## Bloch Sphere Spin Animations

These animations depict an ensemble of uncoupled spins as they undergo various transition excitations in the rotating frame. Spin 1/2 nuclei (or any two-level system) act like a spinning top in a gravitational field. In NMR, echo formation can be easily visualized using this simple simulation. Adding dipolar coupling causes additional dephasing, which we can simulate using density matrix formalism. To request an animation for a particular spin manipulation please contact us.

### Optically Pumped NMR Techniques

Dynamic Nuclear Polarization can be achieved by irradiating a sample with circularly polarized light of a particular frequency. This frequency can be tuned to correspond to the energy of a band-gap transition, thereby exciting a polarized electron-hole pair. Due to the hyper-fine interaction between the spherical orbital electrons and the nuclei, this dynamic polarization can be transferred to the nuclei. Since nuclei typically have longer relaxation times than electrons or electron-hole lifetimes, this technique enables faster nuclear polarization, leading to a better Signal to Noise ratio for NMR.

### Skyrmion Spin Textures & The Quantum Hall Effect

At Landau level filling factor v=1, all electrons are fully polarized (at T=0) and all electron cyclotron orbits completely tile a 2D surface with no overlap. At v>1, the tendency for wavefunction overlap is countered by the Pauli Exclusion Principle (Exchange part of the Coulomb interaction) which requires antisymmetrization. This means that one electron spin is forced to reverse its polarization relative to all the other spins. But in fact, not just one spin is flipped in the final formation! Nature has found a way to lower the entire energy of the system by allowing nearby electron spins topartially flip forming a gradual reversal over many spins. This entire spin-texture is called a Skyrmion and can be considered a single unit with many quasi-particle properties analogous to a 4-dimensional field theory for nucleonic matter.

### Quantum Decoherence & Dipolar Order

Quantum Information Processing and in particular Quantum Computing has been pushed to the forefront of scientific research in the last decade as a result to the clever quantum Fourier transform algorithms conceived by Schor. Spins in semi-conductors is a natural candidate for quantum bits (qubits) because of the already existing semi-conductor industry infrastructure. An important benchmark to study is the length of time that quibits can maintain a predetermined evolution without loss of necessary quantum characteristics. The process is called decoherence and can be studied in NMR using bulk materials (many qubits–as one would require for a real quantum computer). Unfortunately, the theoretical problem of many coupled spins (qubits) has not been solved and no valid approximation can be made for clean systems without loss of dynamical quantum subspaces. Experimentally, we see a variety of phenomenology that would suggest quantum order beyond the standard model of NMR.