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Open Systems & Information Dynamics

Anisotropy-Induced Effects in the Dynamics of an Ion Confined in a Two-Dimensional Paul Trap

M. Scala, Benedetto Militello, Antonio Messina

Published Aug 31, 2006• 1 citation
Publisher

Abstract

We investigate the role of anisotropy in the dynamics of a single trapped ion interacting with two orthogonal laser beams, considering how it modifies a scheme for the generation of Schrödinger cat states and the so called parity effect in two-dimensional isotropic Paul traps. We find that anisotropy gives rise to a richer class for the generated states and to a larger number of observables sensitive to the parity of the number of excitation of the vibrational motion of the ion.

DOI
10.1007/s11080-006-9001-7

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We investigate the role of anisotropy in the dynamics of a single trapped ion interacting with two orthogonal laser beams, considering how it modifies a scheme for the generation of Schrödinger cat states and the so called parity effect in two-dimensional isotropic Paul traps. We find that anisotropy gives rise to a richer class for the generated states and to a larger number of observables sensitive to the parity of the number of excitation of the vibrational motion of the ion.
We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.
In this paper, we generalize the ordinary two-photon Jaynes-Cummings model (TPJCM) by considering the atom (or ion) to be trapped in a simple harmonic well. A typical setup would be an optical cavity containing a single ion in a Paul trap. Due to the inclusion of atomic vibrational motion, the atom-field coupling becomes highly nonlinear what brings out quite different behaviors for the system dynamics when compared to the ordinary TPJCM. In particular, we derive an effective two-photon Hamiltonian with dependence on the number operator of the ion's center-of-mass motion. This dependence occurs both in the cavity induced Stark-shifs and in the ion-field coupling, and its role in the dynamics is illustrated by showing the time evolution of the probability of occupation of the electronic levels for simple initial preparations of the state of the system.
We study some possible sources of decoherence in the generation of nonclassical states of motion of ions in Paul traps by means of numerical simulations based on reported experiments. In particular we study the consequences of the spontaneous decay of the internal energy state |0⟩ i which couples the two hyperfine internal states |1⟩ i and |2⟩ i in the two-photon Raman transitions used to manipulate the ion motional state. We also consider some possible experimental limitations to generate coherent states due to nonlinear effects in the coupling of the centre-of-mass coordinates with the laser field. A similar analysis is performed for carrier pulses taking into account nonlinearities and micromotion. The quantum evolution of the ion internal and centre-of-mass degrees of freedom are studied using amplitude equations derived from Schrödinger's equation. The limitations of such an approach are also discussed.