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Ultimate quantum limits to sensitivity of nano-oscillator based "artificial noses"

par Daniel Braun - 13 juin 2011

Research on nano-mechanical resonators has very rapidly advanced over the last few years, offering the perspective of a completely new type of mass-spectrometry, one of the most important analysis tools of modern chemistry, biology, and environmental sciences. Mass-spectrometry enables the identification of molecules through the precise measurement of their mass.

The principle of operation of the new devices is very simple : A single adsorbed molecule on the nano-mechanical resonator, made example from a carbon nano-tube, slightly lowers the resonance frequency of the resonator, which is measured by an electronic circuit.

What is the ultimate sensitivity of these "artificial noses" ? In 2004, experiments reached a level of sensitivity of femto-grams, then atto-grams, and two years later already zepto-grams. By now sensitivities below the single atom level have been demonstrated by using resonators based on carbon nano-tubes, and the race for ever smaller masses is open.

In an article that will appear in Europhysics Letters (EPL), Daniel Braun from the Laboratoire de Physique Théorique has now shown that the answer to the question of ultimate sensitivity might lie in the use of specially engineered quantum states. Preparing nano-mechanical oscillators in a precise quantum state is a "hot" research topic. In 2010 researchers at the University of California succeeded for the first time in cooling down a piezo-electric resonator (a tiny version of the kind of resonator found in any quartz watch) to its quantum mechanical ground state, and even managed to entangle it in a controlled way with a superconducting circuit.

The work by Daniel Braun shows that for sufficiently long measurement times and given maximal energy, the quantum state that will allow the most sensitive mass measurements is a type of "Schroedinger-cat" state, where the groundstate is superposed with the highest allowed excited state. The smallest detectable mass scales then as the mass of the oscillator itself divided by the number of excitations in the oscillator.

PostScript - 462.9 ko

Unfortunately, "Schroedinger-cat" states consisting of superpositions of two largely different states are notoriously unstable : Omnipresent decoherence due to coupling to the environment reduces them very rapidly to mixtures of classical states. However, even with the existing classical setups, where the oscillator is driven with a frequency close to resonance, it should be possible in principle to reach sensitivities of the order of a thousandth of the mass of a single electron - that is if all experimental imperfections, finite temperature effects, and even damping of the resonator can be neglected. Such highly idealized situations are unlikely to be achieved in actual experiments, but the analysis will serve as an important benchmark. Based on the fundamental quantum Cramér-Rao bound, which can be seen as a generalization of Heisenberg’s uncertainty principle, the sensitivity bounds derived in the work by Daniel Braun provide an ultimate goal that might be reached in principle, but can never be surpassed if measurement time and maximum energy are fixed, no matter what measurements and data-analysis are used.

But further gains of sensitivity can be reached by increasing the average energy of the resonator or integration time, or decreasing the mass of the resonator. If two more orders of magnitude can be gained, the ultimate sensitivity becomes comparable to the relativistic mass equivalent of one electron volt - a typical energy change under the absorption of a single photon of visible light, or the creation of a chemical bond. The new and gentle way of weighing molecules by adsorbing them on a nano-oscillator has the additional advantage of leaving the molecule intact, whereas the ionization step in traditional mass-spectrometers often breaks the molecule apart, thus complicating the analysis. A whole new level of mass-spectroscopy might therefore become possible, where not only the chemical composition, but also information about the structure of the molecule is revealed.

Given the dramatic development of the field, with about ten orders of magnitude in sensitivity gained in just seven years, it appears quite possible that we will see this kind of sensitivity at the chemical bond level a few years down the road, not to speak of numerous applications as artificial noses in every day life : from smart-phone apps for world-wide distributed sensing the quality of air, over explosives detectors, to cancer-sniffing scanners. And their sensitivities will all be limited by the fundamental quantum mechanical bound to be found in the article to appear in EPL.