device physics: no-nuisance noise
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2005 Nature Publishing Group
NEWS & VIEWS NATURE|Vol 437|13 October 2005
(mostly incoherent) switching events and acorresponding loss of information. Butbetween these two information minima, theswitchings acquire maximum coherence withrespect to the applied signal, and an infor-mation maximum occurs. Thus we have anintuitive result from otherwise counter-intuitive behaviour that applying noise canbe helpful.
The result3 conclusively demonstrates stochastic resonance in a nanomechanicaloscillator at megahertz frequencies. But its sig-nificance does not end there. A basic criterionfor the creation of a quantum harmonic oscil-lator is that the energy hf of the oscillator(where h is Plancks constant and f the oscilla-tion frequency) must be larger than the broad-ening of the oscillators energy spectrum thatresults from thermal effects. This energyspread is given by kBT, where kB is Boltzmannsconstant and T is the temperature. At a tem-perature of 48 mK, for example, an oscillationfrequency of 1 GHz ensures that this conditionis met. Thus, the demonstration of stochasticresonance in the megahertz range paves theway for exploring the phenomenon in relatedstructures recently constructed by the samegroup5,6 that have higher, quantum-regimefrequencies.
Specifically, stochastic resonance might be used to enhance and control a quantum-mechanical signal in a nanomechanical oscillator to achieve coherent control ofoscillations between two quantum energy levels, for example. The ramifications of aquantum stochastic resonance effect, and itspossible relevance to low-temperature macro-scopic quantum tunnelling, are fascinating.
Stochastic resonance1,2 encapsulates the sexynotion that moderate (and, ideally, carefullycontrolled) levels of noise in a nonlineardynamical system can actually enhance theinformation throughput and so improvethe sensing and processing of otherwise un-detectable signals. Originally postulated as amechanism to explain how ice ages occur, the effect has since been demonstrated in aplethora of laboratory experiments, and hasalso been proposed to be responsible for theway in which biological sensing mechanismsfunction to take advantage of inherent back-ground noise. Writing on page 995 of thisissue3, Robert Badzey and Pritiraj Mohantydemonstrate the effect in a doubly clampedmechanical beam of nanometre size. But thisis more than just another stochastic resonancedemo: the authors device (besides belongingto the buzzword class nano) also bestrides themurky gap between classical and quantumphysics.
Badzey and Mohantys nanomechanicalbeam, 8 m200 nm300 nm in size, ismade of crystalline silicon of high purity,clamped at either end. When small-amplituderadiofrequency excitations are applied to it,the beam behaves like a damped, driven harmonic oscillator, showing a standard,lorentzian shape (that is, peaked at a resonantfrequency) to its responsepower spectrum.But when the forcing amplitude exceeds a critical value, determined by (among otherthings) the amount of power dissipated as heatand the natural frequency at which the beamresonates, its response becomes nonlinear the beam buckles.
This is not a new phenomenon: the conceptof buckling dates back to the eighteenth cen-tury, when Leonhard Euler developed the par-tial differential equations that describe elasticinstability. This Euler instability dictates thata slender elastic object, clamped at either endand initially in stable equilibrium, will movetransversely if subjected to a longitudinal com-pressive force. If this force is increased beyonda critical value, the object will undergo a transition to an unstable equilibrium point.(Ref. 4 provides a simple derivation of this critical force.)
In Badzey and Mohantys system3, the com-pressive force comes from the application of atransverse driving force that changes thebeams length, making it longer than the dis-tance between its two supports. When thebeam vibrates from side to side, it is subjected
to an additional compressive force from theclamping pads as it passes through equilib-rium. If the driving force is large enough, thebeam responds nonlinearly and acquires twodifferent vibrational modes at a single fre-quency near resonance. Crucially, these buck-led modes are not static, but dynamic, and areunderpinned by a bistable potential-energyfunction; that is, one consisting of two stablestates, or wells, separated by an energy thresh-old. The bistable configuration togetherwith an applied periodic signal whose ampli-tude is smaller than the threshold is a basiccondition for stochastic resonance.
Badzey and Mohanty apply noise to theirsystem and compute a signal-to-noise ratio atthe applied signal frequency for a series ofresponsepower spectra, each taken at a dif-ferent noise power. The resulting curve revealsa maximum signal-to-noise ratio at a criticalnoise power. This is because, when there is toolittle noise, it fails to lift the system over thethreshold between the two states: the systemcannot switch between them, and so there isno flow of information (assumed to occur inthe switching events between wells). Con-versely, too much noise leads to a surfeit of
Figure 1 | Hang in there. A scanning electron micrograph of a set of suspended silicon nanomechanicalbeams with electrostatic control gates. Each beam can be made to move between two buckled states (0 or 1) by applying a field to its control gates. Stochastic resonance could allow enhancedcontrol in switching between the two discrete states, and use of these nonlinear states asnanomechanical memory cells.
No-nuisance noise Adi R. Bulsara
Silence is golden is a maxim of limited applicability where stochasticresonance holds sway. The effect uses noise to boost signal output in certainsystems and has just been seen in oscillators on a very small scale.
13.10 News & Views 957 MH 7/10/05 5:30 PM Page 962
Nature Publishing Group 2005
2005 Nature Publishing Group
NATURE|Vol 437|13 October 2005 NEWS & VIEWS
50 YEARS AGOIn the leading article in Natureof August 20 on EducationalProblems of the ColonialTerritories, it is stated that only some 450 scientists are at present engaged in Colonialresearch Most British scientificworkers are superannuated atthe age of approximately sixty-five. Many of them are capable of another ten years of research,and a moderate amount ofteaching. Some, at least, wouldbe happy to work in a Colonialuniversity or research institute.The necessary qualifications are the capacities to work in atropical or subtropical climate,and to form friendships with non-Europeans I think that thepresence in a Colonial universityof even two or three Fellows ofthe Royal Society carrying outfundamental research withAfrican or Asian colleagueswould help the local populationto generate its own scientificculture. J. B. S. HaldaneFrom Nature 15 October 1955.
100 YEARS AGOThe Citizen, a Study of theIndividual and the Government Prof. Shaler, who is professor ofgeology at Harvard, has setbefore himself the practical andunambitious task of instructingthe youth of the United States inthe first principles of citizenship.In this he has succeeded; hiswork is interesting, suggestiveand extremely sensible Afavourable specimen of his modeof argument may be found in thediscussion of womans suffrage.There is no reference to thevarious views held by thinkersfrom Plato downwards; butprobably Prof. Shalers one-pageargument is quite sufficient, thatwomen, owing to their usuallysecluded lives, are not fitted inthe same way as men to formjudgments on political questions,but that, after all, if a majority of women should desire to vote, it would probably be best to give them the franchise, for the reason that it is mostundesirable to have anyconsiderable body of the people in a discontented state.From Nature 12 October 1905. 50
They could pave the way to experiments in theas yet somewhat esoteric field of quantummeasurement and control. For unsatisfiedsceptics, Badzey and Mohanty have also devel-oped a system of suspended nanomechanicalbeams made of silicon, each of which can be forced electrostatically to switch between its two stable states (Fig. 1). With stochastic resonance allowing enhanced control oversuch switching, these nonlinear states mayeventually be useful as nanomechanical memory cells.
Stochastic resonance, although difficult toimplement in practice, has always been anintriguing option for harnessing the back-ground noise in certain systems. But thehubris of the 1990s was followed by a dearth ofresults to confirm that the mechanism under-lies natural neurophysiological functions, anda general paucity of devices that were readilytunable to take advantage of noise. These factors, together with the witches brew offunding vicissitudes and some questionablepublications, led to a waning of interest. Yetwork such as that of Badzey and Mohanty3shows that the effect can be invoked in a noisy,nonlinear dynamic system under appropriateoperating conditions, and that it can also beexploited in carefully crafted applications. The
effect has also recently been used in biomedi-cine7 and in the amplification of electric fieldsignals in carbon nanotube transistors8. Theseachievements, and the demonstration thatbackground electrical noise is involved in thehunting frenzy of the paddlefish Polyodonspathula as it preys on swarms of the water-fleaDaphnia9,10, indicate that this effect is morethan just a laboratory curiosity. Adi R. Bulsara is at the Space and Naval WarfareSystems Center, 53560 Hull Street, San Diego,California 92152-5001, USA, and is a visitingscientist at the US Office of Naval ResearchGlobal, London, U