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Theory of pulse driven phonon-assisted population inversion and single photon emission from quantum dot excitons: analytical polaron master equation approach

Ross Manson, Kaushik Roy‐Choudhury, Stephen Hughes

Published Dec 24, 2015• 0 citations
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Polaron master equation theory of pulse-driven phonon-assisted population inversion and single-photon emission from quantum-dot excitons

Ross Manson, Kaushik Roy‐Choudhury, Stephen Hughes

We introduce an intuitive and semianalytical polaron master equation approach to model pulse-driven population inversion and emitted single photons from a quantum dot exciton. The master equation theory allows one to identify important phonon-induced scattering rates analytically and fully includes the role of the time-dependent pump field. As an application of the theory, we first study a quantum dot driven by a time-varying laser pulse on and off resonance, showing the population inversion caused by acoustic phonon emission in direct agreement with recent experiments of Quilter et al. [Phys. Rev. Lett. 114, 137401 (2015)]. We then model quantum dots in weakly coupled cavities and show the difference in population response between exciton-driven and cavity-driven systems. Finally, we assess the nonresonant phonon-assisted loading scheme with a quantum dot resonantly coupled to a cavity as a deterministic single-photon source. We also compare and contrast the important single photon figures of merit with direct Rabi oscillation of the population using a resonant $\ensuremath{\pi}$ pulse, and show that the resonant scheme is much more efficient.

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Coherent nonlinear optical response of excitons in quantum dots coupled to phonons

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We introduce an intuitive and semianalytical polaron master equation approach to model pulse-driven population inversion and emitted single photons from a quantum dot exciton. The master equation theory allows one to identify important phonon-induced scattering rates analytically and fully includes the role of the time-dependent pump field. As an application of the theory, we first study a quantum dot driven by a time-varying laser pulse on and off resonance, showing the population inversion caused by acoustic phonon emission in direct agreement with recent experiments of Quilter et al. [Phys. Rev. Lett. 114, 137401 (2015)]. We then model quantum dots in weakly coupled cavities and show the difference in population response between exciton-driven and cavity-driven systems. Finally, we assess the nonresonant phonon-assisted loading scheme with a quantum dot resonantly coupled to a cavity as a deterministic single-photon source. We also compare and contrast the important single photon figures of merit with direct Rabi oscillation of the population using a resonant $\ensuremath{\pi}$ pulse, and show that the resonant scheme is much more efficient.
We investigate pump-induced exciton inversion in a quantum-dot cavity system with continuous wave drive. Using a polaron-based master equation, we demonstrate excited-state populations above 0.9 for an InAs quantum dot at a phonon bath temperature of 4 K. In an exciton-driven system, the dominant mechanism is incoherent excitation from the phonon bath. For cavity driving, the mechanism is phonon-mediated switching between ground- and excited-state branches of the ladder of photon states, as quantum trajectory simulations clearly show. The exciton inversion as a function of detuning is found to be qualitatively different for exciton and cavity driving, primarily due to cavity filtering. The master equation approach allows us to include important radiative and non-radiative decay processes on the zero phonon line, provides a clear underlying dynamic in terms of photon and phonon scattering, and admits simple analytical approximations that help to explain the physics.
We demonstrate an approach to realize the population inversion of a single InGaAs/GaAs quantum dot, which is driven by a laser pulse tuned within the neutral exciton phonon sideband. The inversion is achieved by rapid thermalization of the optically dressed states via phonon-assisted relaxation. A maximum exciton population of 0.67 ±\pm± 0.06 is measured for a laser tuned 0.83 meV to higher energy and the phonon sideband is mapped using a two-color pump-probe technique. Our experiments reveal that, in accordance with theory, the phonon-bath provides additional functionality for an optically driven quantum dot qubit.