Single spin detection

Rugar, D., R. Budakian, H.J. Mamin, and B.W. Chui. 2004. Single spin detection by magnetic resonance force microscopy. Nature 430 329-332. 

Single spin detection by magnetic resonance force microscopy. 

Here, N is the number of qubit copies. To the scheme to work, this force must be comparable to the minimum force detectable by MRFM. For small polarization, the number of detectable qubits depends exponentially on p, just like in the liquid-state approach. However, for p 0.6 and above, there is a crossover from exponential to polynomial dependence ofnoap n l + p)/ l — p) (Figure 7.5). This is the main result of Ladd and co-workers proposal, for it means the system is scalable. Therefore, the usefulness of the scheme relies on the possibility to produce a large enough initial polarization, but there is no need of single spin detection and other difficulties present in the previous model. 

Single spin detection techniques solution for the sensitivity problem... 

In the previous section we have described some very ingenious proposals which, if implemented in practice, could lead to a large scale quantum information processor through NMR. It is important to emphasize that those proposals circumvent the scaling problem present in liquid-state NMR QIP experiments. However, whatever the sample architecture may be, it seems unavoidable the need to detect the NMR signal of very small spin concentrations. Ideally, single spin detection should be possible. Less than two decades ago, such a strict demand could sound hopeless conventional ESR needs a concentration of some... 

Figure 7.10 Single spin detection by MRFM. The result is from Rugar et al. (2004). The two plots correspond to different values of the external field. Changing the external field modifies the resonant slice, which in turn causes a shift in the peak. The average distance between spins in the sample is 300 A. Adapted with permission from [19].

As in the case of the single spin-echo detection, the multiple spin-echoes method attenuates magnetization components with short 72(5 ) values and the magnitude of the attenuation increases with increasing echo... 

As can be understood by looking at Fig. IX.2, only single spin operators correspond to directly detectable magnetization. So, in common NMR experiments, only terms like Ix, Iy, Kx, Ky correspond to an observable, whereas all other terms (IXKX, IxKy, lyKz, etc.) are not directly observable. 

The vector model cannot be interpreted in such a simple way in the case of a spin system with more than one nucleus. For weakly coupled spin systems, the single spin vector model may be applied for each nucleus, one after the other. Thus the coupling with the other nuclei can be incorporated into its precession frequency, since the definition of the weak coupling (J -C vM v,/1) means that the transitions of a nucleus only depend on the spin states of the other nuclei in the first order. The detected signal is the sum of the sine curves provided by the individual environment of the nuclei. 

The calculation method presented here also provides a possible extension of the single spin vector model. This extension is performed in two steps first to weakly coupled spin systems, then to strongly coupled ones. In the first case, the introduction of the well-known product basis functions and their coherences is sufficient while in the latter one the solution is not so trivial. The crucial point is the interpretation of the linear transformation between the basis functions and the eigenfunctions (or coherences) during the detection and exchange processes. These two processes can be described by the population changes of single quantum... 

Figure 12 Using the conventional delay d2 = 1/2/ results in false coherences relating the 1 spin to the sums or differences of the frequencies of the S spins, and intensity distortions. In the worst case this can result in an HMQC spectrum in which only coherences resulting from multiple S spin transitions are seen. Inverse detected HMQC Cl Rh NMR spectrum of [Rh6(CO)i5 P(C6H4F)3 ] left unconventional mixing time = 1 /(5/) gives single spin Rh transitions only, correlations appear at the correct Sju, ri t, conventional mixing time = 1 /(2/), gives multiple Rh spin transitions . Only ONE of these transitions occurs at a Rh chemical shift...

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