Polaron master equation theory of pulse-driven phonon-assisted population inversion and single-photon emission from quantum-dot excitons

Abstract

We introduce an intuitive and semi-analytical polaron master equation approach to model pulsedriven 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 experiment 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, and compare and contrast the important figures of merit with direct Rabi oscillation of the population using a resonant π pulse, where the latter is shown to be much more efficient.

Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems

“…2V ρ ω q (25) being the coupling constants for the electron (e) and hole (h) coupling to the q phonon mode. Here, the formfactors Ψ e(h) are assumed to be spherically symmetric and Gaussian as applies for a parabolic confinement potential and the deformation potential constants D We would like to point out that there have been many suggestions to simulate the QD dynamics under the influence of the carrier-phonon interaction outlined above including correlation expansions 31,32 , analytical solutions for delta excitation 33 , an exact diagonalization approach 34 , quantum jump approaches 35 and various forms of master equations 36-42 some of which account for contributions of arbitrarily high order in the dot-phonon coupling with the help of the polaron transformation 22,[43][44][45][46] . This variety of methods is also a result of the many different optical excitation scenarios that are discussed for QDs which can range from weak cavity couplings to strong pulsed laser excitation.…”

“…A powerful and widely used method that allows such an exact treatment is provided by the path-integral approach 3-6 which exactly takes into account the environment excitations via so called influence functionals for the degrees of freedom of the quantum system 7 . This formalism has been applied in a variety of fields of both physics and chemistry such as energy transfer dynamics [8][9][10][11][12][13][14][15][16] , Landau-Zener transitions 17,18 , quantum mechanical Brownian motion 19 and semiconductor quantum dots with and without optical driving [20][21][22][23][24][25] . Moreover, it has been applied to systems with bosonic and fermionic baths 26,27 , Ohmic and super-Ohmic 23 environments and can also be used to include multiple baths.…”

Intrinsic and environmental effects on the interference properties of a high-performance quantum dot single-photon source

“…To describe the effect of phonon interactions on the exciton dynamics, we shall use a polaron master-equation approach [33,39,47,51]. Here we apply the unitary transformation…”

Phonon-assisted dark exciton preparation in a quantum dot

“…While phonons often limit the preparation fidelity, e.g., in the case of resonant preparation by Rabi rotations 1,2 , recently, phonons have been actively used in optical control schemes of QD states [3][4][5][6][7] . In these protocols, the emission of phonons was exploited to prepare the exciton 3,7,8 or biexciton state of the QD [4][5][6]9 or to depopulate the QD 10 . However, all of these excitation protocols act on the optically active or bright exciton, while the optically inactive or dark exciton does not come into play.…”