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arXiv:quant-ph/0605032 · Applied Physics Letters

Projective measurement in nuclear magnetic resonance

Jae‐Seung Lee, Anatoly K. Khitrin

Published Aug 14, 2006• 17 citations
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Abstract

It is demonstrated that nuclear magnetic resonance experiments using pseudopure spin states can give possible outcomes of projective quantum measurement and probabilities of such outcomes. The physical system is a cluster of six dipolar-coupled nuclear spins of benzene in a liquid-crystalline matrix. For this system with the maximum total spin S=3, the results of measuring SX are presented for the cases when the state of the system is one of the eigenstates of SZ.

DOI
10.1063/1.2337158

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It is demonstrated that nuclear magnetic resonance experiments using pseudopure spin states can give possible outcomes of projective quantum measurement and probabilities of such outcomes. The physical system is a cluster of six dipolar-coupled nuclear spins of benzene in a liquid-crystalline matrix. For this system with the maximum total spin S=3, the results of measuring SX are presented for the cases when the state of the system is one of the eigenstates of SZ.
It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2, a| upward arrow+b| downward arrow, can be converted into a superposition of the two ferromagnetic states of a spin cluster: a| upward arrow upward arrow... upward arrow upward arrow+b| downward arrow downward arrow... downward arrow downward arrow. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labeled 13C-benzene molecules in a liquid-crystalline matrix. In this complex system, the pseudopure ground state and the required controlled unitary transformations have been implemented. The experimental scheme can be considered as an explicit model of quantum measurement.
It is shown that in nuclear magnetic resonance, multiple-quantum (MQ) coherences can be detected "instantly" by exploiting the principle of quantum-mechanical projective measurement. Therefore, the mixing period, which involves collective multispin dynamics and converts MQ coherences into observable single-quantum coherence (magnetization), is not necessary. The experimental examples are given for two finite clusters: benzene in liquid crystal and liquid crystal 4'-n-pentyl-4-cyanobiphenyl, and for solid adamantane with an infinite network of dipolar couplings.
It is experimentally demonstrated that a quantum state, destroyed by uncontrollable natural decoherence, can be purified by using results of projective measurement and converted into a desired target pure state. The physical system is a cluster of seven dipolar-coupled nuclear spins of single-labelled 13 C-benzene in liquid crystal. 13 C spin plays the role of a device for measuring the protons' 'cat' state, a superposition of states with six spins up ( alive ) and six spins down ( dead ). Information about the state, stored in the 13 C spin, is used to bring the protons' subsystem into the target alive state, while the excess entropy produced by decoherence is transferred to the 'measuring device', the 13 C spin.