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International Journal of Modern Physics B

MAXIMALLY ENTANGLED STATES FOR MANY TRAPPED IONS FROM SINGLE RESONANT INTERACTIONS

Lin Li, Dahai Xu, Yonghong Tian, Xiuhua Yuan

Published Jun 20, 2007• 0 citations
Publisher

Abstract

We propose an alternative scheme to generate the GHZ states and cluster states for many trapped ions illuminated by a single laser tuned to the first lower vibrational sideband. The distinct advantage of the present scheme is that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the present scheme is very simple and the interaction time is very short, which is important in view of decoherence.

DOI
10.1142/s0217979207037405

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We propose an alternative scheme to generate the GHZ states and cluster states for many trapped ions illuminated by a single laser tuned to the first lower vibrational sideband. The distinct advantage of the present scheme is that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the present scheme is very simple and the interaction time is very short, which is important in view of decoherence.
Three experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions.In the first scheme,a GHZ state can be simply synthesized in a single step. The second scheme is to prepare fully symmetric W states with two steps.The third scheme describes the sequential generation of linear cluster states.In addition,a method to create a larger cluster state was also presented by fuzing the end qubits of two smaller cluster states in order to decrease the distortion caused by decoherence,which can speed up the generation of large cluster states.The above schemes involve the collective interaction between multiple ions with the vibrational ground state and a large detuned laser. Compared with previous schemes,the above schemes have four advantages.Firstly,they do not require the vibrational mode of ions as memory.Secondly,they do not need to address the ions individually.Thirdly, they are free from the effects of phase fluctuation of laser field.Finally,they need less operations.
We propose a simple and fast scheme for producing maximally entangled states for many trapped ions. The scheme only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the regime, where the Rabi frequency is of the order of the vibrational frequency. Our scheme operates in a fast way and is insensitive to heating of vibrational motion, which is important in view of decoherence. Thus, our scheme opens promising prospects for entanglement engineering in a scalable way.
In this paper, based on the recent experiment by Roos et al. [Science 304, 1478 (2004)], a theoretical scheme is proposed to create the multipartite entanglement of many trapped ions and implement a two-qubit quantum phase gate between two ions in ion trap. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. We also show that the scheme can be used to directly transfer information between two ions. The scheme has the advantage that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed. In view of the decoherence mechanism, the simplification for the entangled state preparation and experimental implementation of quantum logic operation may become crucial.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.