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arXiv:quant-ph/0209137 · Physical Review Letters

Entanglement between an Electron and a Nuclear Spin 12

M. Mehring, Jens Mende, W. Scherer

Published Apr 15, 2003• 118 citations
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Abstract

We report on the preparation and detection of entangled states between an electron spin 1/2 and a nuclear spin 1/2 in a molecular single crystal. These were created by applying pulses at ESR (9.5 GHz) and NMR (21 MHz, 46 MHz) frequencies. Entanglement was detected by using a special entanglement detector sequence based on a unitary back transformation including phase rotation.

DOI
10.1103/physrevlett.90.153001

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•Jan 1, 2006•0 citations
We report on the preparation and detection of entangled states between an electron spin 1/2 and a nuclear spin 1/2 in a molecular single crystal. These were created by applying pulses at ESR (9.5 GHz) and NMR (21 MHz, 46 MHz) frequencies. Entanglement was detected by using a special entanglement detector sequence based on a unitary back transformation including phase rotation.
Procedures of the preparation and detection of entangled electron-nuclear spin states in (15)N@C(60) by combining electron spin resonance and electron nuclear double resonance pulse techniques are presented. A quantitative evaluation of the complete density matrix is obtained by a special density matrix tomography. All four Bell states of a two qubit subsystem were analyzed and experimental decoherence times are presented. In addition, we estimate a quantum critical temperature of T(q)=7.76 K for this system at an electron spin resonance frequency of 95 GHz.
In this work, we have been working on the concept of quantum entanglement. At first, we studied the theory of entanglement in its characterization and measurement, introducing a new scheme for detection of entanglement. The new approach links molecular-spin entities involving nuclear spins to quantum computing as more appropriate physical systems of interest. Then, we continued with the realization of entanglement in experiments. NMR has been the first choice due to its well approved advantages for quantum computing. NMR, however, has not been an appropriate system for demonstrating entangled states. Through a mathematical proof, NMR with low spin polarization has been invalidated for true implementations of non-local quantum algorithms, particularly supserdense coding. The point is that high spin polarization is inevitably required to acquire entanglement while in the current NMR it has been a formidable task to get highly polarized nuclear spins. In order to acquire high spin polarization, introducing electron spins can be much effective because of its three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins. Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that enables us to deal with both electron and nuclear spins. Thus, in this context, it can be more appropriate device for quantum computing. We emphasize that (pseudo)entanglement and interconversion between the entangled states have been realized with ENDOR on extremely stable organic molecular-spin entities. The required experimental conditions to obtain true quantum entanglement are also discussed. The appropriate entanglement witness for the corresponding ensemble quantum computing is introduced and examined.
Modern experimental techniques can generate magnetic fields of the form H(t) = H0 z-hat + H1 [x-hat cos(ωt) + y-hat sin(ωt)], at frequencies within an order of magnitude of the nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) frequencies, ωn0 and ωe0, respectively, when acting on atoms or molecules. We derive simple closed-form expressions for the exact nuclear- and electronic-spin wave functions that enable controlled transitions between entangled states, allowing an atom or molecule to function as a quantum computer. These solutions also enable precise NMR or EPR measurements of nuclear moments in atoms and molecules. We present examples relevant to measurements of the nuclear moments of 14N, 7Li, and 133Cs. Because existing hyperfine measurements of the lowest three nuclear moments of 133Cs are mutually inconsistent, the proposed NMR/EPR experiments provide a route to measuring all seven of its nuclear moments with high precision.
The subject of this thesis are experimental procedures for preparation, manipulation, and detection of specific quantum states of spin systems in the context of quantum computing. Nuclear magnetic resonance (NMR) and electron spin resonance (ESR) methods were used. The systems studied were small molecules in liquid state, small molecules embedded in a liquid crystal matrix, and paramagnetic centers in single crystals. The nuclear 19F spins of 2,3,4-Trifluoroaniline were used as qubits to implement the three-qubit Deutsch-Josza algorithm using high-resolution NMR. A classification of the Deutsch-Josza functions according to the operator representation of the corresponding oracle transformations was given. Different classes of functions may produce full, partial or no entanglement in the output states of the algorithm. This entanglement content is not immediately evident from the output states themselves. A procedure was given for mapping of the output states onto Bell- or GHZ-states by means of local transformations which preserve the entanglement content. A method for the visualization of single-spin unitary transformations was also presented. This visual representation can facilitate analysis and design of shaped rf pulses. For the purpose of quantum computing, it can be useful to suppress couplings between qubits during the application of finite-length single-qubit gates. The feasibility of this idea was demonstrated using small molecules in a liquid crystal matrix. In a series of proof-of-principle experiments, it was shown that the magic-echo sequence can be used to suppress the dipole-dipole coupling between spins and simultaneously selectively address a single spin by a soft rf pulse. The S-bus concept for spin-quantum computing holds some scalability promise and provides a testbed for studies of large, strongly coupled quantum registers. Single-crystal CaF2 weakly doped with Ce was used to implement the concept. The nine 19F nuclear spins adjacent to the paramagnetic Ce-ion serve as qubits while the electron spin plays the role of a quantum bus. The S-bus theory was tested experimentally. Procedures were given for the measurement of parameters characterizing the quantum state of the nuclear spins. An exact numeric treatment of this ten-spin system was done to aid in understanding the experimental findings. For a pair of nuclear spins with negligible direct dipolar coupling, the CNOT operation was implemented. The spin-spin coupling mediated by the bus spin was utilized for that purpose. The four Bell-states of these two distant spins were created. An experiment was performed who's signature allows those four entangled states to be distinguished. The paramagnetic cluster in CaF2:Ce is embedded in an extended network of 19F nuclear spins. This network is a powerful source of decoherence. A number of existing and a newly designed pulse sequence were tested with respect to their ability to suppress decoherence and their aptitude for use in quantum computing.