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Communications in Theoretical Physics

The Test of Complementarity with Trapped Ions

Zheng Shi-Biao

Published Oct 30, 2000• 3 citations
Publisher

Abstract

We propose a scheme to test Bohr complementarity with cold ions confined in a linear trap. In the scheme two ions are first prepared in a maximally entangled state via the excitation by laser fields. Then one ion of the correlated pair is driven by a resonant laser. The path information of this ion to reach one definite state is recorded on the other ion and thus the probability of finding the first ion in a definite state does not exhibit interference. The associated quantum eraser can also be realized.

DOI
10.1088/0253-6102/34/3/575

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We propose a scheme to test Bohr complementarity with cold ions confined in a linear trap. In the scheme two ions are first prepared in a maximally entangled state via the excitation by laser fields. Then one ion of the correlated pair is driven by a resonant laser. The path information of this ion to reach one definite state is recorded on the other ion and thus the probability of finding the first ion in a definite state does not exhibit interference. The associated quantum eraser can also be realized.
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.
Two experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions. In the first scheme, a Greenberger-Horne-Zeilinger state can be simply synthesized in a single step, in view of decoherence mechanism, a reduction of the number of operations for the state preparation is crucial. What’s more, only one laser beam is required in our scheme. The second scheme is to prepare canonical (fully symmetric) W states by two steps. However, in the paper [HÄaner H, HÄansel W, Roos C F, et al. Nature, 2005, 438:643-646.] M steps were required for generating the same W states.
We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximally Greenberger–Horne–Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglement of multiple coherent and squeezing states with desired amplitudes in a reasonable time.