The propagation or time evolution of the quantum mechanical density matrix for systems relevant to quantum information and sensing is discussed. A Lindblad master equation formalism is employed that allows for the inclusion of dephasing, spontaneous emission and dissipation. Two applications are then presented. In the first example, a dissipative plasmonic system is coupled to quantum dots acting as qubits [1,2]. The plasmonic system could be a single metal nanoparticle or an array of metal nanoparticles and can be viewed as an optical resonator. It is shown that entanglement between two or more quantum dots can arise via coupling with the plasmon, and how such entanglements can be generated via pulsed optical excitation. The Purcell effect, or enhanced spontaneous emission rate of the quantum dots in the presence of the resonator, plays a role in the underlying mechanism. In the second example, a nitrogen-vacancy (NV) center, a particular type of defect in a diamond lattice that is a potential qubit owing to its robustness to thermal effects, is coupled to a mechanical resonator in the form of strain modes of the diamond lattice [3]. A reciprocal Purcell effect is identified as being responsible for a possible means of optically cooling the mechanical resonator, which is relevant to quantum sensing. These simulations have been enabled by a scalable software package written by M. Otten [4].

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[1] M. Otten, R. A. Shah, N. F. Scherer, M. Min, M. Pelton and S. K. Gray, Phys. Rev. B 92, 125432 (2015).
[2] M. Otten, J. Larson, M. Min, S. M. Wild, M. Pelton and S. K. Gray, Phys. Rev. A 94,022312 (2016).
[3] E. R. MacQuarrie, M. Otten, S. K. Gray and G. D. Fuchs, Nature Comm. 8, 14358 (2017).
[4] M. Otten, QuaC: Open quantum systems in C. https://github.com/0tt3r/QuaC. Published: 2017.