M. H. Y. Moussa

Here we present a protocol for generating Lissajous curves with a trapped ion by engineering Rashba- and the Dresselhaus-type spin-orbit interactions in a Paul trap. The unique anisotropic Rashba $α_{x}$, $α_{y}$ and Dresselhaus $β_{x}$, $β_{y}$ couplings afforded by our setup also enables us to obtain an "unusual" Zitterbewegung, i.e., the semiconductor analog of the relativistic trembling motion of electrons, with cycloidal trajectories in the absence of magnetic fields. We have also introduced bounded SO interactions, confined to an upper-bound vibrational subspace of the Fock states, as an additional mechanism to manipulate the Lissajous motion of the trapped ion. Finally, we accounted for dissipative effects on the vibrational degrees of freedom of the ion and find that the Lissajous trajectories are still robust and well defined for realistic parameters.

In this letter we present a protocol to engineer interactions confined to subspaces of the Fock space in trapped ions: we show how to engineer upper-, lower-bounded and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upper-bounded (lower-bounded) interaction acting upon Fock subspaces ranging from $\left\vert 0\right\rangle $ to $\left\vert M\right\rangle $ ($\left\vert N\right\rangle $ to$\ \infty$), and the sliced one confined to Fock subspace ranging from $\left\vert M\right\rangle $ to $\left\vert N\right\rangle $, whatever $M<N$. Whereas the upper-bounded JC or AJC interactions is shown to drive any initial state to a steady Fock state $\left\vert N\right\rangle $, the sliced one is shown to produce steady superpositions of Fock states confined to the sliced subspace $\left\{ \left\vert N\right\rangle \text{,}\left\vert N+1\right\rangle \right\} $.

In this paper we extend current perspectives in engineering reservoirs by producing a time-dependent master equation leading to a nonstationary superposition equilibrium state that can be nonadiabatically controlled by the system-reservoir parameters. Working with an ion trapped inside a nonindeal cavity we first engineer effective Hamiltonians that couple the electronic states of the ion with the cavity mode. Subsequently, two classes of decoherence-free evolution of the superposition of the ground and decaying excited levels are achieved: those with time-dependent azimuthal or polar angle. As an application, we generalise the purpose of an earlier study [Phys. Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases acquired by the protected nonstationary states even under a nonadiabatic evolution.

We show how to generate quadratic and bi-quadratic phonon-photon interactions through a driven three-level ion inside a cavity. With such a system it is possible to squeeze the cavity-field state, the ion motional state or even the entangled phonon-photon state. We present a detailed analysis of the cavity-field squeezing process, distinguishing three different regimes of this amplification mechanism: the subcritical, critical, and supercritical regimes, which depend, apart from the coupling parameters, on the excitation of the vibrational state. As an application of the engineered Hamiltonians, we show how to implement a Fock-state filter for the vibrational mode. New aspects of the technique of adiabatic elimination emerge in this analysis.

We describe a proposal to probe the quantum tunneling mechanism of an individual ion trapped in a double-well electromagnetic potential. The time-evolution of the probability of fluorescence measurement of the electronic ground state is employed to characterize the single-particle tunneling mechanism. The proposed scheme can be used to implement quantum information devices.

We investigate the mechanism of damping and heating of trapped ions associated with the polarization of the residual background gas induced by the oscillating ions themselves. Reasoning by analogy with the physics of surface electrons in liquid helium, we demonstrate that the decay of Rabi oscillations observed in experiments on 9Be+ can be attributed to the polarization phenomena investigated here. The measured sensitivity of the damping of Rabi oscillations with respect to the vibrational quantum number of a trapped ion is also predicted in our polarization model.

We present a reliable scheme for engineering arbitrary motional ionic states through an adaptation of the projection synthesis technique for trapped-ion phenomena. Starting from a prepared coherent motional state, the Wigner function of the desired state is thus sculpted from a Gaussian distribution. The engineering process has also been developed to take into account the errors arising from intensity fluctuations in the exciting-laser pulses required for manipulating the electronic and vibrational states of the trapped ion. To this end, a recently developed phenomenological-operator approach that allows for the influence of noise will be applied. This approach furnishes a straightforward technique to estimate the fidelity of the prepared state in the presence of errors, precluding the usual extensive ab initio calculations. The results obtained here by the phenomenological approach, to account for the effects of noise in our engineering scheme, can be directly applied to any other process involving trapped-ion phenomena.