Quantum mechanics on giant scales Quantum nature of light Quantum states of mirrors Nergis Mavalvala @ Ithaca College, December 2008

Quantum vs. Classical World Quantum theory was proposed to explain the microscopic world of atoms Classical mechanics Exact measurement  particles located at a single, well-defined position Continuous energy levels Quantum mechanics Intrinsic uncertainty in measurement  particles has probability of being somewhere Discrete energy levels

A quantum mechanical oscillator Quantum mechanics 1 Particle in a harmonic potential well with simple and familiar Hamiltonian But there is no experimental system as yet that requires a quantum description for a macroscopic mechanical oscillator Potential energy of form kx2 Energy En = (n+½) ħω n = 3 n = 2 n = 1 n = 0 E0 = ½ħω x

Macroscopic oscillators in the quantum regime Useful for making very sensitive position or force measurements Gravitational wave detectors Atomic force microscopes Explore the quantum-classical boundary on all size scales Ground state cooling Direct observation of quantum effects Superpositions Entanglement Decoherence Tools for quantum information systems

Reaching the quantum limit in mechanical oscillators The goal is to measure non-classical effects with large objects like the (kilo)gram-scale mirrors The main challenge  thermally driven mechanical fluctuations Need to freeze out thermal fluctuations Zero-point fluctuations remain One measure of quantumness is the thermal occupation number Want N  1 Colder oscillator Stiffer oscillator

Reaching the quantum limit in macroscopic mechanical oscillators Large inertia requires working at lower frequency (Wosc  1/√Mosc) To reach N = 1 Small m-oscillator  Wosc = 10 MHz and T = 0.5 mK Large object  Wosc = 1 kHz and T = 50 nK 1010 below room temperature !

TRAPPING COOLING Cooling and Trapping Two forces are useful for reducing the motion of a particle A restoring force that brings the particle back to equilibrium if it tries to move Position-dependent force  SPRING A damping force that reduces the amplitude of oscillatory motion Velocity-dependent force  VISCOUS DAMPING TRAPPING COOLING

Mechanical forces Mechanical forces come with thermal noise Stiffer spring (Wm ↑)  larger thermal noise More damping (Qm ↓)  larger thermal noise

Optical forces do not introduce thermal noise Laser cooling Reduce the velocity spread Velocity-dependent viscous damping force Optical trapping Confine spatially Position-dependent optical spring force

A whole host of tricks for atoms and ions (or a few million of them) Cooling and trapping A whole host of tricks for atoms and ions (or a few million of them) Magneto-Optic Traps (MOTs) Optical molasses Doppler cooling Sisyphus cooling (optical pumping) Sub-recoil limit Velocity-selective coherent population trapping Raman cooling Evaporative cooling

1997 Nobel Prize in Physics Steven Chu, Claude Cohen-Tannoudji and William D. Phillips for their developments of methods to cool and trap atoms with laser light This year's Nobel laureates in physics have developed methods of cooling and trapping atoms by using laser light. Their research is helping us to study fundamental phenomena and measure important physical quantities with unprecedented precision.

What about larger objects? Optical trapping of mirrors

Cavity length or laser wavelength Optical cavities Light storage device Two mirrors facing each other Interference  standing wave Intracavity power Cavity length or laser wavelength

How to make an optical spring? Radiation pressure force Detune a resonant cavity to higher frequency (blueshift) Change in cavity mirror position changes intracavity power Change in radiation-pressure exerts a restoring force on mirror Time delay in cavity response introduces a viscous anti-damping force x P

Radiation pressure rules! Experiments in which radiation pressure forces dominate over mechanical forces Opportunity to study quantum effects in macroscopic systems Observation of quantum radiation pressure Generation of squeezed states of light Quantum state of the gram-scale mirror Entanglement of mirror and light quantum states Classical light-oscillator coupling effects en route Optical cooling and trapping Light is stiffer than diamond

Classical Experiments Extreme optical stiffness Stable optical trap Optically cooled mirror

Experimental cavity setup 10% 90% 5 W Optical fibers 1 gram mirror Coil/magnet pairs for actuation (x5)‏

Experimental Platform Seismically isolated optical table Vacuum chamber 10 W, frequency and intensity stabilized laser External vibration isolation

Extreme optical stiffness 5 kHz K = 2 x 106 N/m Cavity optical mode  diamond rod Very stiff, but also very easy to break Maximum force it can withstand is only ~ 100 μN or ~1% of the gravitational force on the 1 gm mirror Replace the optical mode with a cylindrical beam of same radius (0.7mm) and length (0.92 m)  Young's modulus E = KL/A Cavity mode 1.2 TPa Compare to Steel ~0.16 Tpa Diamond ~1 TPa Single walled carbon nanotube ~1 TPa Displacement / Force Phase increases  unstable Frequency (Hz)

Supercold mirrors Toward observing mirror quantum states

Optical cooling with double optical spring (all-optical trap for 1 gm mirror) Increasing subcarrier detuning T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf and N. Mavalvala, Phys. Rev. Lett 98, 150802 (2007)

Optical spring with active feedback cooling Experimental improvements Reduce mechanical resonance frequency (from 172 Hz to 13 Hz) Reduce frequency noise by shortening cavity (from 1m to 0.1 m) Electronic feedback cooling instead of all optical Cooling factor = 43000 Teff = 6.9 mK N = 105 Mechanical Q = 20000 Cooling factor larger than mechanical Q because Gamma = Omega_eff/Q. The OS increases Omega but doesn’t affect Gamma (OS is non-mechanical), so Q must increase to keep Gamma constant. T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, 160801 (2007)

Some other cool oscillators Toroidal microcavity  10-11 g NEMS  10-12 g AFM cantilevers  10-8 g Micromirrors  10-7 g SiN3 membrane  10-8 g NEMs capacitively coupled to SET (Schwab group, Maryland (now Cornell) Kippenberg group (Munich) Harris group (Yale) Bouwmeester group (UCSB) Aspelmeyer group (Vienna) LIGO-MIT group LIGO LIGO  103 g Minimirror  1 g

In the (near?) future: Observable quantum effects

Radiation pressure rules! Experiments in which radiation pressure forces dominate over mechanical forces Opportunity to study quantum effects in macroscopic systems Observation of quantum radiation pressure Quantum state of the gram-scale mirror Generation of squeezed states of light Entanglement of light and mirror quantum states Classical light-oscillator coupling effects en route Optical cooling and trapping Light is stiffer than diamond

Quantum states of light Classical light

Quantum states of light Coherent state (laser light) Squeezed state Two complementary observables Make on noise better for one quantity, BUT it gets worse for the other X1 and X2 associated with amplitude and phase uncertainty X1 X2

Quantum Noise in an Interferometer Caves, Phys. Rev. D (1981) Slusher et al., Phys. Rev. Lett. (1985) Xiao et al., Phys. Rev. Lett. (1987) McKenzie et al., Phys. Rev. Lett. (2002) Vahlbruch et al., Phys. Rev. Lett. (2005) X1 X2 Laser X1 X2 Arbitrarily below shot noise Shot noise limited  (number of photons)1/2 X1 X2 X1 X2 Squeezed vacuum Vacuum fluctuations

How to squeeze photon states? Need to simultaneously amplify one quadrature and de-ampilify the other Create correlations between the quadratures Simple idea  nonlinear optical material where refractive index depends on intensity of light illumination

Radiation pressure: Another way to squeeze light Create correlations between light quadratures using a movable mirror Amplitude fluctuations of light impart fluctuating momentum to the mirror Mirror displacement is imprinted on the phase of the light reflected from it

Radiation pressure: Another way to squeeze light Create correlations between light quadratures using a movable mirror Amplitude fluctuations of light impart fluctuating momentum to the mirror Mirror displacement is imprinted on the phase of the light reflected from it

A radiation pressure dominated interferometer Key ingredients Two identical cavities with 1 gram mirrors at the ends High circulating laser power Common-mode rejection cancels out laser noise Optical spring effect to suppress external force (thermal) noise

Squeezing Squeezing 7 dB or 2.25x T. Corbitt, Y. Chen, F. Khalili, D.Ottaway, S.Vyatchanin, S. Whitcomb, and N. Mavalvala, Phys. Rev A 73, 023801 (2006)

Closing remarks

Classical radiation pressure effects Stiffer than diamond 6.9 mK Stable OS Radiation pressure dynamics Optical cooling 10% 90% 5 W ~0.1 to 1 m Corbitt et al. (2007)

Quantum radiation pressure effects Wipf et al. (2007) Entanglement Squeezing Mirror-light entanglement Squeezed vacuum generation

In conclusion MIT experiments in the extreme radiation pressure dominated regime have yielded several important classical results Extreme optical stiffness  few MegaNewton/m Stiff and stable optical spring  optical trapping of mirrors Optical cooling of 1 gram mirror  few milliKelvin Established path toward quantum regime where we expect to observe radiation pressure induced squeezed light, entanglement and quantum states of very macroscopic objects

And now for the most important part…

Cast of characters MIT Collaborators Timothy Bodiya Thomas Corbitt Sheila Dwyer Keisuke Goda Nicolas Smith Christopher Wipf Eugeniy Mikhailov Edith Innerhofer David Ottaway Sarah Ackley Jason Pelc MIT LIGO Lab Collaborators Yanbei Chen Caltech MQM group Stan Whitcomb Daniel Sigg Rolf Bork Alex Ivanov Jay Heefner Caltech 40m Lab Kirk McKenzie David McClelland Ping Koy Lam Helge Müller-Ebhardt Henning Rehbein http://web.mit.edu/physics/graduate/current/curdocguide.html

Thanks to… Our colleagues at Funding from LIGO Laboratory The LIGO Scientific Collaboration Funding from Sloan Foundation MIT National Science Foundation

The End