gravity, precision measurements and squeezed states of...

Gravity, precision measurements and squeezedstates of light.

Eugeniy E. Mikhailov

The College of William & Mary

April 20, 2007

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 1 / 45

Outline

1 History of gravityNewton’s lawsEinstein’s lawsA bit of astrophysics

2 DetectorsGravitational wave interferometer

3 Quantum OpticsWhat is quantum opticsSqueezed states of lightQuadrature measurements with squeezed lightTools for squeezing

4 Squeezing and interferometers

5 Squeezing experiments

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 2 / 45

Newton’s laws

Laws of motion and law of gravitationsolved problems of astronomy andterrestrial physics.

eccentric orbitstidesperturbation of moon orbit due to sun

Unified the work of Galileo, Copernicusand Kepler.Did not explained precession of Mercuryorbit

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 3 / 45

Einstein’s laws

The General Theory of Relativity andtheory of Gravity (1916)

No absolute motionthus only relative motionSpace and time are not separatethus four dimensional space-timeGravity is not a force acting at adistancethus warpage of space-time

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 4 / 45

General relativity

A geometric theory connecting matter to spacetimeMatter tells spacetime how to curveSpacetime tells matter how to move

important predictionsLight path bends in vicinity of massive object→ confirmed in 1919Gravitational radiation (waves)→ confirmed indirectly in 1974

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 5 / 45

Indirect observation of gravitational wave

Emission of gravitational radiation from pulsar PSR1913+16 leads toloss of orbital energy

orbital period decreased by 14sec from 1975 to 1994measured to 50 msecaccuracydeviation grows quadraticallywith time

Nobel prize in 1997 Taylor and Hulse

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 6 / 45

Gravitational waves (GW)

Predicted by the General Theory of RelativityGenerated by aspherical mass distributionInduce space-time ripples which propagatewith speed of lightNew tool for astrophysics

GW stretch and squeeze space-time thus move freely floating objects

∆L

L

Strain - strength of GW

h =∆LL

(1)

typical strain

h ∼ 10−21 (2)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 7 / 45

Astrophysical sources of GW

Coalescing compact binariesobjects: NS-NS, BH-NS, BH-BHphysics regimes: Inspiral, merger,ringdown

Periodic sourcesspinning neutron stars (pulsars)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 8 / 45

Astrophysical sources of GW (cont)

Burst eventsSupernovae with asymmetriccollapse

Stochastic backgroundright after Big Bang(t = 10−43 sec)continuum ofsources

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 9 / 45

Astrophysics with GWs vs. E&M

E&M (photons)Space as medium for fieldAccelerating chargeAbsorbed, scattered,dispersed by matter10 MHz and upLight = not dark (but >95% ofUniverse is dark)

GWSpacetime itself ripplesAccelerating aspherical massVery small interaction; matteris transparent10 kHz and downRadiated by dark massdistributions

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 10 / 45

New view to the universe

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 11 / 45

Typical strain

L∆

Proton

Two neutron starwith a mass of 1.4 solar masses eachorbiting each other with a frequency f = 400 Hzat a distance 2R = 20 kmwould generate strain h ∼ 10−21

at distance equal to 1023 m(distance to the Virgo cluster)For 4 km base line that would correspond to∆L thousand times smaller than size of proton.

Detection of GW is difficult problem

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 12 / 45

GW acting on matter

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 13 / 45

Interferometric Measurement

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 14 / 45

World wide network of detectors

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 15 / 45

Laser Interferometer Space Antenna (LISA)

Three spacecraft in triangular formationseparated by 5 million kmFormation trails Earth by 20◦

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 16 / 45

Laser Interferometer Gravitational-wave Observatory

L = 4 kmh ∼ 10−21

∆L ∼ 10−18 m∆φ ∼ 10−10 rad

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 17 / 45

LIGO sensitivity goal and noise budget

Displacement noiseseismicthermal suspensionthermal Brownianradiation pressurenoise

Detection noiseelectronicsshot noise

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 18 / 45

LIGO sensitivity, S1-S4 runs

Inspiral search range during S4 was 8MpcEugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 19 / 45

LIGO sensitivity, S5 run, June 2006

10 100 1000 10000Frequency [Hz]

1e-24

1e-23

1e-22

1e-21

1e-20

1e-19

1e-18

1e-17

1e-16h[

f], 1

/Sqr

t[H

z]

LHO 4km - (2006.03.13) S5: Binary Inspiral Range (1.4/1.4 Msun) = 14.5 MpcLLO 4km - (2006.06.04) S5: Binary Inspiral Range (1.4/1.4 Msun) = 15.1 MpcLHO 2km - (2006.06.18) S5: Binary Inspiral Range (1.4/1.4 Msun) = 7.4 MpcLIGO I SRD Goal, 4km

Strain Sensitivity for the LIGO InterferometersS5 Performance - June 2006 LIGO-G060293-02-Z

Inspiral search range during S5 is 14MpcEugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 20 / 45

Upgrade

GoalsFactor of 15 increase insensitivityinspiral range from 20 Mpc to350 MpcFactor of 3000 in event rateOne day > entire 2-year initialdata runQuantum-noise-limitedinterferometer

Howbetter seismic isolationdecreasing thermal noisehigher laser power

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 21 / 45

Limiting noise - Quantum Optical noise

Next generation of LIGO (advanced LIGO) will bequantum optical noise limited at almost all detection frequencies.

shot noiseUncertainty in number ofphotons

h ∼√

1P

(3)

radiation pressure noisePhotons impart momentum tomirrors

h ∼√

PM2f 4 (4)

There is no optimal light power to suit all detection frequency.Optimal power depends on desired detection frequency.

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 22 / 45

Limiting noise - Quantum Optical noise

Next generation of LIGO (advanced LIGO) will bequantum optical noise limited at almost all detection frequencies.

shot noiseUncertainty in number ofphotons

h ∼√

1P

(3)

radiation pressure noisePhotons impart momentum tomirrors

h ∼√

PM2f 4 (4)

There is no optimal light power to suit all detection frequency.Optimal power depends on desired detection frequency.

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 22 / 45

Limiting noise - Quantum Optical noise

Next generation of LIGO (advanced LIGO) will bequantum optical noise limited at almost all detection frequencies.

shot noiseUncertainty in number ofphotons

h ∼√

1P

(3)

radiation pressure noisePhotons impart momentum tomirrors

h ∼√

PM2f 4 (4)

There is no optimal light power to suit all detection frequency.Optimal power depends on desired detection frequency.

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 22 / 45

Limiting noise - Quantum Optical noise

Next generation of LIGO (advanced LIGO) will bequantum optical noise limited at almost all detection frequencies.

shot noiseUncertainty in number ofphotons

h ∼√

1P

(3)

radiation pressure noisePhotons impart momentum tomirrors

h ∼√

PM2f 4 (4)

There is no optimal light power to suit all detection frequency.Optimal power depends on desired detection frequency.

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 22 / 45

What is quantum optics

Classical/Geometrical opticslight is a raywhich propagates straightcannot explain diffraction and interference

Semiclassical opticslight is a wavecolor (wavelength/frequency) is importantamplitude (a) and phase are important, E(t) = aei(kz−ωt)

cannot explain residual measurements noiseQuantum optics

light consists of photons: N = a†adetector measures quadratures: X1 = a† + a and X2 = i(a† − a)

amplitude and phase cannot be measured precisely:⟨∆X 2

1⟩ ⟨

∆X 22⟩≥ 1

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 23 / 45

Quantum noise

Simple photodetector

NV

V ∼ N

∆V ∼√

N

Balanced photodetector

−

50/502N

N

N

V

V = 0

∆V ∼√

N

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 24 / 45

Quantum noise

Simple photodetector

NV

V ∼ N

∆V ∼√

N

Balanced photodetector

−

50/502N

N

N

V

V = 0

∆V ∼√

N

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 24 / 45

Heisenberg uncertainty principle and its opticsequivalent

Heisenberg uncertainty principle∆p∆x ≥ ~/2The more precisely the POSITION is determined,the less precisely the MOMENTUM is known,and vice versa

Optics equivalent∆φ∆N ≥ 1The more precisely the PHASE is determined,the less precisely the AMPLITUDE is known, andvice versa

Optics equivalent strict definition⟨∆X 2

1⟩ ⟨

∆X 22⟩≥ 1

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 25 / 45

Heisenberg uncertainty principle and its opticsequivalent

Heisenberg uncertainty principle∆p∆x ≥ ~/2The more precisely the POSITION is determined,the less precisely the MOMENTUM is known,and vice versa

Optics equivalent∆φ∆N ≥ 1The more precisely the PHASE is determined,the less precisely the AMPLITUDE is known, andvice versa

Optics equivalent strict definition⟨∆X 2

1⟩ ⟨

∆X 22⟩≥ 1

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 25 / 45

Heisenberg uncertainty principle and its opticsequivalent

Heisenberg uncertainty principle∆p∆x ≥ ~/2The more precisely the POSITION is determined,the less precisely the MOMENTUM is known,and vice versa

Optics equivalent∆φ∆N ≥ 1The more precisely the PHASE is determined,the less precisely the AMPLITUDE is known, andvice versa

Optics equivalent strict definition⟨∆X 2

1⟩ ⟨

∆X 22⟩≥ 1

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 25 / 45

Squeezed states of lightUnsqueezed state

Phase squeezed state

Amplitude squeezed state

Squeezed state at π/6 angle

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 26 / 45

Quadrature measurements with unsqueezed light

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 27 / 45

Quadrature measurements with phase squeezed light

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 28 / 45

Quadrature measurements with amplitude squeezedlight

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 29 / 45

Quadrature measurements with light squeezed at π/6angle

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 30 / 45

Tools for squeezing

ω ω2ω

ab

b

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 31 / 45

Tools for squeezing

ω ω2ω

ab

b

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 31 / 45

Tools for squeezing

ω ω2ω

ab

b

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 31 / 45

Two photon squeezing picture

Squeezingresult of correlation of upper and lower sidebands

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 32 / 45

Squeezer appearance

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 33 / 45

Squeezer appearance

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 33 / 45

Squeezer appearance

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 33 / 45

Squeezing and interferometer

Vacuum input

laser

Squeezed input

laser

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 34 / 45

Squeezing and interferometer

Vacuum input

laser

Squeezed input

laser

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 34 / 45

Squeezing and interferometer

Vacuum input

laser

Squeezed input

laser

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 34 / 45

Interferometer sensitivity improvement with squeezingTable top demonstrationPioneered by M. Xiao, L. Wu,and H. J. KimblePhys. Rev. Lett. 59, 278-281 (1987)

Kirk McKenzie et. al.Phys. Rev. Lett. 88, 231102 (2002)The Australian National University

Projectedadvanced LIGO sensitivity

T. Corbitt et.al.Phys. Rev. D 70, 022002(2004) MIT

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 35 / 45

Requirements to squeezer

squeezing at low frequency (10Hz - 10kHz)frequency dependent quadrature (angle) of squeezingstability (long time of operation)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 36 / 45

Fundamental limits for squeezing in non-linear crystalsOptical parametric oscillator (OPO)

ω ω2ω

ab

b

δa = −(i∆a + γa)δa + ε∗bδa† + δNa + ε∗aδb − i aδ∆a + a∗bδε∗ (5)

Noise sources in nonlinear squeezingClassical noise

environment noiseseismic noiseacoustic noise

electronics noise

Quantum noiseseed noise δalosses δNa

pump noise δbphotothermal noise

detuning noise δ∆aphasematching noise δε

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 37 / 45

Fundamental limits for squeezing in non-linear crystalsOptical parametric oscillator (OPO)

ω ω2ω

ab

b

δa = −(i∆a + γa)δa + ε∗bδa† + δNa + ε∗aδb − i aδ∆a + a∗bδε∗ (5)

Noise sources in nonlinear squeezingClassical noise

environment noiseseismic noiseacoustic noise

electronics noise

Quantum noiseseed noise δalosses δNa

pump noise δbphotothermal noise

detuning noise δ∆aphasematching noise δε

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 37 / 45

Fundamental limits for squeezing in non-linear crystalsOptical parametric oscillator (OPO)

ω ω2ω

ab

b

δa = −(i∆a + γa)δa + ε∗bδa† + δNa + ε∗aδb − i aδ∆a + a∗bδε∗ (5)

Noise sources in nonlinear squeezingClassical noise

environment noiseseismic noiseacoustic noise

electronics noise

Quantum noiseseed noise δalosses δNa

pump noise δbphotothermal noise

detuning noise δ∆aphasematching noise δε

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 37 / 45

Fundamental limits for squeezing in non-linear crystalsOptical parametric oscillator (OPO)

ω ω2ω

ab

b

δa = −(i∆a + γa)δa + ε∗bδa† + δNa + ε∗aδb − i aδ∆a + a∗bδε∗ (5)

Noise sources in nonlinear squeezingClassical noise

environment noiseseismic noiseacoustic noise

electronics noise

Quantum noiseseed noise δalosses δNa

pump noise δbphotothermal noise

detuning noise δ∆aphasematching noise δε

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 37 / 45

Fundamental limits for squeezing in non-linear crystalsOptical parametric oscillator (OPO)

ω ω2ω

ab

b

δa = −(i∆a + γa)δa + ε∗bδa† + δNa + ε∗aδb − i aδ∆a + a∗bδε∗ (5)

Noise sources in nonlinear squeezingClassical noise

environment noiseseismic noiseacoustic noise

electronics noise

Quantum noiseseed noise δalosses δNa

pump noise δbphotothermal noise

detuning noise δ∆aphasematching noise δε

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 37 / 45

Fundamental limits for squeezing in non-linear crystalsOptical parametric oscillator (OPO)

ω ω2ω

ab

b

δa = −(i∆a + γa)δa + ε∗bδa† + δNa + ε∗aδb − i aδ∆a + a∗bδε∗ (5)

Noise sources in nonlinear squeezingClassical noise

environment noiseseismic noiseacoustic noise

electronics noise

Quantum noiseseed noise δalosses δNa

pump noise δbphotothermal noise

detuning noise δ∆aphasematching noise δε

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 37 / 45

Squeezed vacuum vs squeezed light pro and contra

squeezed vacuum: a → 0

noise∆a

noise∆

∆a

a

∆a

Prominimal possible seed noisedecoupled from pump noiseangle

Contrano coherent amplitudehard to lock

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 38 / 45

Squeezed vacuum vs squeezed light pro and contra

squeezed vacuum: a → 0

noise∆a

noise∆

∆a

a

∆a

Prominimal possible seed noisedecoupled from pump noiseangle

Contrano coherent amplitudehard to lock

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 38 / 45

Squeezed vacuum vs squeezed light pro and contra

squeezed vacuum: a → 0

noise∆a

noise∆

∆a

a

∆a

Prominimal possible seed noisedecoupled from pump noiseangle

Contrano coherent amplitudehard to lock

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 38 / 45

Setup photo

Laserλ = 1064 nmpower 700 mW

Green pumppower 200 mW

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 39 / 45

Squeezing level vs time (unlocked)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 40 / 45

GW 40m detector and squeezer

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 41 / 45

GW 40m detector with 4dB of squeezed vacuum

Signal to noise improvement by factor of 1.43

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 42 / 45

Cavity parameters with squeezing

Nd:YAGLASER SQZ

NL Servo

PDH Servo

SA

FI

BS

S

PZT2

PZT1HD1

HD2 PD

OC2

EOMAOM

OC1

TESTCAVITY

6 8 10 12 14 16

-2

0

2

4

6

Frequency (MHz)

Quad

ratu

re Va

ria

nce

w.r.t. Shot Nois

e (dB

)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 43 / 45

Cavity parameters with squeezing

Nd:YAGLASER SQZ

NL Servo

PDH Servo

SA

FI

BS

S

PZT2

PZT1HD1

HD2 PD

OC2

EOMAOM

OC1

TESTCAVITY

6 8 10 12 14 16

-2

0

2

4

6

Frequency (MHz)

Quad

ratu

re Va

ria

nce

w.r.t. Shot Nois

e (dB

)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 43 / 45

Cavity parameters with squeezing

Nd:YAGLASER SQZ

NL Servo

PDH Servo

SA

FI

BS

S

PZT2

PZT1HD1

HD2 PD

OC2

EOMAOM

OC1

TESTCAVITY

6 8 10 12 14 16

-2

0

2

4

6

Frequency (MHz)

Quad

ratu

re Va

ria

nce

w.r.t. Shot Nois

e (dB

)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 43 / 45

Cavity parameters with squeezing

Nd:YAGLASER SQZ

NL Servo

PDH Servo

SA

FI

BS

S

PZT2

PZT1HD1

HD2 PD

OC2

EOMAOM

OC1

TESTCAVITY

6 8 10 12 14 16

-2

0

2

4

6

Frequency (MHz)

Quad

ratu

re Va

ria

nce

w.r.t. Shot Nois

e (dB

)

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 43 / 45

Low frequency squeezing with light free noise lock

-96

-95

-94

-93

-92

-91

-90

-89

-88

100 1000 10000

Noi

se (

dBm

)

Freq (Hz)

Noise vs frequency (cavity locked by 10kHz modulation)

shot noisesqueezing

MIT, 2006

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 44 / 45

People

LIGO team40m Interferometer team

Osamu MiyakawaQuantum measurements group in MIT

Nergis Mavalvala (group leader)Crystal squeezers

Keisuke Goda (graduate student)

Eugeniy MikhailovEugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 45 / 45

Summary

Gravitational waves are a purely classical effectTheir detection requires precise measurements at thesub-quantum levelUse of quantum optics is the way to reach sub-quantumsensitivities

Eugeniy Mikhailov (W&M) Gravity and precision measurements AMO seminar April 20, 2007 46 / 45