Page 171 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 159

∆Z 1 2 ≈ = (2n T + ) 1 § 1 ¨ + Q ∆k 2 ¸ · ¸ − 1 , (4)
m
2 ωm ¨ 2 ω
0 © 0 ¹
m
where n = (e = ω k B T − ) 1 − 1 . Then, with = 2 ω defining the zero-point
T 0
uncertainty, the squeezing factor R = ∆ Z = 2 ω becomes,
m
1 0
R = 2n T + 1 < 1, (5)
1+ Q ∆k 2 / m ω 0 2

which, for R < 1, denotes the occurrence of quantum squeezing. Blencowe
and Wybourne [174] found that using typical resonator values, e.g., density,
ρ = . 3 99 × 10 kg / m , Young’s modulus, E = 7 . 3 × 10 N / m , beam to
3
3
11
2
=
substrate distance, g = 50 nm, beam thickness, t 100 nm , and length,
0
L = 2700 nm , the squeezing factor is R ≈ . 0 25, which signals the
realization of quantum squeezing, i.e., noise reduction below that of zero-
point fluctuations in the flexural displacement mode.
4.2.2.2.8 Nanomechanical Laser

This device concept was proposed by Bargatin and Roukes [188]. The
fundamental idea is to engineer a laser-like device in which the resonator is
realized by a nanomechanical beam, whose tip has been functionalized with
a ferromagnetic material, and whose vibration interacts with an adjacent
“active” medium containing nuclear spins biased by an external magnetic
field, B . With the appropriate geometrical configuration, see Fig. 4-8,
0
C an tileve
C an tilever r
Z Z Z
F errom agn etic
F errom agn etic
Sen sitiv
Sen sitive e
Tip
Tip
Slid
Y Y Y Slid e e
X X X
B
B 0 0
P recessin g S p in s s
P recessin g S p in
M icrow ave e
M icrow av
Pu m p in
Pu m p in g g
Figure 4-8. Sketch of mechanical laser. (After [188].)