Saturday, September 19, 2009

Diamonds are a quantum nerds best friend

The past few years have seen significant advances in using NV (Nitrogen Vacancy) centres in diamond as qubits. A helpful review by Wrachtrup and Jelezko is here.
Recently, a group in Stuttgart reported produced a variety of two-particle and three-particle entangled states. They produced Bell states between the nuclear spins of two 13C nuclei associated with the NV centre. They also entangled two electron spin states with the two nuclear spin states to produced GHZ and W states, which have maximum three-particle entanglement.

The energy level structure is shown below.

It is interesting that the ground state of the NV centre is an electron spin triplet. Why?

Here is a possible simple argument to understand the essential physics behind the energy level structure and quantum numbers.
This is inspired by the figure below taken from a paper Jaime Merino, Ben Powell, and I wrote on a completely different topic, sodium cobaltate.

The NV centre has C3v symmetry and there are 4 electrons associated with it, one from each of the carbon atoms and one from the nitrogen atom.

A minimal model for the electronic structure is to take the three degenerate sp3 carbon orbitals and one nitrogen orbital at a lower energy, all directed towards the vacancy. A minimal Hamiltonian is a 3 site Hubbard model.
If t is positive and there are 4 electrons in the carbon orbitals (or t negative and there are 2 electrons) then the ground state is a spin triplet with spatial A symmetry. The blue lines represent spin triplet pairs.

The electronic state shown in the figure has a significant amount of entanglement. It is a resonating triplet bond state. But, this is not the entanglement that is created and manipulated in the experiment.

In passing I also mention that the singlet version of this figure was helpful to me for recent work Seth Olsen and I did in our recent papers on an effective Hamiltonian for flourescent protein chromophores and methine dyes.

I thank Professor Noel Hush for stimulating this post.

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