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arXiv:1208.5001 · Physical Review B

Lindblad theory of dynamical decoherence of quantum-dot excitons

P. R. Eastham, A. O. Spracklen, Jonathan Keeling

Published May 15, 2013• 41 citations
arXivHTMLPDF

Abstract

We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)] but guarantees positivity of the density operator. At sufficiently low temperatures, it gives results equivalent to those of fully non-Markovian approaches [L\"uker et al., Phys. Rev. B 85, 121302 (2012)] but is significantly simpler to simulate. Several applications of this theory are discussed. We apply it to adiabatic rapid passage experiments and show how the pulses can be shaped to maximize the probability of creating a single exciton using a frequency-swept laser pulse. We also use this theory to propose and analyze methods to determine the phonon density of states experimentally, i.e., phonon spectroscopy, by exploring the dependence of the effective damping rates on the driving field.

DOI
10.1103/physrevb.87.195306

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We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)] but guarantees positivity of the density operator. At sufficiently low temperatures, it gives results equivalent to those of fully non-Markovian approaches [L"uker et al., Phys. Rev. B 85, 121302 (2012)] but is significantly simpler to simulate. Several applications of this theory are discussed. We apply it to adiabatic rapid passage experiments and show how the pulses can be shaped to maximize the probability of creating a single exciton using a frequency-swept laser pulse. We also use this theory to propose and analyze methods to determine the phonon density of states experimentally, i.e., phonon spectroscopy, by exploring the dependence of the effective damping rates on the driving field.
The eect of acoustic phonons on dierent light-induced excitations of a semiconductor quantum dot is investigated.Resonant excitation of the quantum dot leads to the Rabi oscillations, which are damped due to the phonon interaction.When the excitation frequency is detuned, an occupation can only occur due to phonon absorption or emission processes.For frequency-swept excitations a population inversion is achieved through adiabatic rapid passage, but the inversion is also damped by phonons.For all three scenarios the inuence of the phonons depends non-monotonically on the pulse area.
We study the evolution of an exciton confined in a quantum dot adiabatically controlled by a frequency-swept (chirped) laser pulse in the presence of carrier-phonon coupling. We focus on the dynamics induced by a linearly polarized beam and analyze the decoherence due to phonon-assisted biexciton generation. We show that if the biexciton state is shifted down by a few meV, as is typically the case, the resulting decoherence is strong even at low temperatures. As a result, efficient state preparation is restricted to a small parameter area corresponding to low temperatures, positive chirps and moderate pulse areas.
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo-dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and the importance of coherence for Rabi oscillations is investigated. The optically induced charge dynamics is discussed with respect to coherent effects. Calculations of the electronic density and pump-probe signals within a microscopic theory of dephasing show coherent transport effects such as gain oscillations, in agreement with recent experimental results.
We study the evolution of an exciton confined in a quantum dot adiabatically controlled by a frequency-swept (chirped) laser pulse in the presence of carrier-phonon coupling. We focus on the dynamics induced by a linearly polarized beam and analyze the decoherence due to phonon-assisted biexciton generation. We show that if the biexciton state is shifted down by a few meV, as is typically the case, then the resulting decoherence is strong even at low temperatures. As a result, efficient state preparation is restricted to a small parameter area corresponding to low temperatures, positive chirps, and moderate pulse areas.