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AIP conference proceedings

Entanglement of Spin States in 15N@C60

W. Scherer

Published Jan 1, 2004• 0 citations
Publisher

Abstract

The endohedral fullerene 15N@C60 comprises an electron spin S = 3/2 coupled to a nuclear spin I = 1/2 and is therefore ideally suited for experimental testing of basic properties of quantum mechanics. We will show that the 15N@C60 molecule represents a multi qubit system where different kinds of entangled states can be generated.
DOI
10.1063/1.1812097

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We have prepared combined electron and nuclear spin pseudoentangled states ${\ensuremath{\Psi}}_{27}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\ensuremath{\Phi}}_{18}^{\ifmmode\pm\else\textpm\fi{}}$ out of the total number of eight quantum states in the multilevel quantum system of a nitrogen atom with electron spin 3/23/23/2 and nuclear spin 1/21/21/2 encaged in the endohedral fullerene 15N@C60^{15}\mathrm{N}@{\mathrm{C}}_{60}15N@C60​. Density matrix tomography was applied to verify the degree of entanglement.
Electron spin resonance (ESR) experiments are used to assess the possibilities for processing quantum information in the electronic and nuclear spins of endohedral fullerenes. It is shown that ¹⁵N@C₆₀ can be used for universal two-qubit quantum computing. The first step in this scheme is to initialize the nuclear and electron spins that each store one qubit. This was achieved with a magnetic field of 8.6 T at 3 K, by applying resonant RF and microwave radiation. This dynamic nuclear polarization technique made it possible to show that the nuclear T₁ time of ¹⁵N@C����� is on the order of twelve hours at 4.2 K. The electronic T₂ is the limiting decoherence time for the system. At 3.7 K, this can be extended to 215 μs by using amorphous sulphur as the solvent. Pulse sequences are described that could perform all single-qubit gates to the two qubits independently, as well as CNOT gates. After these manipulations, the value of the qubits should be measured. Two techniques are demonstrated for this, by measuring the nuclear spin. Sc@C₈₂ could also be useful for quantum computation. By comparing ESR measurements with density functional theory calculations, it is shown how the orientation of a Sc@C₈₂ molecule in an applied magnetic field affects the molecule's Zeeman and hyperfine coupling. Hence the g- and A-tensors are written in the coordinate frame of the molecule. Pulsed ESR measurements show that the decoherence time at 20 K is 13 μs, which is 20 times longer than had been previously reported. Carbon nanotubes have been filled with endohedral fullerenes, forming 1D arrays that could lead to a scalable quantum computer. N@C₆₀ and Sc@C₈₂ have been used for this filling in various concentrations. ESR measurements of these samples are consistent with simulations of the dipolar coupling.
We propose a scheme to implement the two-qubit gates between the nuclear spins of the encapsulated atoms in endohedral fullerenes 15N@C60^{15}\mathrm{N}@{\mathrm{C}}_{60}15N@C60​ or 31P@C60^{31}\mathrm{P}@{\mathrm{C}}_{60}31P@C60​, within today's magnetic resonance techniques. Since there is no interaction between the nuclear spins, this scheme employs the electronic spins as medium and two swap operations are proposed to transfer the information between the nuclear spin 12\frac{1}{2}21​ and the electronic spin 32\frac{3}{2}23​, and between two electronic spins 32\frac{3}{2}23​. These two-qubit gates, along with the single-qubit rotation gates, compose a universal set of quantum gates in fullerene-based quantum computation.
Insight into many-body problems in quantum mechanics may be developed by solving simple models exactly using computational methods. The small size of endohedral-doped fullerene molecules allows the electronic states to be evaluated numerically using a spin model such as the Heisenberg Hamiltonian. The Lanczos algorithm is deployed to compute a few low-energy states of fullerene systems. Since the spin of the dopant electrons can be manipulated using external magnetic fields, the system can be used as a qubit. For sufficiently large couplings between the dopant and the fullerene, the qubit may relax by releasing energy into the carbon cage. The resulting oscillations of the qubit are found to include a high frequency component introduced when the spin accesses multiple states with different energies. The frequency and the amplitude of the qubit's oscillations also depend on the magnitude of external fields and the size of the coupling between the dopant and the fullerene.
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