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Physical Review B

Publisher’s Note: General approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots [Phys. Rev. B84, 081305(R) (2011)]

Dara P. S. McCutcheon, Nikesh S. Dattani, Erik M. Gauger, Brendon W. Lovett, Ahsan Nazir

Published Sep 9, 2011• 8 citations
Publisher
DOI
10.1103/physrevb.84.119903

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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.

arXiv:1208.5001•Physical Review B•May 15, 2013•41 citations
Dara P. S. McCutcheon, 2, ∗ Nikesh S. Dattani, Erik M. Gauger, Brendon W. Lovett, 3 and Ahsan Nazir 1, † Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK London Centre for Nanotechnology, University College London Department of Materials, Oxford University, Oxford OX1 3PH, UK School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh EH14 4AS, UK Blackett Laboratory, Imperial College London, London SW7 2AZ, UK (Dated: May 31, 2011)
We develop a versatile master equation approach to describe the nonequilibrium dynamics of a two-level system in contact with a bosonic environment, which allows for the exploration of a wide range of parameter regimes within a single formalism. As an experimentally relevant example, we apply this technique to the study of excitonic Rabi rotations in a driven quantum dot, and compare its predictions to the numerical Feynman integral approach. We find excellent agreement between the two methods across a generally difficult range of parameters. In particular, the variational master equation technique captures effects usually considered to be nonperturbative, such as multiphonon processes and bath-induced driving renormalization, and can give reliable results even in regimes in which previous master equation approaches fail.
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.