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 $alpha_{x}$, $alpha_{y}$ and Dresselhaus $beta_{x}$, $
beta_{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 paper, we present a protocol to engineer upper-bounded and sliced Jaynes-Cummings and anti-Jaynes-Cummings Hamiltonians in cavity quantum electrodynamics. In the upper-bounded Hamiltonians, the atom-field interaction is confined to a subspace
of Fock states ranging from $leftvert 0rightrangle $ up to $leftvert 4rightrangle $, while in the sliced interaction the Fock subspace ranges from $leftvert Mrightrangle $ up to $leftvert M+4rightrangle $. We also show how to build upper-bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper-bounded and sliced Hamiltonians and Liouvillians can be used, among other applications, to generate steady Fock states of a cavity mode and for the implementation of a quantum-scissors device for optical state truncation.
In this letter we propose a scheme for the preparation of steady entanglements in bosonic dissipative networks. We describe its implementation in a system of coupled cavities interacting with an engineered reservoir built up of three-level atoms. Emb
lematic bipartite ($Bell$ and $NOON$) and multipartite $W$-class states can be produced with high fidelity and purity.
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 uppe
r-bounded (lower-bounded) interaction acting upon Fock subspaces ranging from $leftvert 0rightrangle $ to $leftvert Mrightrangle $ ($leftvert Nrightrangle $ to$ infty$), and the sliced one confined to Fock subspace ranging from $leftvert Mrightrangle $ to $leftvert Nrightrangle $, whatever $M<N$. Whereas the upper-bounded JC or AJC interactions is shown to drive any initial state to a steady Fock state $leftvert Nrightrangle $, the sliced one is shown to produce steady superpositions of Fock states confined to the sliced subspace $left{ leftvert Nrightrangle text{,}leftvert N+1rightrangle right} $.
In this paper we present a method to derive an exact master equation for a bosonic system coupled to a set of other bosonic systems, which plays the role of the reservoir, under the strong coupling regime, i.e., without resorting to either the rotati
ng-wave or secular approximations. Working with phase-space distribution functions, we verify that the dynamics are separated in the evolution of its center, which follows classical mechanics, and its shape, which becomes distorted. This is the generalization of a result by Glauber, who stated that coherent states remain coherent under certain circumstances, specifically when the rotating-wave approximation and a zero-temperature reservoir are used. We show that the counter-rotating terms generate fluctuations that distort the vacuum state, much the same as thermal fluctuations.Finally, we discuss conditions for non-Markovian dynamics.
In this letter we present a strategy that combines the action of cavity damping mechanisms with that of an engineered atomic reservoir to drive an initial thermal distribution to a Fock equilibrium state. The same technique can be used to slice proba
bility distributions in the Fock space, thus allowing the preparation of a variety of nonclassical equilibrium states.
