperatures and across a broad range of exciton-cavity coupling strengths (at least up to $g=1.5$ meV).
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