Decoherence due to an excited state quantum phase transition in a two-level boson model P. P´ erez-Fern´ andez $^{1}$, A. Rela˜ no $^{2}$, J. M. Arias$^{1}$, J. Dukelsky$^{2}$, and J. E. Garc´ıa-Ramos3 1 Departamento de F´ısica At´ omica, Molecular y Nuclear, Facultad de F´ısica, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain 2 Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Spain 3 Departamento de F´ısica Aplicada, Universidad de Huelva, 21071 Huelva, Spain ∗ (Dated: November 17, 2018) Abstract The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modelled as a scalar two-level boson system that can go through either first order or continuous excited state quantum phase transitions, depending on the values of the control parameters. A mean field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behaviour of the decoherence. Only the continuous excited state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor (or the fidelity) goes to zero with a finite size scaling power law. PACS numbers: 03.65.Yz, 05.70.Fh, 64.70.Tg ∗ Electronic address: armando@iem.cfmac.csic.es 1 arXiv:1001.0398v1 [quant-ph] 3 Jan 2010