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arXiv · 0806.0992

Dissipative dynamics of a two - level system resonantly coupled to a harmonic mode

Frederico Brito·Amir O. Caldeira
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Abstract

We propose an approximation scheme to describe the dynamics of the spin-boson model when the spectral density of the environment shows a peak at a characteristic frequency $Ω$ which can be very close (or even equal) to the spin Zeeman frequency $Δ$. Mapping the problem onto a two-state system (TSS) coupled to a harmonic oscillator (HO) with frequency $ω_0$ we show that the representation of displaced HO states provides an appropriate basis to truncate the Hilbert space of the TSS-HO system and therefore a better picture of the system dynamics. We derive an effective Hamiltonian for the TSS-HO system, and show it furnishes a very good approximation for the system dynamics even when its two subsystems are moderately coupled. Finally, assuming the regime of weak HO-bath coupling and low temperatures, we are able to analytically evaluate the dissipative TSS dynamics.

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Frederico Brito, Amir O. Caldeira. 2008-12-11. Dissipative dynamics of a two - level system resonantly coupled to a harmonic mode. https://doi.org/10.1088/1367-2630%2F10%2F11%2F115014

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