A new approach for reconstructing the vibrational quantum state of a trapped ion is proposed. The method rests upon the current ability of manipulating the trapped ion state and on the possibility of effectively measuring the scalar product of the two vibrational cofactors of a vibronic entangled state. The experimental feasibility of the method is briefly discussed.
The spectacular experimental results of the last few years in cavity quantum electrodynamics and trapped ions research has led to very high level laboratory performances. Such a stimulating situation essentially stems from two decisive advancements. The first is the invention of reliable protocols for the manipulation of single atoms. The second is the ability to produce desired bosonic environments on demand. These progresses have led to the possibility of controlling the form of the coupling between individual atoms and an arbitrary number of bosonic modes. As a consequence, fundamental matter-radiation interaction models like, for instance, the JC model and most of its numerous nonlinear multiphoton generalizations, have been realized or simulated in laboratory and their dynamical features have been tested more or less in detail. This topical paper reviews the state of the art of the theoretical investigations and of the experimental observations concerning the dynamical features of the coupling between single few-level atoms and two bosonic modes. In the course of the paper we show that such a configuration provides an excellent platform for investigating various quantum intermode correlation effects tested or testable in the cavity quantum electrodynamics and trapped ion experimental realms. In particular we discuss a mode-mode correlation effect appearing in the dynamics of a two-level atom quadratically coupled to two bosonic modes. This effect, named parity effect, consists in a high sensitivity to the evenness or oddness of the total number of bosonic excitations.
The possibility of revealing non-classical behaviours in the dynamics of a trapped ion via measurements of the mean value of suitable operators is reported. In particular we focus on the manifestation known as `` Parity Effect\rq\rq which may be observed \emph{directly measuring} the expectation value of an appropriate correlation operator. The experimental feasibility of our proposal is discussed.
In this paper we propose the realization of a bosonic-fermionic interaction in the context of trapped ions whose effect upon the ion center of mass degrees of freedom is properly speaking a spatial inversion. The physical system and its features are accurately described and some applications are briefly discussed.
The theoretical foundations of a new general approach to the measurement problem of vibrational observables in trapped ion systems is reported. The method rests upon the introduction of a simple vibronic coupling structure appropriately conceived to link the internal ionic state measurement outcomes to the mean value of a motional variable of interest. Some applications are provided and discussed in detail, bringing to light the feasibility and the wide potentiality of the proposal.
We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation.
A "continuous measurement" Quantum Zeno Effect (QZE) in the context of trapped ions is predicted. We describe the physical system and study its exact time evolution showing the appearance of Zeno Phenomena. New indicators for the occurrence of QZE in oscillatory systems are proposed and carefully discussed.