Decoherence and measurement in NMR It seems that the Bloch equations, or a suitable generalization thereof, are enough to phenomenologically model the measurement process in NMR.  Has anyone attempted a fully quantum mechanical model of the NMR spin system and measurement coil together?  
It seems to me that these coils are intentionally of low quality to ensure no back-action (more phenomenology, so far as I can tell) on the spin system.  But perhaps one can engineer more efficient control or parameter estimation strategies with high quality coils and an accurate quantum mechanical model of the measurement interaction, no?
 A: A generic model of a spin coupled to an oscillator is the Jaynes-Cummings model, for which a full-text arxiv search finds 1820 "Jaynes–Cummings" preprints (ouch!).  So there is a lot of literature out there.
As it happens, inductive circuit oscillators work worse as one makes them smaller-and-smaller, but mechanical oscillators work better-and-better, thus micromechanical systems are well-suited to studying the dynamics of measurement and noise at the classical-quantum boundary, which I take to be the focus of the query.
For an experimental description of single-spin detection via a mechanical detector, see Rugar, Budakian, Mamin, and Chui "Single spin detection by magnetic resonance force microscopy" (Nature 2004), and for a POVM-style quantum analysis of the (noisy) detection process of this experiment, see our UW QSE Group's "Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems" (NJP 2009).   
For a microscopy-centric look into the future see the PNAS survey Spin microscopy's heritage, achievements, and prospects.
Because Jaynes-Cummings dynamics appears in so many guises, it would be a very considerable undertaking to provide a comprehensive literature review.
If we focus on magnetic resonance imaging and spectroscopy, and adopt Shannon channel capacity as a natural figure of merit, then it is straightforward to compute the quantum limits to this channel capacity (slide from a recent talk):

(PDF file)
It is a remarkable fact that over the past 65 years, single-spin magnetic resonance channel capacity has doubled approximately once per year, and there is quantum head-room for approximately 27 more such capacity doublings.
Thus, if one is interested to press against quantum limits to speed and resolution in magnetic resonance imaging and spectroscopy, there is ample of work to be done, and plenty of scope for further improvements.
A: Liquid state or solid state NMR? In the liquid state NMR you can probably model the measurement process and apparatus as a weak measurement to incorporate the effect of the measuring device (say a quantum system with bosonic degrees of freedom). Here is a related paper by Lloyd and Slotine: 
Quantum feedback with weak measurements
which is rather general but is definitely geared towards NMR physics. Despite that, I don't think there is a lot of room for maneuvering with this concept in the liquid state NMR. In solid state NMR (or even quantum dots), one deals with a single copy of the system and the back-action has a more significant effect. As for the high quality coil, superconducting loops are now used as measurement devices for the B field —macroscopic but very quantum systems (similar to a harmonic oscillator but also different). So I'd say the answer is a cautious "yes". The problem is from a practical point of view: there are other sources of noise in control and evolution of the NMR-like spin systems that would make this a far to reach goal.
Sorry, I couldn't leave a comment so I left an answer. 
