E
verything moves! In a world dominated by electronic
devices and instruments it is easy to forget that all
measurements involve motion, whether it be the motion of
electrons through a transistor, Cooper pairs or quasiparti-
cles through a superconducting quantum interference de-
vice (SQUID), photons through an optical interferome-
ter—or the simple displacement of a mechanical element.
Nanoscience today is driving a resurgence of interest in
mechanical devices, which have long been used as front
ends for sensitive force detectors. Among prominent his-
torical examples are Coulomb’s mechanical torsion bal-
ance, which allowed him in 1785 to establish the inverse-
square force law of electric charges, and Cavendish’s
mechanical instrument that allowed him in 1798 to meas-
ure the gravitational force between two lead spheres.
Today, micro- and nanoelectromechanical systems
(MEMS and NEMS) are widely employed in ways similar
to those early force detectors, yet with vastly greater force
and mass sensitivity—now pushing into the realm of
zeptonewtons (10
⊗21
N) and zeptograms (10
⊗21
g). These ul-
traminiature sensors also can provide spatial resolution at
the atomic scale and vibrate at frequencies in the giga-
hertz range.
1
Among the breadth of applications that have
become possible are measurements of forces between in-
dividual biomolecules,
2
forces arising from magnetic reso-
nance of single spins,
3
and perturbations that arise from
mass fluctuations involving single atoms and molecules.
4
The patterning of mechanical structures with nanometer-
scale features is now commonplace; figure 1 and the cover
display examples of current devices.
The technological future for small mechanical devices
clearly seems bright, yet some of the most intriguing ap-
plications of NEMS remain squarely within the realm of
fundamental research. Although the sensors for the appli-
cations mentioned above are governed by classical physics,
the imprint of quantum phenomena upon them can now
be readily seen in the laboratory. For example, the Casimir
effect, arising from the zero-point fluctuations of the elec-
tromagnetic vacuum, can drive certain small mechanical
devices with a force of hundreds of piconewtons and pro-
duce discernible motion in the devices.
5
But it is now pos-
sible, and perhaps even more intriguing, to consider the
intrinsic quantum fluctuations—those that belong to the
mechanical device itself. The continual progress in shrink-
ing devices, and the profound increases in sensitivity
achieved to read out those devices, now bring us to the
realm of quantum mechanical systems.
The quantum realm
What conditions are required to observe the quantum prop-
erties of a mechanical structure, and what can we learn
when we encounter them? Such questions have received
considerable attention from the community pursuing grav-
itational-wave detection: For more than 25 years, that com-
munity has understood that the quantum properties of me-
chanical detectors will impose ultimate limits on their force
sensitivity.
6,7
Through heroic and sustained efforts, the
Laser Interferometer Gravitational Wave Observatory
(LIGO) with a 10-kg test mass, and cryogenic acoustic de-
tectors with test masses as large as 1000 kg, currently
achieve displacement sensitivities only a factor of about 30
from the limits set by the uncertainty principle.
But the quantum-engineering considerations for me-
chanical detectors are not exclusive to the realm of gravi-
tational-wave physics. In the introduction to their pio-
neering book on quantum measurement, Vladimir
Braginsky and Farid Khalili envisage an era when quan-
tum considerations become central to much of commercial
engineering.
7
Today, we are approaching that time—
advances in the sensitivity of force detection for new types
of scanning force microscopy point to an era when me-
chanical engineers will have to include \ among their list
of standard engineering constants.
Several laboratories worldwide are pursuing mechan-
ical detection of single nuclear spins. That goal is espe-
cially compelling in light of the recent success of Dan
Rugar and colleagues at IBM in detecting a single electron
spin with a MEMS device (see figure 1b and P
HYSICS
TODAY, October 2004, page 22).
3
However, nuclear spins
generate mechanical forces of about 10
⊗21
N, more than
1000 times smaller than the forces from single electron
spins. One ultimate application of this technique, struc-
tural imaging of individual proteins, will involve millions
of bits of data and require measurements to be carried out
not on the current time scale of hours, but over microsec-
onds. Detecting such small forces within an appropriate
measurement time will necessitate new quantum meas-
urement schemes at high frequencies, a significant chal-
lenge. Yet the payoff, originally envisaged by John Sidles,
will be proportionately immense: three-dimensional,
chemically specific atomic imaging of individual macro-
molecules.
8
The direct study of quantum mechanics in micron- and
submicron-scale mechanical structures is every bit as at-
tractive as the actual applications of MEMS and NEMS.
9
With resonant frequencies from kilohertz to gigahertz, low
36 July 2005 Physics Today
© 2005 American Institute of Physics, S-0031-9228-0507-010-9
Keith Schwab
is a senior physicist at the National Security
Agency’s Laboratory for Physical Sciences in College Park,
Maryland.
Michael Roukes
is Director of the Kavli Nanoscience
Institute and is a professor of physics, applied physics, and bio-
engineering at the California Institute of Technology in Pasadena.
Nanoelectromechanical structures are starting to approach the ultimate quantum
mechanical limits for detecting and exciting motion at the nanoscale. Nonclassical states of
a mechanical resonator are also on the horizon.
Keith C. Schwab and Michael L. Roukes
Putting Mechanics into
Quantum Mechanics
dissipation, and small masses (10
⊗15
–10
⊗17
kg), these devices
are well suited to such explorations. Their dimensions not
only make them susceptible to local forces, but also make it
possible to integrate and tightly couple them to a variety of
interesting electronic structures, such as solid-state two-
level systems (quantum bits, or qubits), that exhibit quan-
tum mechanical coherence. In fact, the most-studied sys-
tems, nanoresonators coupled to various superconducting
qubits, are closely analogous to cavity quantum electrody-
namics, although they are realized in a very different pa-
rameter space.
Quantized nanomechanical resonators
The classical and quantum descriptions of a mechanical res-
onator are very similar to those of the electromagnetic field
in a dielectric cavity: The position- and time- dependent me-
chanical displacement u(r,t) is the dynamical variable anal-
ogous to the vector potential A(r, t). In each case, a wave
equation constrained by boundary conditions gives rise to a
spectrum of discrete modes. For sufficiently low excitation
amplitudes, for which nonlinearities can be ignored, the en-
ergy of each mode is quadratic in both the displacement and
momentum, and the system can be described as essentially
independent simple harmonic oscillators.
Spatially extended mechanical devices, such as those
in figure 1, possess a total of 3A modes of oscillation, where
A is the number of atoms in the structure. Knowing the
amplitude and phase of all the mechanical modes is equiv-
alent to having complete knowledge of the position and mo-
mentum of every atom in the device. Continuum mechan-
ics, with bulk parameters such as density and Young’s
modulus, provides an excellent description of the mode
structure and the classical dynamics, because the wave-
lengths (100 nm–10 mm) of the lowest-lying vibrational
modes are long compared to the interatomic spacing.
It is natural to make the distinction between nano-
mechanical modes and phonons: The former are low-
frequency, long-wavelength modes strongly affected by the
boundary conditions of the nanodevice, whereas the latter
are vibrational modes with wavelengths much smaller
than typical device dimensions. Phonons are relatively un-
affected by the geometry of the resonator and, except in
devices such as nanotubes that approach atomic dimen-
sions, are essentially identical in nature to phonons in an
infinite medium.
It is an assumption that quantum mechanics should
even apply for such a large, distributed mechanical struc-
ture. Setting that concern aside for the moment, one can
follow the standard quantum mechanical protocol to es-
tablish that the energy of each mode is quantized:
E ⊂ \w(N ⊕
1
/2), where N ⊂ 0, 1, 2, . . . is the occupation fac-
tor of the mechanical mode of angular frequency w. The
http://www.physicstoday.org
July 2005 Physics Today 37
2mm
a
c
e
b
d
f
Source Drain
Gate
W
dz
Figure 1. Nanoelectro-
mechanical devices.
(a) A 20-MHz nanome-
chanical resonator ca-
pacitively coupled to a
single-electron transistor
(Keith Schwab, Labora-
tory for Physical Sci-
ences).
11
(b) An ultrasen-
sitive magnetic force
detector that has been
used to detect a single
electron spin (Dan
Rugar, IBM).
3
(c) A tor-
sional resonator used to
study Casimir forces and
look for possible correc-
tions to Newtonian grav-
itation at short length
scales (Ricardo Decca,
Indiana University–
Purdue University Indi-
anapolis). (d) A paramet-
ric radio-frequency me-
chanical amplifier that
provides a thousandfold
boost of signal displace-
ments at 17 MHz
(Michael Roukes, Cal-
tech). (e) A 116-MHz
nanomechanical res-
onator coupled to a
single-electron transistor
(Andrew Cleland, Uni-
versity of California,
Santa Barbara).
10
(f) A tunable carbon
nanotube resonator op-
erating at 3–300 MHz
(Paul McEuen, Cornell
University).
14
quantum ground state, N ⊂ 0, has a zero-point energy of
\w/2 and is described by a Gaussian wavefunction of width
∀x
2
¬
1/2
⊂ Dx
SQL
⊂
=
\/(2mw). This quantity, known as the
standard quantum limit, is the root mean square ampli-
tude of quantum fluctuations of the resonator position.
7
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 around
10
⊗15
kg, has Dx
SQL
⊂ 10
⊗14
m, some 10
5
–10
6
times larger than
Dx
SQL
for the macroscopic test masses in the gravitational-
wave detectors. Although 10
⊗14
m represents a distance
only a little larger than the size of an atomic nucleus, it is
readily detectable by today’s advanced methods, such as
those described below. At the other extreme, a carbon
nanotube 1 mm long has Dx
SQL
10
⊗10
m, about the size of
a small atom. That relatively large value, although small
by absolute standards, makes nanotubes and nanowires
very attractive for displaying and exploring quantum phe-
nomena with mechanical systems.
A crucial consideration for reaching the quantum limit
of a mechanical mode is the thermal occupation factor N
th
,
set by the mode frequency w and the device temperature
T. The average fluctuating energy of an individual me-
chanical mode coupled to a thermal bath is expected to be
where N
th
follows the Bose–Einstein distribution. For high
temperatures this expression reduces to the classical
equipartition of energy: Each mode carries k
B
T of energy.
Figure 2a displays the deviation from classical behavior
that occurs at low temperatures: When k
B
T \w, N
th
is
less than 1 and the mode becomes “frozen out.” For a
1-GHz resonator, this freeze-out occurs for T < 50 mK—a
regime well within the range of standard dilution refrig-
erators employed in low-temperature laboratories. Further-
more, a 1-GHz device can be readily shielded from parasitic
external driving forces. Nanomechanical resonators with
a fundamental flexural resonance exceeding 1 GHz have
been demonstrated by one of us (Roukes) at Caltech,
1
al-
though position-detection
schemes with the band-
width and sensitivity to
measure the tiny ampli-
tude of the zero-point fluc-
tuations are still under
development.
Fluctuations, both
thermal and quantum, are
of great practical and fun-
damental importance:
They set ultimate limits
for sensitive force detec-
tion and for the coherence
time of quantum states.
These limits are deter-
mined by the nanores-
onator quality factor Q,
which parameterizes the
coupling strength to the
thermal bath. Currently,
all atomic-force microscopes
and experiments are in the
high-temperature limit:
k
B
T \w and ∀E¬k
B
T
per mode. For an acoustic-
frequency mechanical res-
onator typically found in
an atomic-force microscope setup, with a resonant fre-
quency around 5 kHz, a mass of 10
⊗12
kg, and a quality
factor Q on the order of 10
4
, one finds at room temperature
that N
th
⊂ 10
9
and the rms displacement fluctuations,
=
∀x
th
2
¬⊂10
⊗9
m, are more than 10
4
times larger than Dx
SQL
for this device. Thermal fluctuations limit the force sensi-
tivity to 240 aN/Hz
1/2
(where 1 aN ⊂ 10
⊗18
N). By cooling a
very thin and compliant low-frequency cantilever to near
200 mK, the IBM group has been able to reduce the fluc-
tuations to 6 × 10
⊗13
m and achieve a record force sensi-
tivity of 0.8 aN/Hz
1/2
.
Despite the close analogy between the quantization of
the motion of an extended mechanical device and the quan-
tization of the electromagnetic field in a cavity, some im-
portant fundamental differences exist. The total zero-point
energy in a mechanical system is finite because the num-
ber of mechanical degrees of freedom is finite. Also, even
for a rectangular flexural resonator, the mechanical mode
structure is very complex and differs from the harmonic
structure for a rectangular electromagnetic cavity res-
onator. In addition, due to the resonator’s finite stretching
and consequent tensioning, there is an intrinsic mechani-
cal nonlinearity that is easily observable for modest me-
chanical amplitudes. The nonlinearity provides a
mode–mode coupling, analogous to photon–photon cou-
pling in nonlinear dielectrics, and drives instabilities. This
nonlinearity has already been put to effective use for both
parametric mechanical amplification and square-law me-
chanical detection, as described below.
The challenge of motion transduction
A prerequisite for attaining the ultimate potential from
nanomechanical devices is displacement sensing—that is,
reading out the NEMS motional response induced by an
applied stimulus. Most typically, this requirement distills
to transduction, or conversion, between the mechanical
and electrical domains: Ultimately one wants a voltage sig-
nal that provides the time record of the NEMS response.
Many displacement-sensing techniques for mechanical de-
vices have been proposed and demonstrated (see figure 3);
perhaps not surprisingly, displacement transducers that
∀¬⊂ ⊂EN\w \w
th
1
2
1
e
\w /kT
B
1⊗
(
(
⊕
,
38 July 2005 Physics Today
http://www.physicstoday.org
100
10
1
0.5
OCCUPATION FACTOR N
th
1 mK 10 mK 100 mK 1 K
TEMPERATURE
1 ms
100 ns
100 sm
10 sm
1sm
Ground state
1 MHz
10 MHz
100 MHz
1 GHz
60
40
20
0
NOISE POWER (fm /Hz)
2
19.656 19.658 19.660 19.662 19.664
FREQUENCY (MHz)
t
v
t
N
3.8 fm/Hz
1/2
T
N
= 73 mK
= 75
th
ab
Figure 2. Quantum limits. (a) The occupation factor
N
th
(black curves) of various mechan-
ical resonator frequencies is a function of resonant frequency and temperature
T
. Shown
in red is the lifetime t
N
of a given number state for a 10-MHz resonator with quality factor
Q ⊂ 200 000 (recently demonstrated at the Laboratory for Physical Sciences).
11
Also in
red is the expected decoherence time t
v
for a superposition of two coherent states in that
resonator displaced by 100 fm. (b) The measured noise-power spectrum of the thermal
motion (black line, with a Lorentzian fit in red) atop the white noise (blue baseline) of the
position detector. The curve corresponds to the green point in panel a, with
T
⊂ 73 mK
and
N
th
⊂ 75. These data show the closest approach to date to the uncertainty-principle
limit: The detector noise gives a displacement sensitivity a factor of 5.8 from the quantum
mechanical limit.
are important for microscale devices do not prove optimal
for nanoscale devices. For example, such optical methods
as fiber-optic interferometry and reflecting off a cantilever
(the so-called optical lever) have been used extensively in
MEMS, especially on commercially available scanning
probe microscopes. However, because nanomechanical de-
vices are small compared to the wavelength of light, dif-
fraction dramatically complicates such approaches. Near-
field optical methods may play an important future role.
But optical adsorption and the resulting heating of the me-
chanical structure prove problematic for the most sensi-
tive regimes. So it appears that optimal coupling at the
quantum limit may be difficult to achieve optically. Nev-
ertheless, optical techniques have recently enabled the de-
tection of microcantilever motion induced by a single elec-
tron spin.
3
Piezoresistive displacement transduction has found
widespread applications in larger micron-scale devices.
Use of this technique for nearly quantum-limited detection
of NEMS devices, however, does not appear to be straight-
forward. The dissipation involved will cause appreciable
heating of tiny devices, which will likely preclude opera-
tion at ultralow temperatures.
One technique that has been immensely successful is
magnetomotive detection, which utilizes the electromotive
force generated by a metallic conductor (typically a metalli-
zation layer) affixed to a mechanical device that moves in
a large magnetic field—on the order of several tesla. This
technique is especially well suited for low-temperature
measurements for which the imposition of large magnetic
fields is commonplace; it has been employed to monitor the
highest-frequency devices measured to date, with funda-
mental flexural modes exceeding 1 GHz.
1
Unfortunately,
magnetomotive motion detection becomes increasingly
awkward at higher frequencies. The effective electrical im-
pedance, which arises from electromechanical coupling to
the motional part of the device, scales inversely with fre-
quency and hence tends to be swamped by parasitic, static
circuit impedances as the frequency increases into the
gigahertz domain. But even at lower frequencies, at hun-
dreds of megahertz, observing the thermal fluctuations of
a nanomechanical resonator by this technique has so far
proven elusive—the intrinsic noise of state-of-the-art cryo-
genically cooled amplifiers is too high to surmount the
bugaboo of insufficient mechanical-to-electrical transduc-
tion efficiency. The problem is generic for most motion-
transduction methods at microwave frequencies.
Using parametric amplification, the Caltech group
has demonstrated an attractive way to work around this
problem. They employ the Euler instability—the nonlin-
earity that causes a beam under compression to buckle—
to realize a high-frequency amplifier that works entirely
on mechanical principles. Their device, depicted in figure
1d, provides stable gain and up to a thousandfold dis-
placement amplification in response to a weak stimulus
force at 17 MHz. With sufficient gain in the mechanical do-
main, the challenge of displacement transduction becomes
substantially easier and thermomechanical fluctuations in
a cryogenically cooled device have indeed been observed
with such an amplifier.
Some of the most exciting recent transduction efforts
are focused on coupling high-frequency nanomechanical
systems to various nanoelectronic and mesoscopic devices
that serve essentially as integrated amplifiers. Examples are
quantum point contacts, quantum dots, or single-electron
transistors (SETs) used in configurations where the mo-
tion of a nanomechanical device modulates the electron
transport properties. Among these readout strategies, the
SET—shown by many research groups to be a very sensi-
tive detector of charge—has now enabled nearly quantum-
limited position detection for NEMS devices. Figures 1a
and 1e each show a charged nanomechanical resonator
capacitively coupled to an SET. The resonator’s motion
induces a change in the charge on the gate electrode of the
SET; the resulting change in the SET’s conductance can be
directly monitored. Careful consideration of noise sources
indicates that the SET can provide motion detection with
sensitivity down to the quantum limit.
Robert Knobel and Andrew Cleland at the University
of California, Santa Barbara,
10
were the first to demon-
strate position detection using an SET. They used the de-
vice as a narrowband mixer—with a bandwidth of only
100 Hz—and detected the flexural resonance of a 100-MHz
device. Their effort yielded continuous position detection
http://www.physicstoday.org
July 2005 Physics Today 39
B
e
–
e
–
V
DS
b
c
a
Amp
Source
I
DS
Drain
Figure 3. Detection techniques for nanomechanical dis-
placement. (a) An optical detection scheme that is typically
used in atomic-force microscopy but that does not work
well for NEMS. Light from an optical fiber reflects off the
resonator and returns up the fiber. (b) A magnetomotive
technique that measures the electromotive force generated
when the metal layer on top of the resonator moves in the
magnetic field B. (c) Coupling to a mesoscopic detector
such as a quantum dot, a quantum point contact, or a single-
electron transistor. The current
I
DS
through the detector is
modulated by the NEMS motion.
to within a factor of about 100 of the quantum limit, but
their detection bandwidth was very limited.
Recently a group led by one of us (Schwab) at the Lab-
oratory for Physical Sciences has shown that a radio-
frequency SET can simultaneously provide both large
bandwidth (75 MHz) and ultrasensitive detection.
11
The
group directly detected the motion of a 20-MHz resonator
(figure 1a), which had a Q of 50 000, and demonstrated
nanomechanical measurements only a factor of about 6
from the quantum limit, the closest approach to date for
any position measurement (see figure 2b). With such posi-
tion sensitivity, they observed random vibrations driven by
the thermal energy at an effective temperature as low as
60 mK. The experiment essentially constituted millikelvin
noise thermometry on a single mechanical degree of free-
dom. At the experiment’s lowest temperature, the thermal
occupation factor N
th
for the mechanical mode was on the
order of 58; that low value indicates that the quantum
ground state (N
th
< 1) of NEMS devices is within reach.
Necessary steps toward achieving that goal include opti-
mized transduction at higher resonant frequencies and im-
provements in thermalization, that is, the cooling of the
mechanical mode.
Cooling is less straightforward than one might ini-
tially assume. Precisely in the regime where device modes
become frozen out (and quantum effects begin to emerge),
thermal conductance quantization (see P
HYSICS TODAY,
June 2000, page 17) imposes limits on the rate at which a
nanoscale device can thermalize to its environment.
12
Work-arounds are few. One can perhaps attempt to engi-
neer the modes mediating thermal contact—to optimize
heat transfer while preserving the quantum nature of the
specific mechanical mode under study—but it is not clear
how practical this approach will be. Perhaps a more prom-
ising alternative is active cooling of the mechanical mode
through controllable external interactions.
13
For example,
using very low-noise temperature detection to provide op-
timal feedback, it should be possible to actively cool the
mechanical mode close to the ground state. The prospects
are reminiscent of the strategy taken with trapped atoms:
Laser-cooling of samples into a low-energy state allows for
various quantum measurements before the atoms begin to
warm up from their interaction with the environment.
Ultimately, molecular mechanical systems, assembled
with atomic precision, will subsume today’s nanomechan-
ical systems patterned by top-down methods. Devices
based on single-wall carbon nanotubes offer very exciting
possibilities because nanotubes are electronically active
and naturally form nanoelectronic devices such as single-
electron transistors. Exploiting the strain dependence of
electron transport through a carbon nanotube, Paul
McEuen’s group at Cornell University has recently de-
tected the vibrational mode spectrum of a suspended nano-
tube (see figure 1f).
14
Although the “bottom up” fabrication
is today still an art rather than a technology, nanotube
and nanowire NEMS offer great promise for achieving
both very high resonant frequencies and sensitive force
detection.
Uncertainty-principle limits on position detection
How precisely can one continuously measure the position of
an object? This basic question is of central importance for
mechanical force detection, such as in atomic-force mi-
croscopy. It is clear that quantum mechanics should place
limits on the ultimate answer, since it’s possible to construct
from continuous measurement records both the mechanical
resonator’s position and its momentum. One should not ex-
pect to be able to violate the uncertainty principle.
To continuously record the position, one must couple
the mechanical device to some form of linear detector;
practically, the detector would take the form of a displace-
ment transducer (such as one that linearly converts posi-
tion to voltage) and an amplifying device. During the de-
velopment of the maser in the 1960s, it became clear that
the performance of any linear amplifier is limited by the
uncertainty principle. In the context of position detection,
the ultimate sensitivity was clarified by Carleton Caves
and colleagues
6
: Even for optimal engineering, the meas-
urement record is obscured by an equal contribution of
quantum noise from the mechanical resonator plus its
transducer and from the subsequent linear amplifier used
as a readout. With the resonator at zero temperature, the
minimum possible variance of the position record is
Two distinct forms of noise arise from the readout
process and affect nanomechanical measurements. The
first, measurement noise, is independent of the resonator
and is added to the output signal. In practice, this contri-
bution may take the form of electrical or photon shot noise.
The second is the somewhat more subtle back-action noise,
which emanates from the readout and drives the resonator
stochastically. Back-action noise might arise from fluctuat-
ing potentials or currents that are, in turn, converted by the
transducer into physical forces subsequently imposed on the
mechanical device. Electrical engineers are familiar with
these two forms of noise from linear amplifiers and repre-
sent them as voltage and current noise, respectively. Opti-
mally engineered coupling between the resonator and the
amplifier is achieved when the two amplifier noise contri-
butions are equal. But very few linear amplifiers, even when
optimized in this way, can approach the quantum limit. Ac-
cordingly, reaching the quantum limit for position detection
involves choosing an amplifier that is capable of quantum-
limited detection in principle, and that can be optimally cou-
pled to the mechanical resonator in practice.
Coupling nanomechanics to quantum systems
A large effort in condensed matter physics today is focused
on investigating the coherent quantum mechanical be-
havior of individual solid-state devices. That research
began with mesoscopic physics in the 1980s and continues
today, motivated by interest in quantum information and
computation. Beautiful and convincing quantum behav-
ior—quantized energy, coherent evolution, superposition
states, and entanglement—has been observed with vari-
ous single-electron devices, SQUIDs, and quantum dots. A
growing number of researchers now believe that we have
the necessary tools to observe similar behavior in small
mechanical structures.
To explore quantum effects in NEMS, it is essential to
move beyond continuous measurement and linear cou-
pling: Continuous linear measurements cannot distin-
guish between classical and quantum oscillators. The
quantum properties of the most heavily studied simple
harmonic oscillator—the modes of the electromagnetic
field—have been revealed by coupling to a nonlinear de-
tector such as a photon counter (for energy detection) or to
a coherent two-level system, as in a single atom in an elec-
tromagnetic cavity.
Analogous measurement concepts in nanomechanics
are starting to take shape. Reviewing the experimental
status of quantum nondemolition measurements in 1996,
Braginsky and Khalili wrote that “no experimental
scheme had been proposed so far” for measuring the en-
ergy of a mechanical resonator.
7
The Caltech group has set
\
mw ln 3
.
Dx
QL
⊂ 1.35 x
SQL
D
=
40 July 2005 Physics Today
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