Improved scheme for generation of vibrational trio coherent states of a trapped ion

Abstract

Following the pair coherent state (PCS) [1], which has proved very important in quantum optics [2], atom-field dynamics [3], quantum-mechanics-versus-local-realism test [4], continuous-variable quantum nonlocality [5] and quantum information [6], the so-called trio coherent state (TCS) [7] and their cat-type superpositions [8] have also been introduced recently. This novel family of states has been shown inherently nonclassical exhibiting new types of multimode antibunching, higher-order squeezing and violation of Cauchy-Schwarz inequalities. Although the recognized kinds of nonclassical states have been numerous to date (see, e.g. [9]), it is not yet justified that all of them acquire actual applications. It is also not excluded that “really needed” states remain undiscovered or they are among the existing ones with their necessary properties unnoticeable. In that sense, any further detailed study of a known state or introduction of a new state would be perhaps equally welcome. As for the TCS, because of their three-mode nature, they would play a significant role in phenomena in which the PCS could not. For example, with the TCS one might predict that “one-event” continuous-variable local realism violating experiments could be found in a way more or less similar to those devised by Greenberger-Horne-Zeilinger [10] or/and by Hardy [11] for observables with discrete spectra. However, before any expected experiment can be done, a primary question arises: how can one produce the TCS in practice ? This question was answered in [7] for electromagnetic fields interacting with an atom when there is strong competition between trio parametric conversion and trio absorption. Here we shall concern with generation of TCS in the center-of-mass motion of a trapped ion. The motivation is that advanced laser-cooling techniques applied to single trapped ions allow to cool them down near their zero-point vibrational energy (see, e.g., Ref. [12]). In that quantized regime, the ion vibrational modes can be looked upon as ideal bosons which are almost uninfluenced by the environment resulting in negligible decoherences. This fact greatly favors potential implementations such as designing quantum logic gates in a quantum computer [13] (in particular, the controlled-NOT gate has been realized in two Ca ions in a Paul trap individually radiated by focused lasers [14]). Laser-driven trapped ions placed inside optical cavities can also entangle the cavity mode simultaneously with the internal and external degrees of freedom of the ion [15]. Previously, the vibrational TCS in a 3D trap was shown to be generated by a scheme using eight lasers [16] (compare with schemes for the vibrational PCS in a 2D trap [17]). In this Letter we shall improve the scheme proposed in [16] by reducing the number of used lasers from eight to five. Moreover, we shall carry out detailed simulation to reveal that the time needed to generate the vibrational TCS can be made shorter in the improved version than in the original one [16]. The vibrational TCS, denoted by |ξ, p, q〉 with ξ = r exp(iφ) and p, q integers, is a three-mode entangled continuous superposition of coherent states of the form

Cite this paper

@inproceedings{YiImprovedSF, title={Improved scheme for generation of vibrational trio coherent states of a trapped ion}, author={Hyo Seok Yi and Ba An Nguyen and Jaewan Kim} }