Overlapping Resonances in the Resistance of Superposition States to Decoherence Asoka Biswas $^{1}$, Moshe Shapiro$^{2}$, and Paul Brumer1 $^{1}$Chemical Physics Theory Group, Department of Chemistry, and Center of Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada $^{2}$Department of Chemistry, University of British Columbia, Vancouver, V6T1Z1, Canada and Chemical Physics Department, The Weizmann Institute of Science, Rehovot 76100, Israel (Dated: June 20, 2018) Overlapping resonances are shown to provide new insights into the extent of decoherence expe- rienced by a system superposition state in the regime of strong system- environment coupling. As an example of this general approach, a generic system comprising spin-half particles interacting with a thermalized oscillator environment is considered. We find that (a) amongst the collection of parametrized Hamiltonians, the larger the overlapping resonances contribution, the greater the maximum possible purity, and (b) for a fixed Hamiltonian, the larger the overlapping resonances contribution, the larger the range of possible values of the purity as one varies the phases in the system superposition states. Systems displaying decoherence free subspaces show that largest overlapping resonances contribution. PACS numbers: 03.65.Yz,03.67.Pp 1 Abstract arXiv:1001.4134v1 [quant-ph] 23 Jan 2010