Students:
Young-Shin Park
Scott Lacey
Mark Kuzyk
Laser Cooling of an Optomechanical MicroresonatorLaser Cooling of an Optomechanical Microresonator
Hailin Wang
Oregon Center for Optics, University of Oregon
Supported by NSF and DARPA
Introduction:
What is optomechanicsOptical control of mechanical motion
Optomechanical resonator: Silica microsphere
Optical and mechanical properties
Toward ground state cooling: Combining cryogenic and laser cooling
Summary and outlook
OutlineOutline
Optomechanical ResonatorOptomechanical Resonator
Optomechanical coupling:
• Circulating optical power exerts a radiation pressure force on the mirror.
• The mirror displacement changes the cavity frequency, 0.
• Back Action: 0 in turn induces changes in the circulating optical power.
For a review, see Kippenberg and Vahala, Science 321, 1172 (2008).
0 0( )
( )x t
tL
effmm m
Ftx
dt
tdx
dt
txd )(
)()( 2
2
2
L
m0
Su
pp
ort
lifetime:
F
F: Radiation pressure force:
Time Domain: Dynamical BackactionTime Domain: Dynamical Backaction
V.B. Braginsky, 1977; M. I. Dykman, 1978.
L
m0
Su
pp
ort
lifetime:
F
rad> 0, damping
rad< 0, amplificationeffrad mdx
dF
The delayed backaction leads to a radiation pressure force that depends on the velocity.
Optical spring effects
0)()()(
)()( 2
2
2
txdt
tdx
dt
txdmmradm
The induced change in the circulating optical power is delayed by the cavity lifetime.
)()]([)(dt
dxx
dx
dFtxFtF
Spectral Domain: Stokes and Anti-Stokes ProcessesSpectral Domain: Stokes and Anti-Stokes Processes
• Anti-Stokes process leads to cooling or damping.• Stokes process leads to amplification.
L
m0
Su
pp
ort
F
Scattering of photons from a mechanical vibration
Photons
m
L 0
mAnti-Stokes
Cavity resonance
L0
mStokes
Cavity resonance
““Putting the Mechanics Back in Quantum Mechanics”Putting the Mechanics Back in Quantum Mechanics”
• Quantum behavior in a macroscopic mechanical system
– Macroscopic superposition and entanglement
– Decoherence
– Quantum measurements
– The quantum-classical boundary.
• Sensitive or precision measurements
– Force, mass, etc.
– Displacement
Cooling of a macroscopic mechanical oscillator to its motional ground state.
Schwab and Roukes, Physics Today, 58(7), 36 (2005).
1)/exp(
1
TkN
B
Similar to parametric down conversion.
)(2 abbaH
S
m
L
LS
0
Stokesm
)(1 abbaH
Quantum state transfer between optical and mechanical states.
AS
m
L
Anti-Stokes
L AS
0
m
Zhang et al., PRA 68, 013808 (2003); Genes et al., PRA 78, 032306 (2008).
• The quantum correlations become important at relatively low phonon occupation.
The system is driven by a classical laser field at L.
a+ and b+ are creation operators for the cavity and the mechanical modes, respectively.
Tool Box for Quantum OpticsTool Box for Quantum Optics
Diedrich et al., Phys. Rev. Lett. 62, 403 (1989).
vResolved sideband limit:
Cooling the mechanical motion of an
ion to its motional ground state.
Photon
vvL 0
AS
S
| g, N1>
| e, N1>
| e, N >
| g, N >| g, N+1 >
0L
| e, N+1 >
v
L
Phonon emission(gain)Phonon ab
sorption(Cooling)
Stokes
Anti-Stokes
Laser Cooling of Trapped IonsLaser Cooling of Trapped Ions
Wilson-Rae et al., Phys. Rev. Lett. 99, 093901 (2007); Marquardt et al., Phys. Rev. Lett. 99, 093902 (2007).
AS
S
| n, N1>
| n+1, N1>
| n+1, N >
| n, N >| n, N+1 >
0L
| n=1, N+1 >
m
L
2
2 << 1
16 m
N
L ASS
m
Resolved sideband limit: m
Resolved-sideband cooling can in principle cool an optomechanical system to its motional ground state.
Resolved-Sideband Optomechanical CoolingResolved-Sideband Optomechanical Cooling
Cohadon et al., Phys. Rev. Lett. 83, 3174 (1999). N ~ 170,000Kleckner et al., Nature 444, 71 (2006). N ~ 220,000Poggio et al., Phys. Rev. Lett. 99, 017201 (2007). N ~ 23,000
Gigan et al., Nature 444, 67 (2006). N ~ 740,000Arcizet et al., Nature 444, 71 (2006). N ~ 260,000Schliesser et al., Phys. Rev. Lett. 97, 243905 (2006). N ~ 3,900Corbitt et al., Phys. Rev. Lett. 98, 150802 (2007). N ~ 108
Thompson et al., Nature 452, 72 (2008). N ~ 1,000Schliesser et al., Nature Phys. 4, 415 (2008). N ~ 1,000 (Sideband cooling)
Dynamical backaction cooling
Active feedback cooling
Ground state cooling Resolved-Sideband cooling + Cryogenic cooling
Optomechanical Cooling at Room TemperatureOptomechanical Cooling at Room Temperature
Cooling rate Heating rate
m
bathBradm Q
TkN
)(
Frequency
m/Mechanical Q
MaterialBath temperature
Final phonon occupation
118 MHz4.0
3,400silica 1.4 K37
65.2 MHz3.4
2,000silica 1.65 K
63 ± 20
0.95 MHz1.25
30,000silicon nitride
5.3 K32
MPQ/EPFL IQOQI/Cornell U. of Oregon
Cryogenic cooling
+Sideband Cooling 20 m
Schliesser et al., Nature Phys. 5, 509 (2009).
Park and Wang, Nature Phys. 5, 489 (2009).
Groblacher et al., Nature Phys. 5, 485 (2009).
Quantum correlations can already persist at this level of phonon occupations.
Route to “the Ground State”Route to “the Ground State”
Optomechanical CrystalsOptomechanical Crystals
Eichenfield et al., Nature 462, 78 (2009).
• Applications in photonics:
Sensing
Optical routing and switching
Introduction:
What is optomechanicsOptical control of mechanical motion
Optomechanical resonator: Silica microsphere
Optical and mechanical properties
Toward ground state cooling: Combining cryogenic and laser cooling
Summary and outlook
OutlineOutline
• Q-factors as high as 1010 can be achieved.
Extremely small absorption and scattering loss in high purity silica
Nearly atomically smooth silica surface.
Braginsky et al., Phys. Lett. 137, 393 (1989).
Whispering gallery modes form via total internal reflections along the equator.
CO2
laser
30
Silica MicrosphereSilica Microsphere
• WGMs cannot be excited via geometric optical processes.
• Excite WGMs with evanescent waves via a tapered fiber
• Excite WGMs with evanescent waves via frustrated total internal reflection
Launching WGMs via Evanescent WavesLaunching WGMs via Evanescent Waves
Difficult to implement at cryogenic temperature
Cai et al., PRL 85, 74 (2000).
Develop a new technique for direct free-space excitation of WGMs
RadiusR
effV
=critical angle
Glancing incidence
Barrier
The angle of incidence is no longer conserved in a deformed resonator.
22
2 )1()1()(
r
ll
crVeff
Quantum analogy:
The evanescent escape rate:
• depends on ,
• increases exponentially as approaches the critical angle.
EEE2
2
2
22 )1(
cc
02
22 EE
c
Evanescent Escape of WGMsEvanescent Escape of WGMs
Strong evanescent escape occurs in these regions where the angle of incident reaches a minimum.
sinc
sin
00.5
1.0
)2cos(1)( r
Evanescent Escape in a Deformed ResonatorEvanescent Escape in a Deformed Resonator
S. Lacey et al., Phys. Rev. Lett. 91, 033902 (2003).
Deformed Silica MicrospheresDeformed Silica Microspheres
• Deformed micropheres are formed by fusing two regular microspheres of similar size with a CO2 laser.
• Deformation is controlled by repeated heating.
b
ba
Deformation
zx
zy
yx
20 m
a
b%7.4 %4.13
%4.2
CO2
Q-Factor and Emission Patterns vs Deformation Q-Factor and Emission Patterns vs Deformation
800.4 800.8
800.542 800.543
800.924 800.925
Wavelength (nm)
Q ~104
Q ~3x107
Q ~7x107
0 45 90 135 180
(degrees)
Inte
nsity
(ar
bitr
ary
units
)Lacey et al., Phys. Rev. Lett. 91, 033902 (2003).
Free space evanescent excitation of WGMsFree space evanescent excitation of WGMs
Launching WGMs in free-space by focusing a laser beam in areas 45o from a symmetry axis.
-0.5 0.0 0.50.0
0.2
0.4
0.6
0.8
1.0
Tra
nsm
issi
on
Detuning(GHz)
Approaching the sphere
Park et al., Nano Lett. 6, 2075 (2006)
Excitation efficiency as high as 50% can be achieved.
Silica Microsphere as Optomechanical ResonatorSilica Microsphere as Optomechanical Resonator
Optical resonator :
Whispering gallery modes
• Frequency ~ 1014 Hz
• Optical Q-factor ~ 108
• Mode volume ~ 100 m3
20 m
Mechanical resonator:
Breathing modes
• Frequency ~ 100 MHz
• Mechanical Q-factor ~
10,000
• Effective mass ~ 35 ng
Frad
50 100 150 200
-70
-60
-50
-40
Optically Active Mechanical ModesOptically Active Mechanical Modes
D = 30 m
Frequency (MHz)
Noi
se P
owe
r S
pect
rum
(d
Bm
)
25 30 35 4050
100
150
200
Mec
hani
cal f
requ
ency
(M
Hz)
Diameter (m)
(n, l )=(1,0)
(n, l )=(1,2)
Size dependence
Finite element Analysis
(n, l )=(1,2) (n, l )=(1,0) (n, l )=(1,4) (n, l ) = (radial, angular)
Park and Wang, Opt. Express 15, 16471 (2007).
Optical Homodyne Detection of Mechanical VibrationsOptical Homodyne Detection of Mechanical Vibrations
2|| loccavout EEI inE
Local
Oscillator
Ecav
outE
• The breathing mechanical motion induces a phase shift in the circulating cavity field.
• Homodyne detection measures the induced phase shift.
• The oscillating phase shift leads to resonances at m in the noise power spectrum of the homodyne measurement.
Hzm /10 18
Sensitivity!!!
Mechanical Quality FactorMechanical Quality Factor
99.22 99.24 99.26
2
4
6
Nois
e p
ow
er
spect
rum
(10-3
3 m
2/H
z)
Frequency (MHz)
18,000mQ
Mechanical loss of a silica
microresonator
• Clamping loss due to the fiber stem
• Collisions by surrounding gases
• Acoustic attenuation (below room
temp.)
imm
mmQ
Mechanical quality
factor
(n, l )=(1,2)
in vacuumStem size: ~ 1/10 of microsphere diameter
Temperature Dependence of Mechanical Q-factorTemperature Dependence of Mechanical Q-factor
Dynamics of the dangling bonds leads to acoustic attenuation.
Phillips, Amorphous Solids (1981).Pohl et al., Rev. Mod. Phys. 74, 991 (2002).Vacher et al., Phys. Rev. B 72, 214205 (2005).
1 10 1000
50
100
150
200
Mech
anic
al l
inew
idth
(kH
z)
Temperature (K)
MHz 1102/ m
000,10mQ
500mQ
400,3mQ
Thermally activationTunneling
Acoustic attenuation in silica becomes important below room temperature Amorphous solid
Mechanical damping due to acoustic attenuation remains significant at a few K.
Introduction:
What is optomechanicsOptical control of mechanical motion
Optomechanical resonator: Silica microsphere
Optical and mechanical properties
Toward ground state cooling: Combining cryogenic and laser cooling
Summary and outlook
OutlineOutline
Experimental SetupExperimental Setup
Opto-mechanical cooling
Cryogenic cooling
He4 cryostat
The same laser beam is used for both radiation pressure cooling and homodyne detection.
112.5 113.0 113.5
Nois
e s
pect
rum
Frequency
Tbath = 20K
103
104
1 10 10010-2
10-1
100
Ave
rage p
honon o
ccupatio
nNois
e s
pect
rum
are
a (
a.u
.)
Bath temperature (K)
N
orm
aliz
ed a
rea
Avera
ge p
honon
occu
patio
n
Bath temperature (K)
22
meff
effB
m
Tkx
(n, l) = (1, 2)
2)(2
2
22
dx
k
m
xk
mT
B
meff
B
meffeff
Equipartition Theorem
1 10 1000
50
100
150
200
Mec
hani
cal l
inew
idth
(kH
z)
Temperature (K)
114.5
115.0
115.5
Mechanical frequency (M
Hz)
Cryogenic CoolingCryogenic Cooling
Resolved-sideband cooling at Resolved-sideband cooling at TTbathbath=3.6 K=3.6 K
123.0 123.3 123.60
5
10
15
20
Frequency (MHz)
Nois
e s
pect
rum
(10
-36 m
2 /Hz)
P = 10 mW
40 mW
60 mW
83 mW
Nois
e p
ow
er
spect
rum
(1
0-3
6m
2/H
z)
L 0
/ = 23 MHz
m
• The spectrally-integrated area decreases with laser power.
• The linewidth of the mechanical resonance increases with laser power.
Qm = 1600 (due to ultrasonic attenuation in silica at low temperature)
D = 25.5 m(n, l) = (1, 2)
1 10 1000.1
1
61
100
606
Average phonon occupation
Inte
grat
ed a
rea
Incident power (mW)
B
meffeff k
xmT
2
Teff ~ 1 K
-1.5 -1.0 -0.5-50
0
50
eff (
kHz)
Fre
quen
cy s
hift (
kHz)
Laser detuning (/m)
100
200
300
Pin = 20 mW 60 mW 83 mWPth = 35 mW
Radiation Pressure CoolingRadiation Pressure Cooling
kHz 802/ m
(No free parameters)
])(4)(4
[
)(4
4
])(4)(4
[
)(4
4
2222
22
2
2222
22
2
m
m
m
m
m
thm
mm
m
thm
P
P
P
P
Pth: threshold power for parametric oscillation
L 0
/ = 23 MHz
m
Resolved-Sideband Cooling at Resolved-Sideband Cooling at TTbathbath=1.4 K=1.4 K
• Quantum correlations can already persist at this level of phonon occupation.
• Limited by ultrasonic attenuation
Qm = 3400 at 1.4 K (Qm = 10,300 at 300 K)
/ 2 119 MHzm
L 0
/ 2= 30 MHz
D = 26.5 m, (n, l) = (1, 2)
1 10 1000.1
1
25
100
246
Incident power (mW)
Average phonon occupation
Inte
grat
ed a
rea
Teff ~ 210 mKNfinal ~ 37
B
meffeff k
xmT
2
Acoustic Attenuation at Low TemperatureAcoustic Attenuation at Low Temperature
Silica
Pohl et al., Rev. Mod. Phys. 74, 991 (2002).
• At ultrasonic frequency, acoustic attenuation decreases rapidly below T ~ 2 K and diminishes at T ~ 200 mK.
Combined resolved-sideband cooling with cryogenic cooling by using a silica optomechanical resonator.
Demonstrated Nfinal ~ 37 and Teff ~ 210 mK, limited by acoustic attention in silica.
Future work
Using a 3He cryostat to lower the bath temperature and to minimize the acoustic attenuation.
Using a crystalline optomechanical resonator.
Pursuing quantum optics with optomechanical resonators.
SummarySummary
Cavity QED + Cavity OptomechanicsCavity QED + Cavity Optomechanics
Coupling a mechanical oscillator to a spin excitation.
Park et al., Nano Lett. 6, 2075 (2006); Larsson et al., Nano Lett. 9, 1447 (2009).
Nanocrystals m
Nitrogen vacancy center in diamond
Electromechanical System Electromechanical System
A nanomechanical beam is capacitively coupled to a single electron transistor or to a superconducting microwave resonator.
LaHaye et al., Science 304, 74 (2004); Teufel et al., Phys. Rev. Lett. 101, 197203 (2008)
• Nanomechanical beam : m ~ 10-12 g; /220 MHz• Temperature < 50 mK (dilution refrigerator)• Lowest thermal phonon occupation: N ~ 25
Mechanical Displacement: CalibrationMechanical Displacement: Calibration
Schliesser et al., New J. of Phys. 10, 095015 (2008).
100.8 100.9 101.0
1
10
100
Noi
se s
pect
rum
(10
-32m
2/H
z)
Frequency (MHz)
MHz 90.1002/
MHz 98.1002/ m
inE
Local
Oscillator
Ecav
outE
• Mimic the phase shift due to the mechanical vibration by phase-modulating the input optical field:
• Correspondence between rm and :
tiinin eEE sin
mm
rR
0 ( ) mmm ,,
(with an E-O modulator)
Dependence on Laser DetuningDependence on Laser Detuning
m
m
0Not sensitive !
148.2 148.5 148.8
Nois
e p
ow
er
spect
rum
(a.u
.)
Frequency (MHz)
The sensitive of the direct homodyne detection depends on the laser detuning.= L 0
L 0
-200 -100 0 100 200
Inte
nsity
Noi
se a
mpl
itude
(a.
u.)
Detuning (MHz)
WGM resonance
Pow
er s
pect
rum
at
m
Laser detuning, (MHz)
Intensity
m m
The same laser beam can be used for both radiation pressure cooling and homodyne detection.
5 10 15 20 25
0.5
1.0
1.5
WG
M r
eso
nance
shift
(G
Hz)
Temperature (K)
Blue shiftRed shift
01 1
( )d dR dn
dT R dT n dT
Nonlinear Optical Properties at Low TemperatureNonlinear Optical Properties at Low Temperature
Regenerative pulsation at 18.5 K
Park and Wang, Opt. Lett. 32, 3104 (2007).
St. Paul’s Cathedral, London
Lord Rayleigh,1842-1919
Echo Wall of the Temple of Heaven,Beijing, Ming dynasty, 1420
Whispering Gallery Acoustic WavesWhispering Gallery Acoustic Waves
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