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arXiv:cond-mat/0403348 · Physical Review A

Short-time decoherence for general system-environment interactions

Denis Tolkunov, Vladimir Privman A

Published Jun 7, 2004• 52 citations
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Abstract

A short-time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator $\ensuremath{\Lambda}$ and its conjugate ${\ensuremath{\Lambda}}^{\ifmmode\dagger\else\textdagger\fi{}}$ in order to evaluate the onset of decoherence at low temperatures in quantum systems interacting with the environment. The developed approach is complementary to Markovian approximations and appropriate for the evaluation of quantum computing schemes. An example of a spin system coupled to a bosonic heat bath via $\ensuremath{\Lambda}\ensuremath{\propto}{\ensuremath{\sigma}}_{\ensuremath{-}}$ is worked out in detail.

DOI
10.1103/physreva.69.062309

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A short-time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ and its conjugate \ensuremathΛ\ifmmode†\else\textdagger\fi{\ensuremath{\Lambda}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremathΛ\ifmmode†\else\textdagger\fi in order to evaluate the onset of decoherence at low temperatures in quantum systems interacting with the environment. The developed approach is complementary to Markovian approximations and appropriate for the evaluation of quantum computing schemes. An example of a spin system coupled to a bosonic heat bath via \ensuremathΛ\ensuremath∝\ensuremathσ\ensuremath−\ensuremath{\Lambda}\ensuremath{\propto}{\ensuremath{\sigma}}_{\ensuremath{-}}\ensuremathΛ\ensuremath∝\ensuremathσ\ensuremath−​ is worked out in detail.
We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.
Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.