Ion crystals in optical resonators

CECILIA CORMICK; GIOVANNA MORIGI

Praga

Conferencia; Frontiers of Quantum and Mesoscopic Thermodynamics; 2011

We study the dynamics of a chain of ultracold ions, which is confined inside a standing-wave optical resonator, in the regime in which a dipolar transition of the ion couples with a cavity mode and the cavity is pumped. A similar situation has been recently experimentally realised in [1]. In this regime the ions motion is determined by the trapping potential, the Coulomb repulsion, and the quantum potential of the cavity field. We analyze the different regimes that can be attained when the detuning and intensity of the pump fieldare varied. We first consider the case in which the cavity field represents a negligible perturbation to the dynamics of the ions, and study how to obtain information about the structure and dynamics of the ion chain by measuring the light at the cavity output. We then consider the case when the mean number of cavity photons is large and the electromagnetic field can be treated as classical, and study the mapping of the system dynamics to the well-known Frenkel-Kontorova model [2]. We finally analyze the behaviour of thesystem when the back-action of the cavity field on the ions dynamics cannot be neglected [3]. For this situation, we study the normal modes of the chain, focusing in particular on the linear-zigzag structural transition [4].References[1] P. F. Herskind, A. Dantan, J. P. Marler, M. Albert and M. Drewsen, Nat. Phys. 5, 494 (2009).[2] I. Garcia-Mata, O. V. Zhirov and D. L. Shepelyansky, Eur. Phys. J. D 41, 325 (2007).[3] J. K. Asboth, P. Domokos, H. Ritsch and A. Vukics, Phys. Rev. A 72, 053417 (2005).[4]S. Fishman, G. De Chiara, T. Calarco and G. Morigi, Phys. Rev. B 77, 064111 (2008).