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Quantum acoustics
jilawww.colorado.edu/~lehnertk
Konrad Lehnert
Post-docs
Tobias Donner
Francois Mallet
Tauno Palomaki
Collaborators
John Teufel
Ray Simmonds
Kent Irwin
Cindy Regal
Graduate students
Jennifer Harlow
Reed Andrews
Hsiang-Shen Ku
William Kindel
Manuel CastellanosBeltran
Nathan Flowers-Jacobs
Precision measurement tools were
once mechanical oscillators
Huygens pendulum clock
The Cavendish balance
for weighing the earth
Modern measurement tools exploit optics
and electronics, not mechanics
Image: Cundiff lab JILA
Laser light
Described by:
Maxwell’s equations
electricity
Optical probes are ill-suited to directly
measuring many interesting systems
non-atomic
system
100 nm
nuclear spins
in a virus
100 nm
electrons in an
aluminum ring
(Harris lab, Yale)
Systems with:
dense low-energy spectra
nanometer length scales
weak coupling to light
quantum
probe: light
Mechanical oscillators enable
measurements of non-atomic systems
non-atomic
system
mechanical
intermediary
Systems with:
dense low-energy spectra
nanometer length scales
weak coupling to light
quantum
probe: light
Mechanical oscillators are tools that access
the nano-world
Atomic Force Microscope
20 mm
Perkins lab, JILA
Mechanical oscillator
nanometer probe
universal coupling (senses any force)
Optical interferometer detects oscillator motion
Mechanical oscillators form ultrasensitive,
mesoscopic magnetometers
nanoscale MRI of a single virus
Rugar Lab, IBM
1/2
S tot

0.8
aN/Hz
f
Mechanical oscillators as quantum coherent
interfaces between incompatible systems
Mechanical oscillators are classical
quantum
system
kBT
 1
hm
Cleland group UCSB
Nature 464, 697-703 (1 April 2010)

environment
kBT
Quantum regime
•state preparation
•state measurement
mechanical
oscillator
hm
   kBT  1
   h
  m

quantum
probe
Cavity optomechanics: Use radiation pressure for
state preparation and measurement
Fabry-Perot cavity with
oscillating mirror
H垐 hc  a†a  12   hm b†b  12   H I
Hˆ I  Fˆ  xˆ  ha†agxzp (b†  b)
Infer motion through optical phase
Cool with cavity-retarded radiation force
g 2 xzp2

Pcirc
2
4hc 
Aspelmeyer lab, IOQOI, Vienna
g ~100 MHz/nm
Images of cavity optomechanical systems
Caltech, Vahala
MPQ, Kippenberg
10 ng
IOQOI: Zeilinger and
Aspelmeyer
Yale, Harris
ENS: Pinard and Heidmann
1g
UCSB: Bouwmeester
MIT, Mavalvala
Microwave cavity optomechanics
Reduce coupling to the environment by lowering
temperature: microwave optomechanics
Microwave “light” in ultralow temperature cryostat
coupling
m
k
cavity
LC oscillator
Fabry-Perot cavity
m
k
Strategy
Cool environment to T << 1 K
High Q mechanical oscillators
   kBT  1
   h
  m
Cavity optomechanical system realized from a
nanomechanical wire in a resonant circuit
150 mm
g ~ 2 30 kHz/nm
Wire response
microwave
resonant
circuit
Qm=300,000
c
 7 GHz
2
drive frequency (MHz)
400 mm
Nanomechanical motion monitored with a
microwave Mach-Zehnder interferometer
phase reference
e
f
N /
1
c
N A  40
S21
0
2
Infer wire motion from phase shift
c gx
f 

c
c
f
0
Phase sensitivity limited by amplifier (HEMT)
N A  12 noise quanta
Sf 

N /
photon flux
2
f
c
SS
Thermal motion of beam calibrates
interferometer noise (imprecision)
260 mK
147 mK
50 mK
S
T
x
S
imp
x
Minimum imprecision
Sximp  145 ZPE
Sximp  290  SQL
Imprecision at the SQL
Sxsql  h / mmm
frequency (MHz)
Determine measurement imprecision
C. A. Regal, J. D. Teufel, KWL Nature Phys. (2008)
S
imp
x
Amplifier added noise mimics quantum
inefficiency

1

2N A  1
Excellent microwave amplifier:
NA = 40  = 1.2%
Efficient quantum measurement
A single quadrature amplifier preserves
entropy with photon number gain
in
out
NA , G

V (t )  Vq X垐
1 cos t  X 2 sin t

X2
2
1
in
out
in
X垐

GX
1
1
1 in
out
垐
X2  X2
G
out
2
4
X1
i
out
out
out
out
垐
垐
X1 X 2  X 2 X1 
2
NA  0
Incorporate quantum pre-amplifier into the MachZehnder interferometer
JPA
HEMT
N A  NJPA 
NHEMT
GJPA
Josephson parametric amplifier (JPA)
makes more photons without more entropy
Diagram conceals some complexity
Dilution refrigerator
50 cm
mechanics
JPA
SQUIDs embedded in a cavity form an optical
parametric amplifier at microwave frequency
amplified
signal out
Pump +
signal in
Shorted end
30 mm
Kerr medium
Input port
array of 250 SQUIDS
embedded in a CPW resonator
M. A. Castellanos-Beltran, KWL, App. Phys. Lett. (2008)
Imprecision noise is below the standard quantum
limit with the JPA
Qm  131,500
T  131 mK
h
4
frequency (MHz)
Sx / S  0.83
sql
x
Sxsql  5.7 fm/ Hz
All sources of loss and added noise yield an
interferometer with 30% quantum efficiency
S
imp
x
( N A  12 )he

g 2 Pcirc
2
c
Shot-noise limit
NA = 0
This interferometer
NA = 1.3  = 0.3
SQL
Pcirc (nW )
J. D. Teufel, T. Donner, M. A. Castellanos-Beltran,
J. Harlow, KWL, Nature Nanotech., 4, 820-823 (2009).
Can we measure
zero-point motion?
YES!
The SQL is a compromise between imprecision
and backaction
S
imp
x
N A  40
NA  0
( N A  12 )he

g 2 Pcirc
2
c
( N A  12 )he
P 
g 2 Sxsql
sql
circ
Sximp
2
c
Sximp
SxBA
Pcirc is constrained
-dumb heating
-superconductivity
log Pcirc
Imprecision at the SQL S
sql
x
h

mm  m
Radiation pressure cooling
Radiation pressure can cool the beam to ground
state in the resolved sideband limit
D.O.S
m
cavity
lineshape
e
g 2 xzp2

Pcirc
2
4hc c
Hˆ I  hgxzp  a†ab†  a†ab

c
Requirements for sideband cooling to the ground state
resolved sideband limit m  e
high frequency, high quality beams Qm 
strong coupling   nbath 0m
kBTbath
 nbath
hm
Radiation pressure changes the wire’s
damping rate and resonance frequency
c
amplifying
driving
detuning
cavity
lineshape
e
x
  [S f (m )  S f (m )]
h
kHz
†
f  hga a g  6.4
nm
F. Marquardt et al., PRL 99 093902 (2007)
cooling
damping

Mechanical response measures
antisymmetric force noise
2
zp
2
m
m
detuning (MHz)
S
Coupling to radiation is too weak to cool wire to
motional ground state
Tcryo = 50 mK
P = 0.008
P = 1.3
Frequency (MHz)
J. D. Teufel, J. W. Harlow, C. A. Regal, KWL Phys. Rev. Lett. 101, 197203 (2008).
kBTbeam
 700
hm
kBTbeam
 140
hm
Cooling and measuring mechanical motion
Sx (fm2/Hz)
capacitor built with suspended
micromechanical membrane*
SxT
10 mm
Electrical circuit
resonant at 7 GHz
Sximp
Frequency (MHz)
John Teufel and
Ray Simmonds
*K. Cicak, et al APL 96, 093502 (2010)
. J. D. Teufel et al arXiv:1011.3067
Conclusions
•Measure and manipulate nanomechanical elements
with microwaves
• Optomechanical performance: in quantum regime!
cooling: 0.35 phonons
imprecision: 0.83 X SQL
force: 0.5 aN/Hz1/2
• Microwave Mach-Zehnder
interferometer
quantum efficiency 30%
Graduate and post-doc positions available
Funding: NSF, NIST, DARPA, NASA