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