Antoine HeidmannPierre-François Cohadon, Tristan Briant

Pierre Verlot, Alexandros Tavernarakis, Chiara Molinelli, Aurélien Kuhn

Quantum Physics with MirrorsQuantum Physics with Mirrors

Towards quantum opto-mechanical systems…

1 – Use light to detect mechanical motion

2 – Couple light to mechanical motion via radiation pressure

Control quantum fluctuations of light

Laser cool a macroscopic systemdown to its ground state

Reach quantum limits induced by radiation pressure

Requires a very sensitive measurement of the recoil(and a very movable system)

First quantum optomechanical system in 1920?

Double-slit experiment

Does interferences disappear?

Experiment not done yet!Measure which path photon takes via recoil (due to radiation pressure)

Optical measurement of displacements

Laser telemetry: often used to measure car speed!

Robotics

Lunar laser ranging

…

Scientific applications:

Very sensitive interferometric measurement

Measurement of relative lengths of the 2 arms

Output intensity variation:

Gravitational waves generated by accelerated masses

Induce a deformation of space-time

Modification of distances between test masses

Example: detection of gravitational waves

Modification on Earth:

Example: detection of gravitational waves

• 3-4 km arms• 10 W incident power

Ligo, Virgo …

Detection of cataclysmic events (end of life of a binary system)

Example: detection of gravitational waves

Frequency (Hz)

Sens

itivi

ty(H

z-1/2

)

1 10 100 100010-24

10-23

10-22

Shot noise

Thermal noise of suspensions

Sismic noise

Thermal noiseof mirrors

Current sensitivity:

Detection of cataclysmic events (end of life of a binary system)

Two conjugate quantum noises:

Quantum noises in interferometers

• Laser noise (shot noise)• Mirror motion due to radiation pressure

Orders of magnitude: for 1 W

Radiation pressure force:

: fluctuating photon flux

Quantum noises in interferometers

Quantum limits in next generation of interferometers

Studies of quantum noise reduction

No experimental demonstration ofquantum radiation-pressure effects yet!

Two conjugate quantum noises:• Laser noise (shot noise)• Mirror motion due to radiation pressure

Cavity finesse Sensitivity

Movingmirror

Experimental test of radiation-pressure effects

Very sensitive optomechanical sensor based on a high-finesse cavity

Amplification of displacements by the cavity:

Quantum noises in an optomechanical sensor

Noises in the reflected phase:

Shot noise(incident phase noise) Thermal noise

of mirrors

Radiation pressure noise

Signal

An experimental challenge:

• High sensitivity (cavity finesse , incident power )• High mechanical response (frequency , mass , quality factor )• Low temperature

Towards high-finesse optomechanical systems

Gravitational interferometer mirrorHigh displacement sensitivity

Nanoresonator (Schwab 2004)High mechanical response

Mass ~ kgLength ~ km

Frequency ~ Hz

Mass ~ pgLength ~ nm

Frequency ~ GHz

Same (quantum) physics:• Quantum limits in measurement

(back-action effect)• Quantum optics experiments

(squeezing, QND measurement)• Mechanical systems in quantum regime

(ground state, entanglement, decoherence)

Internal vibration modes of cm-scale mirror

Micromirror (MEMS)

Mass ~ g to µgLength ~ mm

Frequency ~ MHz

1 mm

Quantum optics: QND measurement

A typical QND measurement with atoms:

• Signal beam intensity fluctuations modulate the effective length of the cavity• Phase of the meter beam monitors these fluctuations

(from Grangier et al., Nature 1998)

Possible quantum experiments:

A cavity with a moving mirror is equivalent to a cavity with a nonlinear medium

Optical length n(I )L ⇔ Physical length L(I )

• Squeezing• QND measurement

Experimental setup

Two beams are sent in the cavity:• Intensity fluctuations of the signal beam

drive the mirror into motion• Resulting displacements are monitored

by the meter beam phase

Intensity-phase optomechanical correlationsDirect manifestation of radiation-pressure-induced displacements

Experimental setup

Highly stabilized laser source, frequency locked onto the cavity resonance

Phys. Rev. Lett. 99, 110801 (2007)

A classical intensity noise mimics the quantum noise, so that

Experimental results: noises in phase space

Intensity signal noise:

Phase meter noise:

Strong correlations between the two trajectories

Observation of optomechanical correlations even forLevel equivalent to the one expected for quantum noise at low temperature

Non-demolition measurement

Conditional intensity distribution deduced from the phase measurement:

Initial intensity distribution Conditional distribution

Shrinking of the distribution:

Phys. Rev. Lett. (submitted 2008)

Use optomechanical coupling to reach the ground state of the mirror and observe its zero-point position fluctuations

Towards the quantum regime of a micromirror

• Observation of the residual quantum motion:

• Temperature requirement:

Cryogenic and laser cooling

Nanometric mechanical systems

K.C. Schwab, U. Maryland, 2004

A.N. Cleland, UCSB, 2003

High resonance frequencyup to 1 GHz

Cryogenic operationdown to ~ 50 mK

Capacitive detection

At room temperature, observation of sharp mechanical resonances

Micromirror displacements at the attometer level

Phys. Rev. Lett. 97, 133601 (2006)

At room temperature, observation of sharp mechanical resonances

Micromirror displacements at the attometer level

Phys. Rev. Lett. 97, 133601 (2006)

Frequency

Noi

se

anti-Stokes process Stokes process

Cooling Heating

Energy transfer between the optical mode and the mechanical mode by radiation pressure

Optomechanical scattering

Phonon absorption Phonon creation

Nature 444, 71 (2006)

Negative detuning:Enhancement of anti-Stokes process

Positive detuning:Enhancement of Stokes process

Laser cooling

Thermal noise spectrum

Cooling down to 10 K, heating up to 2000 K

Airy peak of the cavity

Related experiments

UCSB

MIT

Garching / Caltech

LKB

Munich Yale

Vienna

Cryogenic + laser cooling down to

Conclusion

• Optical measurement at the level• Observation of optomechanical correlations• Back-action effects in measurements,

laser cooling of micromirrors…

High-sensitivity optomechanical sensor are close to quantum limits

• Universal coupling from kg to ng systems

• Mechanical properties can be manipulated by light and vice versa

• Quantum regime of micromirrors:entanglement and decoherence of macroscopic objects

Coupling mechanical resonators with light