Automatical generation of nonadiabatic conditional geometric phase shift   via a noncoplanar fiber system
  A new scheme of realizing the nonadiabatic conditional geometric phase shift via a noncoplanar (and coiled) fiber system is presented in this Letter. It is shown that the effective Hamiltonian that describes the interaction of polarized photons with the fiber medium is just the Wang-Keiji type of Hamiltonian. This, therefore, means that the coiled fiber system may be an ideal implementation of realizing the nonadiabatic geometric phase gates for the topological quantum computation. The remarkable feature of the present method is that it can automatically meet the conditions and requirements proposed in the Wang-Keiji scheme: (i) in the coiled fiber system, the dynamical phase of photon wavefunction caused by the interaction Hamiltonian automatically vanishes; (ii) the Wang-Keiji requirement for the parameters in the Wang-Keiji Hamiltonian can be exactly satisfied automatically in the fiber system; (iii) the conditional initial state can be easily achieved by manipulating the initial wave vector of polarized photons. Due to these three advantages, the coiled fiber system may be a potentially practical way of achieving the nonadiabatic conditional geometric phase shift (and hence the nonadiabatic geometric quantum gates). 
Jian Qi Shen