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Register a new userPhonon-induced dephasing in quantum dot-cavity QED: Limitations of the polaron master equation
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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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We present a semi-analytic and asymptotically exact solution to the problem of phonon-induced decoherence in a quantum dot-microcavity system. Particular emphasis is placed on the linear polarization and optical absorption, but the approach presented herein may be straightforwardly adapted to address any elements of the exciton-cavity density matrix. At its core, the approach combines Trotters decomposition theorem with the linked cluster expansion. The effects of the exciton-cavity and exciton-phonon couplings are taken into account on equal footing, thereby providing access to regimes of comparable polaron and polariton timescales. We show that the optical decoherence is realized by real phonon-assisted transitions between different polariton states of the quantum dot-cavity system, and that the polariton line broadening is well-described by Fermis golden rule in the polariton frame. We also provide purely analytic approximations which accurately describe the system dynamics in the limit of longer polariton timescales.
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