Download Observing Radiation Pressure Shot Noise on a Solid Object

Observing Radiation Pressure Shot Noise
on a Solid Object
Cindy Regal
Tom Purdy
Bob Peterson
Ben Yu
KITP, QuControl, 2013
0.5 mm
Boulder, CO, USA
Orientation and outline
• (Quantum) Cavity Optomechanics
Measure and control motion of objects in
interferometers near quantum limits
• One degree of freedom
• larger – size, mass
• complex?
Ligo.caltech.edu
0.5 mm
x
Outline
• Experiment presented: Observation of
radiation pressure shot noise (RPSN)
• Backaction branch of quantum-limited
continuous position measurement
(fixed meas. time)
• (Quantum) Cavity Optomechanics
Measure and control motion of objects in
interferometers near quantum limits
P / P SQL
Ligo.caltech.edu
0.5 mm
Outline
• Experiment presented: Observation of
radiation pressure shot noise (RPSN)
• Backaction branch of quantum-limited
continuous position measurement
• Physical object: Very thin vibrating membrane
• Si3N4 (50 nm by mm-scale)
(fixed meas. time)
• (Quantum) Cavity Optomechanics
Measure and control motion of objects in
interferometers near quantum limits
P / P SQL
Ligo.caltech.edu
0.5 mm
Outline
• (Quantum) Cavity Optomechanics
Measure and control motion of objects in
interferometers near quantum limits
• Experiment presented: Observation of
radiation pressure shot noise (RPSN)
• Backaction branch of quantum-limited
continuous position measurement
• Physical object: Very thin vibrating membrane
• Si3N4 (50 nm by mm-scale)
GHz
l
L
• Quantum information applications
• Mechanically mediated interactions
• Microwave - Optical
Ligo.caltech.edu
MHz
metal
0.5 mm
C
dielectric
Electromechanics: Lehnert Group (JILA)
Introduction
Heisenberg uncertainty
and precision measurement
Heisenberg Microscope:
Always some physical origin
Heisenberg’s book, 1930…
Free mass limit
Measure to Dx at time t
Momentum uncertain to
Dp ³ / 2Dx
At later time…
Dx(t ') = Dx(t) +
(t '- t)
2mDx(t)
See for example: Braginsky and Thorne, Science (1980)
Walls and Milburn, Quantum optics
Our version
Movable
End Mirror
Detector
lots of photons (108)
Shot noise
harmonic
oscillator
N
Shot noise of radiation pressure drives up mirror
Full answer – modern quantum optics
Standard Quantum Limit
Shot noise
Imprecision
White Sz
RPSN
Backaction
White SF
Szimp SFba ³
Our measurements
focus on behavior at
resonance w m
Zero Point Motion
PSQL
Measurement strength, laser power
Frequency
Frequency
c m (w ) SF (w )
2
Frequency
Standard Quantum Limit
Shot noise
Imprecision
White Sz
Thermal motion
Technical noise
Optical power limits
…
Our measurements
focus on behavior at
resonance w m
RPSN
Backaction
White SF
Zero Point Motion
PSQL
Measurement strength, laser power
Frequency
Frequency
c m (w ) SF (w )
2
Frequency
Subset of spectrum of optomechanics experiments
Optomechanics
Electromechanics
Effectively moving mirrors
Moving capacitor plate
trapped atoms
Kippenberg, EPFL
Lehnert/Simmonds, Boulder
Piezoelectrics
Painter, Caltech
Gravitational wave detectors
Cleland/Martinis
UCSB
Closely related optomechanics experiments
Optomechanics
Electromechanics
Effectively moving mirrors
Moving capacitor plate
Kippenberg, EPFL
Lehnert/Simmonds, Boulder
“Laser” cooling to near the mechanical ground state
(combined with cryogenic cooling)
Painter, Caltech
Frequency
Observation of sideband
asymmetry, Painter group
Frequency
Closely related optomechanics experiments
trapped atoms
Observation of RPSN heating with atom gas
And ponderomotive squeezing
Stamper-Kurn group, Berkeley
Frequency
Closely related optomechanics experiments
Experimental studies of classical analogs:
Heidmann group, Paris
Frequency
Gravitational wave detectors
Our optomechanical device
(2,2) drum mode
• Stoichiometric silicon nitride* sits in optical
standing wave near end of cavity
• 50 nm thick drum - highly stressed, nm=1 MHz
• Increases oscillator energy compared to thermal
scales while keeping dissipation similar
Q ~ 10 6 -10 7
Transmission
Cavity resonance shifts
with membrane position
Laser Frequency
*Introduced to optomechanics: Harris group at Yale, Thompson et al. Nature 2008
A cryogenic, three-element Fabry-Perot cavity
0.5 mm
Challenge:
• Stability and alignment of cryogenic device
Membrane
Mirror
Piezoelectric
Actuator
Invar Spacer
Membrane
Optical Mode
Cryogenic
optomechanical device
device
Cryogenic
optomechanical
Experiment at 4 kelvin – simple in many ways
RPSN experiment setup
PD
Membrane
Signal Beam
PD
PBS
PBS
Mirror
Mirror
Meter Beam
“Signal Beam (S)”
 High Power
 On resonance
 RPSN
 Optical force readout
“Meter Beam (M)”
 Low Power
 Red detuned
 Optical damping/cooling
 Displacement readout
T. P. Purdy, et al., Science (2013)
P. Verlot, et al., PRL (2009)
Observing radiation pressure shot noise heating
Meter Beam
Dominant
damping
Domin
4He
Cryostat
T0 = 5 K
G M =1.4 kHz
Three heat baths at different
temperatures coupled to the
resonator with differing strengths
Signal Beam
RPSN
G 0 = 0.5 Hz
T0 G 0 + TM G M + TS G S
Teff =
G0 + GM + GS
Equilibrium Temperature
Radiation pressure shot noise heating
RPSN
C
1
~
Frequency
Thermal nth 1+ ( kw/2m ) 2
100
Thermal Motion
10
Zero Point Motion
SQL
1
0.01
0.1
1
10
100
Parameters for seeing RPSN heating
RPSN
C
1
~
Frequency
Thermal nth 1+ ( kw/2m ) 2
Cooperativity
photon number
coupling
4Ng 2
C=
kG 0
cavity
damping
mechanical
damping
Thermal phonons (4 K bath)
nth =
kbT0
wm
Meter beam damping:
• Plays no role in this ratio
• (Very important) convenience
Radiation pressure shot noise heating
kHz
Device A
Q0=3X106
Frequency (MHz)
100
Device B
Q0=1.4X107
10
Thermal Motion
1
10
100
Check for physical heating
3
(2,2) mode
well coupled
2
1
(4,4) mode
poorly coupled
0
0
1
2
3
4
Signal beam: Record of optical force
Meter
PD
Membrane
1.54 1.55
1.56
Signal
PD
PBS
Mirror
Mirror
1.54 1.55 1.56
Frequency (MHz)
• AM quadrature - shot noise
intensity fluctuations - record
of the optical force on the
resonator
Two beam cross correlation
Cross correlation between
meter & signal
10-26
0.15
10-28
Contributions:
• RPSN to thermal 40%
• Loss (ports, path, QE) 40%
10-30
1.54
1.55
Frequency (MHz)
1.56
Two beam cross correlation
Test for trivial correlations
Mechanical
Transducer
Excess
Membrane
Motion
PZT
White Noise
10-26
10-15
10-28
10-16
10-30
1.54
1.55
1.56
Frequency (MHz)
1.54
1.55
1.56
Frequency (MHz)
Classical intensity noise limit
Intensity
Modulator
Excess
Intensity
Noise
White Noise
10-24
10-26
10-28
10-30
1.54
1.55
1.56
Frequency (MHz)
Consistency with quantum noise
Vacuum Noise
from the
input port
in phase
Classical
Laser
Noise
phase shift
Vacuum Noise
from the
output port
classical noise
(mostly) quantum noise
270
180
90
1.54
1.55
1.56
Frequency (MHz)
Microwave to optical quantum link
GHz
l
L
C
MHz
metal
dielectric
Electromechanics: Lehnert Group (JILA)
Analogous experiments: UCSB
See for ideas:
J. Zhang…S. L. Braunstein, PRA (2003)
C. A. Regal and K. W. Lehnert, J. Phys. Conf. Series (2011)
A. Safavi-Naeini…O. Painter, New J. Phys. (2011)
J. Taylor et al., PRL (2011)
T. Palomaki…K. W. Lehnert, Nature in press (2013)
4Ng2
C=
> nth
kG 0
Transfer rate between phonons
and (itinerant) photons exceeds
rate at which single phonon
leaves to environment
Conclusions and directions
• To do − Standard quantum limit for
continuous position measurement
• There is a lot of quantum optics to
pursue in these systems, optical
squeezing, backaction evasion,…
• Elucidating to study these with
physical object in interferometer
driven by quantum noise
Collaborators:
Konrad Lehnert Group, JILA
Ray Simmonds Group, NIST
Group members: Optomechanics
Bob Peterson Ben Yu
Thomas Purdy
Single neutral atoms
Adam Kaufman Brian Lester