Decoherence-free dynamical and geometrical entangling phase gates

It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [ Phys. Rev. Lett. 89 187903 (2002)] and employing entangling Raman- or STIRAP-like transitions that restrict the time evolution of the system onto stable ground states.