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2 Putting Mechanics into Quantum Mechanics -- Cooling by Laser Irradiation

2 Putting Mechanics into Quantum Mechanics -- Cooling by Laser Irradiation

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7 Nanomechanics – Nanophotonics – Nanofluidics



information technology. What happens to the superposition as one goes to objects

of more and more atoms (see [7.26])? The most favored answer to this question

involves a phenomenon known as decoherence [7.27]. Crudely speaking, decoherence is a sort of leaking away of quantum behavior when a particle interacts with

its surroundings. Decoherence predicts, that the quantum-classical transition is not

really a matter of size, but of time. So larger objects, which generally have more

ways of interacting, decohere almost instantaneously. Even in a perfect vacuum,

particles will decohere through interactions with photons in the omnipresent cosmic

microwave background. The decoherence description shows that there is no abrupt

boundary, no critical size, at which quantum behavior switches to classical.

An alternative theory of quantum-classical transition suggests, that the “collapse”

of superposition, rather than being a gradual affair resulting from environmentinduced decoherence, is a rather abrupt event that is mediated by gravity [7.28,

7.29]. It is thought [7.29, 7.26] that the cost in gravitational potential energy in

keeping objects in a superposition becomes too great as objects get bigger, so that

the objects “go classical” on a definite timescale, which is estimated [7.29] to be

about a second for dust particles [7.26].

Assuming that quantum mechanics applies for mesoscale structures, the energy

of each resonator mode is given by E = hω(N + 1/2) where N = 0, 1, 2 . . . is the

occupation factor of the mechanical mode of the frequency ω. The quantum ground

state N = 0 has a zero-point energy of hω/2 and is described by a Gaussian wave



1

function of the width (x2 ) /2 = xSQL = h/(2mω). This quantity, known as the

standard quantum limit, is the root-mean-square amplitude of quantum fluctuations

of the resonator position [7.30]. The larger the zero-point fluctuations, the easier

they are to detect. For example, a radio-frequency (10–30 MHz) nanomechanical

resonator with a typical mass of ∼ 10−12 g has xSQL = 10−14 m, only a little

larger than the size of an atomic nucleus.

This xSQL value is readily detectable by today’s advanced methods (see

Sect. 7.1 and [7.15]). A much larger xSQL ≈ 10−10 m of a 1 μm long carbon

nanotube makes this device very attractive for displaying and exploring quantum

phenomena with mechanical systems. A crucial consideration for reaching the quantum limit of a mechanical mode is the thermal occupation factor Nth given by the

average energy

1

1

E = ω Nth = ω ( + ω/k T )

B

2 e

of a mechanical mode coupled to a thermal bath where Nth follows the Bose–

Einstein distribution. Figure 7.4 a displays the deviation from classical behavior

ω, Nth is less than 1 and the mode

that occurs at low temperatures. When kB T

becomes “frozen out,” which occurs for a 1 GHz resonator for T < 50 mK – a

regime well within standard dilution refrigeration [7.15]. For displacement sensing of nanoelectromechanical systems (NEMS) optical detection is complicated

dramatically by diffraction effects and transduction is performed from the mechanical to an electrical signal by making use of amplifiers such as quantum dots or



7.2



Putting Mechanics into Quantum Mechanics – Cooling by Laser Irradiation



321



Fig. 7.4 (a) Quantum limits. The occupation factor Nth (black curves) for various mechanical

resonator frequencies is a function of resonant frequency and temperature T. Shown in red is the

lifetime τN of a given number state for a 10 MHz resonator with a quality factor Q = 200,000

[7.31]. Also in red is the expected decoherence time τφ for a superposition of two coherent states in

that resonator displaced by 100 fm. (b) Detection techniques for nanomechanical displacements in

a nanoelectromechanical system (NEMS). Coupling of the NEMS to a mesoscopic detector such as

a quantum dot or a single-electron transistor. The current IDS through the detector is modulated by

the NEMS motion. (Reprinted with permission from [7.15]. © 2005 American Institute of Physics)



single-electron transistors (SET; see Fig. 7.4b). The resonator’s motion induces a

change in the charge on the gate electrode of the SET and the SET’s conductance

can be directly monitored, so that nanomechanical measurements only a factor

of about 6 from the quantum limit could be performed [7.31] with an occupation factor Nth = 58 of the mechanical mode. This demonstrates that the quantum



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7 Nanomechanics – Nanophotonics – Nanofluidics



ground state (Nth < 1) is within reach [7.15]. The generation and detection of the

uniquely quantum states of a small mechanical device, such as energy eigenstates

(so-called Fock states), superposition states, or entangled states, which are predicted

for temperatures up to even ∼ 20 K [7.32] are particularly interesting because the

mechanical structures may be considered “bare systems” [7.15]: There is no macroscopic quantum condensate to protect the device from excitation or decoherence

[7.15]. However, cooling of NEMS to low temperatures is less straightforward than

initially thought [7.15] and active cooling through controllable external interactions

such as laser cooling of a nanomechanical resonator mode to its motional ground

state has been proposed [7.33]. In fact, stimulated by theoretical work [7.34, 7.35],

laser cooling was demonstrated to reduce the temperature of micromirrors by more

than two orders of magnitude [7.36–38]. In addition, by sideband laser irradiation

of a silica microresonator (Fig. 7.5), cooling has been observed [7.24]. This cooling

is due to light absorption in a sideband with lower energy and subsequent emission

of higher-energy light.

By optical sideband cooling, mechanical resonators can be refrigerated to fewer

than 60 phonons and will soon be operating in the mechanical quantum regime.

There may be surprises waiting in the quantum behavior of these very large

(observable to the naked eye) systems [7.39].

Quantum-limited displacement sensitivities can also be achieved by making use

of a superconducting interference device (SQUID) which can detect flexing displacement of a bar down to about 10−13 m. This may correspond to a sensitivity

that is 36 times larger than the bar’s quantum zero-point displacement uncertainty

[7.40, 7.41].

For approaching the regime where quantum aspects are important, a coupling

of nanomechnical resonators is suggested [7.43] with quantum-controlled atomic

ensembles into an entangled Einstein–Podolsky–Rosen state.



Fig. 7.5 Resolved-sideband regime of a mesoscopic optomechanical oscillator. Scanning electron

microscope image of the silica microtoroidal optical cavity supporting both optical resonances and

radial breathing modes with a high quality factor Q = 30,000, held by a nanosized “needle” pillar.

An image of an intentionally broken cavity structure is also shown with a 500 nm diameter pillar

which reduces the coupling to the pillar and enables high Q factors. (Reprinted with permission

from [7.24]. © 2008 Nature Publishing Group)



7.3



Nanoadhesion: From Geckos to Materials



323



7.3 Nanoadhesion: From Geckos to Materials

Nanosized attachment structures enable some larger animals, such as geckos, or

small insects (see Fig. 7.6) to easily climb vertical walls and even walk on the ceiling. This is made possible by a hierarchical structure of fibrils that become smaller

toward the contact region of the feet with the surface and that attach the feet strongly

but reversibly to a variety of surfaces – smooth or rough, hydrophilic or hydrophobic, clean or containing contaminants. The surface is contacted by thousands of

200 nm long and 15 nm thick stiff keratin structures (elastic modulus E ≈ 1 GPa

[7.45]) called spatulae – thin fibers tipped with tapered plates – which form individual attachment points [7.46]. Such a structure may rely solely on van der Waals

forces [7.47] to stick to the surface because of the multiple attachment points and the

nanosized structure of the contacting elements. A water layer present on the majority

of real surfaces may enhance adhesion by capillarity (see [7.46]). This demonstrates

the close links between mechanics, chemistry, and physics when considering adhesion. Geckos can move on a vertical stone wall during heavy rain although van der

Waals interaction between two surfaces is already negligibly small at a separation of

a few nanometers. Thus, the first step in building up adhesive contact is to squeeze

out most of the water between the gecko’s toe pad and the stone wall. This is a

complex problem in elastohydrodynamics (see [7.45]).

During pull-off, the bond between the toe pad and the substrate is not broken

uniformly over the contact area but rather via crack propagation (or peeling) from

the periphery to the center in analogy with peeling adhesive tape (Fig. 7.7). The

normal component of the pull-off force of a tape is given by F⊥ = F sin θ =

γ B sin θ (1 − cos θ ), where θ is the peel angle, γ the adhesion energy per unit

area, and B the width of the film. The gecko adheres by applying muscle force that

keeps the angle θ between its legs and the substrate very small. This maximizes

the pull-off force which is important on rough and contaminated surfaces. The toe



Fig. 7.6 (a) Examples of natural fibrillar attachment structures of the foot pads of the beetle, fly,

spider, and gecko. They consist of a hierarchical arrangement of nanoscale fibrillar structures called

setae. The tips of the fibrils are terminated by flat plate-like structures called spatulae (circled)

[7.42]. (b) Example of a spatulated fibrillar array of the green anole lizard (Anolis carolinensis)

[7.44]. (Reprinted with permission from [7.42] (a) and [7.44] (b). © 2007 Materials Research

Society)



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7 Nanomechanics – Nanophotonics – Nanofluidics



Fig. 7.7 Peeling adhesive tape from a substrate. (a) The peel angle θ is small, the pull-off force

is large, while the opposite is true when the peel angle is large (b). (c) The gecko removes the

contact to the substrate by rolling its toes upward from the substrate. (Reprinted with permission

from [7.48]. © 2006 National Academy of Sciences USA)



pad-substrate bond can be quickly broken for fast motion by rolling or peeling

the toe, from the tip, off the substrate (Fig. 7.7c). It has been suggested that the

gecko keeps its toe pads clean for good adherence by scratching away solid particles

trapped on the toe pad surface [7.45].



7.3.1 Materials with Bioinspired Adhesion

The details of the mechanism for attachment and detachment of animal feet with

nanoscopic structures remain complex and difficult to reproduce artificially but several laboratories have designed biologically inspired artificial surfaces for enhanced

and removable adhesion. A gecko tape has been developed by transferring arrays

of carbon nanotubes (8 nm in diameter) on a polymer tape simulating the structure found on the foot of a gecko lizard. The gecko tape can support a sheer stress

(36 N/cm2 ) nearly four times higher than the gecko foot, can be used repeatedly, and

sticks to a variety of surfaces, including Teflon [7.49]. A biologically inspired adhesive, consisting of an array of nanofabricated polymer pillars coated with a synthetic

polymer that mimics the wet adhesive proteins found in mussel holdfasts, maintains

its adhesive performance for over a thousand contact cycles in both dry and wet

environments [7.50]. Tapes with sub-micrometer poly (glycerol sebacate acrylate)

(PGSA) pillars and a coating of oxidized dextran with aldehyde functionalities were

developed for bonding to wet tissues in medical application. When implanted into

rats, the coated tapes show enhanced adherence and cause minimal inflammation

[7.51]. Furthermore, bioinspired micropatterned surfaces with switchable adhesion

have been designed [7.52].



7.3.2 Climbing Robots and Spiderman Suit

Biologically inspired adhesives may also be employed for the design of vertically

climbing robots [7.53] or a Spiderman suit [7.54]. Whereas conventional robots

are vacuuming horizontal household floors, exploring the surface of Mars and

performing other tasks that humans find tedious or hazardous, robots with gecko



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