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Spin microscopy's heritage, achievements, and prospects
Achieving 3dimensional, indepth, atomicresolution biological microscopy of undenatured specimens is one of the oldest dreams of science, and for good reason: it unites the thrilling prospect of opening vast new scientific frontiers with cuttingedge technical challenges from every domain of mathematics, science, and engineering.
In a recent issue of PNAS, a team from IBM Research led by Dan Rugar and John Mamin has taken us a giant step closer to this goal (1) by using magnetic resonance force microscopy (MRFM) to obtain 3dimensional images of tobacco mosaic viruses having voxel resolution down to ≈4 nm. Our comments on the IBM experiment will be modeled on a 1946 letter from John von Neumann to Norbert Wiener (,2), in which von Neumann discusses, at considerable length, both the practical problem of achieving atomicresolution biological microscopy and the potential applications of this capability. Von Neumann's letter invites Wiener to consider whether atomicresolution biological microscopy might be achieved “by developments of which we can already foresee the character, the caliber, and the duration. And are the latter two not excessive and impractical?”
We adopt von Neumann's question as this commentary's focus, and we seek to describe paths by which mathematicians, scientists, and engineers—of almost every discipline—can contribute to, or benefit from, this centuriesold quest.
We begin by conceiving of spin microscopy in terms of communication: we regard sample spins as being modulated by Alice so as to create a signal force f(t) that is observed by Bob (Fig. 1).
We ask the natural question, how fast can Alice transmit information to Bob? This rate, called the channel capacity, is rigorously bounded by Claude Shannon's 1949 Capacity Theorem as
The meaning of these parameters and their values in the IBM experiments are as follows: Alice's rootmeansquare force signal is f_{sig} ≃ 10 aN, Bob's MRFM cantilever has mass m ≃ 0.26 ng, frequency ω_{0}/(2π) ≃ 2.9 kHz, force noise S_{f}^{1/2} ≃ 10 aN/
Inserting these IBM device parameters into Eq. 1, we compute a capacity bound of C ≲ 40 bits/s. This figureofmerit, and elaborations of it, will be the main focus of this commentary. Von Neumann and Wiener would recognize this approach as a Fermi calculation, and perhaps would be pleased that the methods of their colleague Enrico Fermi are now regarded as essential to design and systems engineering (5).
Multiple paths of inquiry depart from this Fermi calculation starting point. Communication theorists will recognize that a stronger capacity bound is obtained by specifying S_{f} and S_{q} individually, rather than constraining only their product S_{f} S_{q} as in Eq. 1. The resulting expression is more complicated than ,Eq. 1 (and is not given here) but the bound obtained is not much stronger: C ≲ 8.5 bits/s. This means that the IBM team has balanced force and measurement noise nearly optimally. Good.
Imaging researchers will appreciate that 8.5 bits/s is painfully slow, equivalent to transmitting a 90kB image file in 24 h. Together with inevitable realworld inefficiencies, this explains the lengthy 120h acquisition time of the IBM images (1). Slow imaging is a generic challenge in magnetic resonance, and an array of remediating techniques stand ready to be applied, including signal multiplexing, incorporation of ab initio information into modulation and deconvolution algorithms, and (very recently) sparse sampling. Researchers will not soon exhaust these possibilities.
It is good to acquire data faster, so let us now consider paths for boosting the raw channel capacity of Eq. 1.
Quantum information researchers will recognize that the noise product S_{f}S_{q} is subject to a fundamental (and rigorous) inequality S_{f}S_{q} ≥ ℏ^{2} (onesided) (equation 6.7 in ref. 6), which is called the standard quantum limit (SQL). Eq. 1 then implies the testmass capacity bound We see that if the noise in the IBM experiment were reduced to its quantum limit, such that (S_{f}S_{q})^{1/2} was reduced from ≈3.0 × 10^{4} ℏ to ≈1ℏ, the information flow would increase by ≈170, and the imaging time would drop from 120 h to ≈40 min, which is comparable to traditional imaging methods.
Again, our Fermi calculation illuminates multiple paths of inquiry. Condensed matter physicists will recognize the need to understand the force noise S_{f}. Sensor scientists will perceive an opportunity to reduce the measurement noise S_{q}. Nanotechnologists will conceive of lowermass, sharpertipped MRFM cantilevers. Spin physicists and chemists will seek to augment signal strength via dynamic polarization. Biologists will appreciate that sample preparation is an immensely challenging and creative scientific discipline in its own right. Again, researchers will not soon exhaust these possibilities.
In the early days of MRFM, it was foreseen that progress in these areas eventually would arrive at atomicresolution spin microscopy. For example, a 1992 MRFM theory article (7) analyzed a device having (per ,Eq. 2) a singleproton quantum capacity bound of ≈3,300 bits/s. Nowadays, this early MRFM vision has not altered much … except that the MRFM community has developed a sober appreciation of the immense challenges of approaching quantum limits, in particular, in demonstrating the requisite systemslevel innovation and integration. The IBM team has consistently led the world in innovative MRFM systems integration, achieving numerous important milestones such as the first MRFM experiment (,8), the first detection of statistical polarization by MRFM (,9), the first detection of gradient suppression of spin diffusion (,10), the first MRFM detection and imaging of a single (electron) spin (,11), and now the first highresolution MRFM biological images (,1).
Let us consider one final Fermi calculation, with a view toward illuminating some of the paths that lie ahead. We notice that an MRFM cantilever and a spinj particle in a magnetic field both have uniform energylevel spacing, so that an MRFM cantilever can be regarded as a largej spin. This simple change of variables induces an equivalence f_{sig}/(mω_{0}ℏ)^{1/2} ↔
Hooke's centuriesold vision may become a twentyfirst century reality.
Now we adopt a point of view that would have seemed fantastical to von Neumann and Wiener's generation: we regard Eq. 3 as a literal description of a spin microscope. Suppose, for example, that Bob observes a single electron spin that is acted on at a distance of (say) 25 nm by the 85 pT (rms) field of Alice's single proton. Then, ,Eq. 3 tells us that the Alice–Bob singlespin channel has a spin capacity bound of ≈5.0 bits/s.
What was a fantastical dream in the twentieth century is becoming a concrete reality in the twentyfirst century, thanks to recent work on diamondspin imaging (13–,16) that has greatly expanded our conception of the challenges and opportunities of quantum spin microscopy (,17).
Now for the third time our Fermi calculation (Eq. 3) illuminates multiple paths of inquiry. To cite just one example: the obvious parameter to improve in ,Eq. 3 is the quantum number j_{B}. Ought we to begin conceiving of spin microscopes having resonant ferromagnetic receivers with j_{B} ≃ 10^{6}, for a further 1,000× gain in the capacity bound?
Such possibilities refocus our attention on the key question that von Neumann asked Wiener: Can atomicresolution microscopy be achieved by developments of which we can already foresee the character, the caliber, and the duration? And are the latter two not excessive and impractical?
The caliber (meaning “size”) of the effort is easiest to foresee: the IBM device is comparable in complexity and sophistication to a small earthorbiting satellite—or to a laser printer. These technologies required a considerable investment in talent and resources to become practical realities, and achieving atomicresolution spin imaging likely will prove similar. As for the duration of the effort, it likely will be mainly determined by the resources and talent invested in the effort (as with most technologies).
The character of the effort likely will be largely determined by whether quantum theorists and systems engineers can keep up with the experimental physicists. New methods originating in quantum information and simulation theory, in condensed matter physics, and ab initio quantum chemistry are rapidly accelerating the pace and retiring the risks of developing not only quantum spin microscopes, but all technologies that press against quantum limits.
Medical researchers (the tribe to which the author belongs) have aspirations too. We are tantalized by a vision of medical practice becoming fully curative and regenerative. We are frustrated—as the generation of von Neumann and Wiener was frustrated—by the limitations of our present tools. We desire—as Feynman famously desired—to “just look at the thing” (18). And we plan—as every previous generation has planned—for these aspirations to become realities.
Acknowledgments
This work is dedicated to the families of the Ceremony in Honor of Wounded Marines, 12 May 2006, Marine Corps Barracks, Washington, DC.
Footnotes
 ^{1}Email: sidles{at}u.washington.edu

Author contributions: J.A.S. wrote the paper.

The author declares no conflict of interest.

See companion article on page 1313 in issue 5 of volume 106.
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