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Sensing the quantum motion of nanomechanical oscillators
Konrad Lehnert Post-docs Tauno Palomaki Joseph Kerckhoff Collaborators John Teufel Cindy Regal Ray Simmonds Kent Irwin
Graduate students Jennifer Harlow Reed Andrews Hsiang-Shen Ku William Kindel Adam Reed
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
Imag
e: C
undi
ff la
b JI
LA
Laser light electricity
Optical and electrical measurement tools: Large dynamic range
Compact, high-Q mechanical oscillators are ubiquitous in information technology
Quartz crystal oscillator: in everything electronic
Surface acoustic wave filters: In radios, tuners, mobile phones
Applications: Timing and filtering
1 mm
Q ~ 100,000
sound speed << light speed Compact and high-Q oscillators
system
optical or electrical probe
Optical probes are ill-suited to directly measuring many interesting systems
100 nm 100 nm
Systems with:
dense low-energy spectra
nanometer length scales
weak coupling to light
nuclear spins in a virus
electrons in an aluminum ring (Harris lab, Yale)
probe field
mechanical intermediary
Mechanical oscillators enable measurements of non-atomic systems
Systems with:
dense low-energy spectra
nanometer length scales
weak coupling to light
system
Mechanical oscillators are tools that access the nano-world
Mechanical oscillator nanometer probe universal coupling (senses any force)
Optical interferometer detects oscillator motion
Perkins lab, JILA
20 µm
Atomic Force Microscope
nanoscale MRI of a single virus Rugar Lab, IBM
Mechanical oscillators form ultrasensitive, mesoscopic magnetometers
tot 1/20.8 aN/HzfS =
mechanical oscillator
environment
quantum system
Mechanical oscillators as quantum coherent interfaces between incompatible systems
γ
bathBk T
mω
quantum probe
Γ
1B
m
k T>>
ω
Mechanical oscillators are classical
Quantum regime •state preparation •state measurement •state manipulation
1B
m
k Tγ < Γ ω
Cleland group UCSB Nature 464, 697-703 (1 April 2010)
Cavity optomechanics: Use radiation pressure for state preparation and measurement
Fabry-Perot cavity with oscillating mirror
( ) ( )† 12
† 12
ˆ ˆc m IH Ha a b b= + ω ++ +ω
† †ˆ ˆˆ ( )I zpH F a ax x bg b= ⋅ = +
Infer motion through optical phase Cool with cavity-retarded radiation force
Aspelmeyer lab, IOQOI, Vienna
~ 2 10 Hzzpgx G≡ π×
Images of cavity optomechanical systems
UCSB: Bouwmeester
ENS: Pinard and Heidmann
Caltech, Painter
EPFL, Kippenberg
Yale, Harris
MIT, Mavalvala
2 1 MHzG ≈ π×
Microwave cavity optomechanics
coupling
cavity
Fabry-Perot cavity LC oscillator
Strategy
Cool environment to Tbath << 1 K
High Q mechanical oscillators
mk
mk
Reduce coupling to the environment by lowering temperature: microwave optomechanics
Microwave “light” in ultralow temperature cryostat
bath 1B
m
k Tγ < Γ ω
Braginsky, V. B., V. P. Mitrofanov, and V. I. Panov, 1981, Sistemi s maloi dissipatsei (Nauka, Moscow) [English translation: Systems with Small Dissipation (University of Chicago, Chicago, 1985)].
Superconducting electromechanics used in resonant mass gravitational wave detectors
Meter sized superconducting cavity with mechanically compliant element
Resonant electromechanics used in surveillance
Soviet passive bug hidden in the United States Seal
Henry Cabot Lodge, Jr. May 26, 1960 in the UN
Images appear in http://www.spybusters.com/Great_Seal_Bug.html
Wire response
drive frequency (MHz)
Cavity optomechanical system realized from a nanomechanical wire in a resonant circuit
Qm=300,000
400 µm
microwave resonant circuit
7 GHz2
cω=
π
150 µm
2 0.3 HzG = π×
200 kHzκ =
Parallel-plate capacitor geometry enhances microwave—mechanics interaction
capacitor built with suspended micromechanical membrane*
15 mµ
*K. Cicak, et al APL 96, 093502 (2010) . J. D. Teufel et al arXiv:1011.3067
Electrical circuit resonant at 7 GHz
2 50 HzG ≈ π×
Nanomechanical motion monitored with a microwave Mach-Zehnder interferometer
φ
0
2π
1
0
cω
221S
∆φ
c gx∆ω= =
κ∆φ
κ
Infer wire motion from phase shift
phase reference
12 noise quanta
/ photon fluxAS
NN
φ
+= =
τ
Phase sensitivity limited by amplifier (HEMT)
40AN ≈
/N τeω
cω
φ
ωd
frequency (MHz)
260 mK 147 mK
Thermal motion of beam calibrates interferometer noise (imprecision)
50 mK
C. A. Regal, J. D. Teufel, KWL Nature Phys. (2008)
impxS
Determine measurement imprecision
TxS
impxS
()
2H
z/H
zc
S ω
imp 290 SQLxS = ×
Minimum imprecision
sqlx
m
Sm
=ω γ
Imprecision at the SQL
imp 145 ZPExS =
Amplifier added noise mimics quantum inefficiency
η
12 1AN
η =+
NA = 40 η = 1.2%
Excellent microwave amplifier:
Efficient quantum measurement
Linear amplifiers must add noise
Phase-preserving linear amplifiers at least double quantum noise
12AN ≥
( )1 2ˆ ˆ( ) cos sinqV t V X t X tω ω= +
1X
2X
in )( iout n
AVV G N+=
out
A single quadrature amplifier preserves entropy with photon number gain
1X
2X
1 2 2 1ˆ ˆ ˆ ˆ
2out out out out iX X X X− =
1 1
2 2
ˆ ˆ
1ˆ ˆ
out in
out in
X GX
X XG
=
=
0AN ≥
2 4
2 1
in out
NA , G in out
( )1 2ˆ ˆ( ) cos sinqV t V X t X tω ω= +
JPA HEMT
Incorporate quantum pre-amplifier into the Mach-Zehnder interferometer
HEMTJPA
JPAA
NN NG
= +
Josephson parametric amplifier (JPA) makes more photons without more entropy
Diagram conceals some complexity
50 cm
mechanics
JPA
Dilution refrigerator
signal port Kerr medium pump port
pump signal in
amplified signal out
Realization of Josephson parametric amplifier
array of 480 SQUIDs embedded in a CPW resonator
30 µm
M. A. Castellanos-Beltran, K. D Irwin, KWL, et al, Nature Phys. (2008)
JPA 0.1N <
Imprecision noise is below the standard quantum limit with the JPA
frequency (MHz)
Q 131,500131 mK
m
T=
=
sql
/x
xS
S
sql/ 0.83x xS S =sql 5.7 fm/ HzxS =
4ω
J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. Harlow, KWL, Nature Nanotech., 4, 820-823 (2009).
Frequency (MHz)
S x (f
m2 /H
z)
efficient interferometer (JPA)
HEMT only
resolve n = 0.1 •10 minutes with JPA •1 week with HEMT
Detecting near ground state motion requires a quantum efficient interferometer
Radiation pressure cooling
cavity lineshape D.O.S.
ωm
ωc
ωd
ω
( )† ††ˆI zp aH g babx a a= +
Radiation pressure can cool the beam to ground state in the resolved sideband limit
24 dGNΓ =
κ
Nd cavity photons from cooling drive
( )† †ˆdI bH G a bN a+=
linearized interaction around strong cooling drive
Radiation pressure changes the wire’s damping rate and resonance frequency
detuning
ωdω
cω
γ
detuning (MHz)
cooling damping
amplifying driving
m∆ω
Mechanical response measures antisymmetric force noise
2
2 [ ( ) ( )]zpf m f m
xS SΓ = ω − −ω
F. Marquardt et al., PRL 99 093902 (2007)
†f Ga a= 2 0.1 HzG = π×
Coupling to radiation is too weak to cool wire to motional ground state
2(p
m/H
z)xS
Frequency (MHz)
140B
m
k T=
ω
P = 0.008
P = 1.3
J. D. Teufel, J. W. Harlow, C. A. Regal, KWL Phys. Rev. Lett. 101, 197203 (2008).
Tbath = 50 mK 700B
m
k T=
ω
Nd
Use parallel-plate capacitor geometry to enhance coupling in microwave optomechanics
capacitor built with suspended micromechanical membrane*
15 mµ
*K. Cicak, et al APL 96, 093502 (2010) . J. D. Teufel et al arXiv:1011.3067
Electrical circuit resonant at 7 GHz
m 2 10.5 MHz2 30 Hz
ω πγ π
= ×= ×
c 2 7.5 GHz2 250 kHz
ω πκ π
= ×= ×
S x (f
m2 /H
z)
Frequency (MHz)
Thermal motion reveals large coupling
50 HzG =
2B s
m m
k xk Tnω ω
= =
n os
cilla
tor p
hono
ns
Tbath refrigerator temperature (mK)
Cooling mechanics to motional ground state
n = 22
S x (f
m2 /H
z)
n = 0.93
n = 8.5
n = 2.9
n = 27
Frequency (MHz)
Increasing strength of measurement and cooling
Nd
Cooling mechanics to motional ground state S c
(rad
2 /Hz)
n = 0.36
n = 0.55
n = 0.93
Frequency (MHz)
G / π ground state and strong coupling
n = 0.38
n = 0.42
J. D. Teufel, T. Donner, KWL et al Nature, 475, 359–363 (2011).
Manipulating mechanics with
microwave
Strong coupling enables coherent control of mechanics
time (µs)
swap states of cavity and mechanics
κ
V out
(mV
)
dG N > κ
dG N
Agile state control provided by extreme resolved sideband limit
ω
mω
cavity preparation
cavity – mechanics interaction Nd (t)
κ/ 50mω κ =
cω
cavi
ty
resp
onse
linearized phonon – photon interaction • beam splitter • time dependent
( )† †ˆ ( )dIH G tN ab ba+=
Mechanical oscillators are long-lived coherent memories
( )c mP ω − ω
( )cP ωprepare swap measure
intt
time (µs)
V out
(mV
)
220 π × κ
Mechanical oscillators are long-lived coherent memories
( )c mP ω − ω
( )cP ωprepare swap measure
intt
time (µs)
V out
(mV
)
220 π × κ
Mechanical oscillators are long-lived coherent memories
int ( )t sµ
V out
(mV
)
Ramsey like oscillation in coupled microwave-mechanical system
Quantum states of the micro-drum harmonic oscillator are long-lived
1 6.1 nsT = 1
1 bath
100 s1/T
T n≈ µ
= γCleland group UCSB Nature 464, 697-703 (1 April 2010)
Microwave to optical quantum state transfer
Hofheinz…Martinis, Cleland, Nature (2009)
Microwaves: Arbitrary quantum states Require ultralow temperatures Optics: Communication and storage
Ingredients for two cavities coupled to one oscillator
Si3N4 membrane
(0,0)
(1,1)
Mechanics and optics couple to different antinodes
GHz
MHz
L C
λ
metal dielectric
Membrane in free-space cavity Superconducting LC circuit
Conclusions •Measure, cool, 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%
Funding: NSF, NIST, DARPA QuEST, DARPA QuASR, NASA