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arXiv:1105.6015 · Physical Review B

A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots

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

Published Aug 25, 2011• 155 citations
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Abstract

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.

DOI
10.1103/physrevb.84.081305

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General approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots (vol 84, 081305, 2011)

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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)]

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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.
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We employ a generalized approach to the master equation for driven open NNN-level (N>2N>2N>2) quantum systems using Lewis-Riesenfeld invariants, which avoids the driving-strength restrictions inherent to conventional approaches. We show that the invariant-based master equation provides a unifying generalized framework, which reduces to the frequently employed laboratory-frame master equations and the less frequently employed rotating-frame master equation framework under appropriate simplifications. Extending the prototypical two-level system, we show that the inclusion of another state coupled to the ground state via reservoir-induced dephasing gives rise to qualitatively new dissipative behaviors that are, in general, not captured by standard approximations. We also apply the invariant-based master equation framework to a driven quantum dot coupled to a leaky cavity, demonstrating the framework's ability to capture relevant dissipative dynamics without additional assumptions. Our work paves the way for quantum-control applications in the presence of dissipation.