Trapped ion spin-phonon chains: frustrated phases and applications in quantum metrology

Diego Porras

University of Sussex

Ions interacting with lasers or magnetic field gradients can be used to implement a variety of strongly coupled spin-phonon models. The latter include cooperative Jahn-Teller or Rabi lattice models. By including the effect of optical phases on spin-phonon couplings, the system exhibits magnetic frustration as a result of the interplay between dressed spin-phonon couplings and long-range interactions. We predict a variety of interesting phenomena as a result of the large number of quasi-degenerate low-energy states, like the strong sensitivity of the system to external fields. Our results show that trapped ion systems are ideally suited to assess the efficiency of quantum annealing in finding the global ground state of frustrated Ising systems. Furthermore, we show that the sensitivity of spin-phonon systems close to a quantum phase transition can be used as the basis of a quantum metrological scheme for measuring external magnetic fields.