quantum measurement in an optomechanical...

2445-03

Advanced Workshop on Nanomechanics

Tom Purdy

9 - 13 September 2013

JILA - NIST & University of Colorado U.S.A.

Quantum Measurement in an Optomechanical System

Tom Purdy, JILA – NIST & University of Colorado with Bob Peterson, Ben Yu, Nir Kampel, Alec Jenkins, Cindy Regal

T P d JILA NIST & U i it f Ci iti l dl d

1

10

100

0.01 0.1 1 10 100

SQL

Thermal Motion

Measurement Laser Power

Pos

ition

Unc

erta

inty

1.0

0.8

0.6 1.56 1.54 1.52 1.50

Range of Optomechanical Systems Big Small

10 kg 10 km 10 ng 1 mm 10-25 kg 10 nm

1 m

A. Kaufman, et al., PRX 2, 041014 (2012)

Ligo.caltech.edu

Ligo.caltech.edu

4 km

10-18 m

LIGO Membrane Optomechanics

Single Atom in Optical Tweezers

Sept. 9, 2013 Frontiers in Nanomechanics

Nanomechanics Macroscopic Systems

3

• Raman Sideband Cooling • Optical Tweezers • Electromagnetically

Induced Transparency

• High precision interferometry • Squeezed light • Quantum Nondemolition

Measurements

Big Small

10 kg 10 km 10 ng 1 mm 10-25 kg 10 nm Ligo.caltech.edu

4 km

10-18 m

LIGO Membrane Optomechanics

Single Atom in Optical Tweezers

Range of Optomechanical Systems

Sept. 9, 2013 Frontiers in Nanomechanics Tom Purdy JILA

Nanomechanics Macroscopic Systems

Tom Purdy JILA 4

• Membrane Cavity Optomechanical System

• Raman Sideband Cooling • Introduction to quantum measurement • Observing quantum measurement

backaction • Using mechanical motion to measure

light • Building better mechanical resonators

Overview


(1,1)

(2,2)

(4,4)

• Si3N4 dielectric membrane

• 0.5 mm X 0.5 mm X 50 nm

• High Tension ~ GPa

• High Mechanical Quality Factor

• MHz mechanical resonance frequencies

• 10% reflectivity, low optical absorption

• Low mass ~10 ng

Thompson, et al., Nature 452 72 (2008) Wilson et al., PRL 103 207204 (2009) Karuza, et al., NJP, 14, 095015 (2012) Purdy, et al., NJP, 14 115021 (2012)

Membrane Optomechanical System


Verbridge, et al., JAP 99, 124304 (2006) Southworth, et al., PRL 102, 225503 (2009) Unterreithmeier, et al., PRL 105, 027205 (2010) Wilson-Rae, et al., PRL 106, 047205 (2011) Yu et al., PRL 108, 083603 (2012)

Tom Purdy JILA 6

Mirror Mirror

Membrane

Optical Intensity

Optical Frequency

Tran

smis

sion

Photodetector

Input laser

Mechanical Displacement Spectrum

Optomechanical Coupling


Tom Purdy JILA 7

1”

Mirror

Piezoelectric Actuator

Membrane

Invar Spacer

• Compact, low vibration, low drift design

• Cryogenically compatible (4K flow cryostat)

• High optical finesse (<30,000)

• Low mechanical dissipation

small

4 K

Optomechanical Device


8 0mn1mn

2mn

3mn

m

C

Anti-Stokes m = Mechanical frequency

m = Cavity frequency

= number of photons

mn = number of mechanical vibrational quanta

Raman Sideband Cooling

Laser Cooling


Monroe…Wineland, PRL 75, 4011 (1995) Teufel, et al., Nature 475, 359 (2011) Chan, et al., Nature 478, 89 (2011) Tom Purdy JILA

9 0mn1mn

2mn

3mn

m

C

Anti-Stokes

Inpu

t Las

er

m

Optical Frequency

Raman Sideband Cooling

Laser Cooling


Monroe…Wineland, PRL 75, 4011 (1995) Teufel, et al., Nature 475, 359 (2011) Chan, et al., Nature 478, 89 (2011) Tom Purdy JILA

Tom Purdy JILA 10

10-17 1.53 1.52 1.51

10-16

10-15

Frequency (MHz)

Total motion Thermal motion

Laser Cooling

Purdy, et al., NJP, 14 115021 (2012) Jayich, et al., NJP 14, 115018 (2012)


Increasing Laser Power

Tom Purdy JILA 11

10-17 1.53 1.52 1.51

10-16

10-15

Frequency (MHz)

Laser Cooling

Purdy, et al., NJP, 14 115021 (2012) Jayich, et al., NJP 14, 115018 (2012)


Increasing Laser Power

Tom Purdy JILA 12

Ligo.caltech.edu

2physics.com

Dis

plac

emen

t Spe

ctra

l D

ensi

ty N

oise

[m/H

z1/2]

Quantum Limits of Optical Detection


Laser

Photodetector

Test mass

Test mass

Beamsplitter

~kg

Fundamental Sensitivity Limits: • Optical Shot Noise • Radiation Pressure Shot Noise

Limits theoretically identified decades ago, Caves, PRL 45 75 (1980) Unruh, Quant. Opt., Exp. Grav., and Meas. Th. (1982) Braginsky, et al., Science 209, 547 (1980) But little experimental work until recently LIGO, Nature Phys. 7, 962 (2011) Purdy, et al., Science 339, 801 (2013) Hertzberg, et al., Nature Phys. 6, 213 - 217 (2010)

Interferometric Gravitational Wave Detector: It’s like trying to infer the position of the moon by measuring the ocean’s tides, but 1015 times harder

W. Heisenberg, Physical Principles of the Quantum Theory (1930)

Tom Purdy JILA 13

Camera

electron

photon

Microscope

Heisenberg’s Microscope Thought Experiment

2/baimp px


Tom Purdy JILA 14

Camera

electron

photon

Microscope

Heisenberg’s Microscope Thought Experiment

2/baimp px


Standard Quantum Limit

1

10

100

0.01 0.1 1 10 100

Standard Quantum

Limit


Pos

ition

Unc

erta

inty

Shot Noise – statistical fluctuations of the

number of photons detected in a given time interval

Radiation Pressure Shot Noise – Randomly varying optical force fluctuations due to shot noise

Tom Purdy JILA 15

baimpFz SS


Tom Purdy JILA 16

PD

PD PBS PBS

Mirror Mirror

Membrane

Signal Beam High Power (strong measurement) On resonance RPSN Displacement information imprinted in optical phase

Meter Beam Low Power Red detuned Optical Cooling Displacement readout

Meter Beam

Signal Beam

Optical Frequency F

Quantum Measurement Experiment Setup


Tom Purdy JILA 17

Signal Beam OFF

Signal Beam ON

Dis

plac

emen

t Spe

ctru

m

as m

easu

red

by m

eter

bea

m

Radiation Pressure Shot Noise


Tom Purdy JILA 18

1

10

100

0.01 0.1 1 10 100

SQL

Thermal Motion


Pos

ition

Unc

erta

inty

Purdy, et al., Science 339, 801 (2013) Murch, et al., Nature Physics 4, 561 (2008) Naik, et al., Nature 443, 193 (2006) John Teufel, unpublished



Tom Purdy JILA 19

Signal Beam Optical Power ( W)

Pos

ition

Unc

erta

inty

As

mea

sure

d by

the

Sig

nal B

eam

Approaching the Standard Quantum Limit


Thermal Motion

SQL 1

10

1 10

20

3

2

1

0

(2,2) mode – well coupled

(4,4) mode – poorly coupled

Signal Beam Power 0


Tom Purdy JILA 21

Recoil motion

1

10

100

0.01 0.1 1 10 100

Thermal Motion

Quantum Measurement of Light


Quantum Noise Cancellation

1. Membrane senses signal beam intensity fluctuations 2. Meter beam reads out membrane displacement 3. Active feedback cancels signal beam intensity fluctuations

PD

PD PBS PBS

Meter Beam

Signal Beam

Intensity Modulator

Amp

FFG ,

Sept. 9, 2013 Frontiers in Nanomechanics Tom Purdy JILA 22

Wiseman and Milburn, PRA, 49:1350 (1994) Mancini and Wiseman, J. of Opt. B, 2:260 (2000) See also Haroche group Cavity QED work


PD

PD PBS PBS

Meter Beam

Signal Beam

Intensity Modulator

Amp

FFG ,

1.2

1.1

1.0

0.9

0.8

1.52 1.51 1.50

8

6

4

2

0 1.52 1.51 1.50

(rel

ativ

e to

shot

noi

se) Meter Beam Signal Beam

23

Feedback ON

Feedback OFF



(Electronic Gain)

1.1

1.0

0.9

0.8 1 10 100

R=2.6 R=1.3 R=0.7

3

2

1

0 100 50 0

Signal Beam Power ( W)

R

RPSN to Thermal Force Ratio

Tom Purdy JILA 25

1.0

0.8

0.6

1.0

0.8

0.6

1.0

0.8

0.6

1.56 1.54 1.52 1.50

0.6

1.0

0.8

a

Self-Squeezing of Light

Purdy, et al., PRX, in press (2013) arXiv:1306.1268 Safavi-Naeini, et al., Nature 500, 185 (2013) Brooks, et al., Nature 488, 476 (2012)

Optical Frequency

Tran

smis

sion

Tom Purdy JILA 26

0.8

0.6

0.4

0.2

0.0

60 40 20 0

Thermal Noise

Quantum Efficiency

b

1.0


Purdy, et al., PRX, in press (2013) arXiv:1306.1268 Safavi-Naeini, et al., Nature 500, 185 (2013) Brooks, et al., Nature 488, 476 (2012)

Optical Frequency

Tran

smis

sion


1.2

1.1

1.0

0.9

0.8

2.5 2.0 1.5 1.0

(rel

ativ

e to

shot

noi

se)

(1,1) (1,2) (2,2)

(1,3) (2,3) (2,4)

(3,4) (1,5)

(2,5)


inI

inQ

outQ

inI

outI

rXXX

XX

Nonlinear Optics: Complex Kerr Medium Self Phase Modulation Squeezed Light

quadrature phase

quadratue amplitude

Q

I

X

X

sincos QI XXX

1

.5

2

5

0 90 180

Phase Space Distribution

28

)(sin)(Im2)()2sin()(Re1)()( 22* rrrXXS

Shot Noise

Self-Squeezing of Light Nonlinear Optics: Complex Kerr Medium

Amplitude Phase

29

Tom Purdy JILA 30


kHz kHz


31

Building Better Mechanical Resonators

asymmetric modes

are dipole-like. Radiate more, lower Q

The membrane acts as an acoustic radiatior. Energy is dissipated when the radiated waves encounter lossy boundary.

I. Wilson-Rae, et al., PRL (2011) P.-L. Yu, T. P. Purdy, and C. A. Regal, PRL (2012)

symmetric modes are quadrupole-like (or higher order).

Radiate less, higher Q

(3,3)

(1,3)


Building Better Mechanical Resonators Eliminate acoustic radiation

Wilson-Rae, et al., PRL 106, 047205 (2011) Yu et al., PRL 108, 083603 (2012)

Acoustic radiation shield at GHz: J. Chan et al., APL (2012) Painter Group

Qext > 108

High

low

Mechanical D

isplacement (log scale)

Qext ~ 106


Building Better Mechanical Resonators Driven

displacemen

t (m) Acoustic

Band Gap

Phononic Crystal Bare Substrate

Frequency (kHz)

Work in progress: Measuring band gaps


Conclusions

• Optomechanics experiments in a strong measurement regime

1. Observe radiation pressure shot noise 2. Create squeezed light

• This resource is useful to: 1. Avoid measurement backaction using

squeezed light 2. Perform microwave ↔ optical state

transfer at the single quanta level

The Regal Optomechanics Lab: Bob Peterson Ben Yu Nir Kampel Alec Jenkins Cindy Regal Electromechanics Collaborators: JILA: Reed Andrews Konrad Lehnert NIST: Kat Cicak Ray Simmonds John Teufel

Acknowledgements

Research Funded by: NSF, DARPA, ONR


quantum measurement in an optomechanical...

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