arXiv:quant-ph/0011094

Experimental Test of Complementarity by Nuclear Magnetic Resonance Techniques

Xiwen Zhu, Ximing Fang, Xinhua Peng, Mang Feng, Kelin Gao, Du, Fei

Published Nov 22, 2000• 0 citations

Abstract

We have tested complementarity for the ensemble-averaged spin states of nuclei $^{13}$C in the molecule of $^{13}$CHCl$_{3}$ by the use of the spin states of another nuclei $^{1}$H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.

DOI: 10.48550/arxiv.quant-ph/0011094

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arXiv:quant-ph/0011094

Experimental Test of Complementarity by Nuclear Magnetic Resonance Techniques

Xiwen Zhu, Ximing Fang, Xinhua Peng, Mang Feng, Kelin Gao, Du, Fei

Published Nov 22, 2000• 0 citations

arXiv HTML PDF

Abstract

We have tested complementarity for the ensemble-averaged spin states of nuclei

^{13}

C in the molecule of

^{13}

CHCl

_{3}

by the use of the spin states of another nuclei

^{1}

H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.

DOI: 10.48550/arxiv.quant-ph/0011094

Related papers

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We tested wave-particle duality with the ensemble-averaged spin states of 13 C nuclei in 13 CHCl 3 using the spin states of 1 H nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.We tested wave-particle duality with the ensemble-averaged spin states of 13 C nuclei in 13 CHCl 3 using the spin states of 1 H nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.

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We have tested complementarity for the ensemble-averaged spin states of nuclei

^{13}

C in the molecule of

^{13}

CHCl

_{3}

by the use of the spin states of another nuclei

^{1}

We analyze an interferometric complementarity between one- and two-particle interference in the general case:

V_{i}^{2}+V_{12}^{2}\leq 1

(i=1

2)

, and further examine the relation among one-particle interference visibility

V_{i}

, two-particle interference visibility

V_{12}

and the predication

P_{i}

of the path of a single particle. An equality

V_{i}^{2}+V_{12}^{2}+P_{i}^{2}=1

(i=1

2)

is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement

E

of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.

One of the milestones of quantum mechanics is Bohr's complementarity principle. It states that a single quantum can exhibit a particlelike

or

a wavelike behavior, but never both at the same time. These are mutually exclusive and complementary aspects of the quantum system. This means that we need distinct experimental arrangements in order to measure the particle or the wave nature of a physical system. One of the most known representations of this principle is the single-photon Mach-Zehnder interferometer. When the interferometer is closed an interference pattern is observed (wave aspect of the quantum) while if it is open, the quantum behaves like a particle. Here, using a molecular quantum information processor and employing nuclear magnetic resonant (NMR) techniques, we analyze the quantum version of this principle by means of an interferometer that is in a quantum superposition of being closed and open, and confirm that we can indeed measure both aspects of the system with the same experimental apparatus. More specifically, we observe with a single apparatus the interference between the particle and the wave aspects of a quantum system.