Quantum mechanics on giant scales Gravitational wave detectors Quantum nature of light Quantum states of mirrors Nergis Mavalvala @ UMass, March 2010

Outline Quantum limit in gravitational wave detectors Origins of the quantum limit EM vacuum fluctuations Interactions of light with mirrors Getting past the quantum limit Experiments Quantum optics Quantum optomechanics Necessary building blocks in the classical regime Progress toward the quantum regime

Gravitational waves (GWs) Prediction of Einstein’s General Relativity (1916) Indirect detection led to Nobel prize in 1993 Ripples of the space-time fabric GWs stretch and squeeze the space transverse to direction of propagation Emitted by accelerating massive objects Cosmic explosions Compact stars orbiting each other Stars gobbling up stars “Mountains” on stellar crusts 

GW detector at a glance Mirrors hang as pendulums Quasi-free particles Respond to passing GW Filter external force noise 4 km 20 kW Optical cavities Mirrors facing each other Builds up light power Lots of laser power P Signal  P Noise  10 W

LIGO: Laser Interferometer Gravitational-wave Observatory 3 k m ( ± 1 s ) MIT 4 km NSF Caltech LA 4 km http://ligo.mit.edu

Quantum noise in Initial LIGO Shot noise Photon counting statistics Radiation pressure noise Fluctuating photon number exerts a fluctuating force

Advanced LIGO Quantum noise limited Radiation pressure noise Stronger measurement  larger backaction Shot noise More laser power  stronger measurement

Origin of the Quantum Noise Vacuum fluctuations

Quantum states of light Heisenberg Uncertainty Principle 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 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) Goda et al., Nature Physics (2008) Radiation pressure noise Quantum fluctuations exert fluctuating force  mirror displacement X1 X2 Laser X1 X2 Shot noise limited  (number of photons)1/2 Arbitrarily below shot noise X1 X2 X1 X2 Vacuum fluctuations Squeezed vacuum

Quantum Enhancement Squeezed state injection

Squeezing injection in Advanced LIGO Laser GW Detector SHG Faraday isolator Squeezing source The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. ponderomotive squeezer. OPO Homodyne Detector Squeeze Source GW Signal

Advanced LIGO with squeeze injection Radiation pressure Shot noise

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

Squeezed state generation Vacuum (shot) Noise power (dBm/rtHz) Squeezed Dark Time (s) Frequency (Hz) Goda et al., Opt. Lett. (2008) Vahlbruch et al., New J. Phys. 9, 371 (2007)

Squeezing injection in a prototype interferometer K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K.McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008) 2.9 dB or 1.4x

Radiation pressure The other side of the quantum optical coin

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 ground state of the gram-scale mirror Entanglement of mirror and light quantum states Classical light-oscillator coupling effects en route (dynamical backaction) Optical cooling and trapping Light is stiffer than diamond

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 For small m-oscillator Wosc = 10 MHz and T = 0.5 mK For larger objects Wosc = 1 kHz and T = 50 nK 1010 below room temperature !

Mechanical vs. optical forces Mechanical forces  thermal noise Stiffer spring (Wm ↑)  larger thermal noise More damping (Qm ↓)  larger thermal noise Optical forces do not affect thermal noise spectrum Fluctuation-dissipation theorem Connect a high Q, low stiffness mechanical oscillator to a stiff optical spring  DILUTION Dilution – a fraction of the energy of the oscillator is stored in the optical field instead of in the elastic flexing of the wire, or in the acoustic modes The optical spring shifts the oscillator's resonant frequency while leaving its mechanical losses unchanged. The mechanical quality factor $Q_M$, as limited by those losses, is increased by the factor $\Omega_{\rmeff} / \Omega_M$, where $\Omega_M$ is the natural frequency of the free mechanical oscillator. We refer to this as ``optical dilution'', analogous to the phenomenon of ``damping dilution'' that accounts for the fact that the $Q$ of the pendulum mode can be much higher than the mechanical $Q$ of the material of which it is made~\cite{saulsonPRD1990,dilution}. This mitigation of intrinsic thermal noise is possible because a fraction of the energy is stored in the (noiseless) gravitational field. In the case of the pendulum, the dilution factor depends on the amount of elastic energy stored in the flexing wire compared to the energy stored in the gravitational field -- approximated by the ratio of the gravitational spring constant to the mechanical spring constant. Optical dilution accounts for the fact that thermal noise in our mechanical oscillator is reduced due to energy stored in the optical field (the optical spring force acts similar to the gravitational force). True for any non-mechanical force ( non-dissipative or “cold” force ), e.g. gravitation, electronic, magnetic

The optical spring effect and 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

Optical springs and damping Restoring Damping Anti-damping Anti-restoring Radiation pressure of light in an optical cavity  force on mirror Detune a resonant cavity to higher frequency (blueshift) Real component of optical force  restoring But imaginary component (cavity time delay)  anti-damping Unstable Can stabilize with feedback Cavity cooling Optical spring Blue shift (flaser > fcavity) optical spring Red shift (flaser < fcavity)  cavity cooling

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)‏

Multicolor optical cavity Two colors resonant at different (adjacent) orders Each can have arbitrary detuning Intracavity power Cavity length or laser wavelength

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 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)

Double optical spring  stable optical trap Two optical beams  double optical spring Carrier detuned to give restoring force Subcarrier detuned to other side of resonance to give damping force with Pc/Psc = 20 Independently control spring constant and damping Stable! T. Corbitt et al., Phys. Rev. Lett 98, 150802 (2007)

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)

Active feedback cooling Measure mirror displacement Filter displacement signal Feed it back to mirror as a force Controller PDH Laser Continuous measurement  measurement-induced decoherence EOM PBS QWP Continuous measurement  measurement-induced decoherence

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)

Quantum measurement in gravitational wave detectors

Even bigger, even cooler Initial LIGO detectors much more sensitive  operate at 10x above the standard quantum limit But these interferometers don’t have strong radiation pressure effects (yet)  no optical spring or damping Introduce a different kind of cold spring  use electronic feedback to generate both restoring and damping forces Cold damping ↔ cavity cooling Servo spring ↔ optical spring cooling SQL

Active feedback cooling + spring Measure mirror displacement Filter displacement signal Feed it back to mirror as a force Controller PDH Laser EOM PBS QWP

Cooling the kilogram-scale mirrors of Initial LIGO Teff = 1.4 mK N = 234 T0/Teff = 2 x 108 Mr ~ 2.7 kg ~ 1026 atoms Wosc = 2 p x 0.7 Hz LIGO Scientific Collaboration

Other cool oscillators

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

Next steps … Marching on toward the quantum limit

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 ground 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 (dynamical backaction) Optical cooling and trapping Light is stiffer than diamond

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

Classical noise, be vanquished Squeezed Vacuum fluctuations Two identical cavities with 1 gram mirrors at the ends Common-mode rejection cancels out laser 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)

Present status Blue curve = noise with 50 mW of input power and detuning = 1 Red line = noise level required to observe sqz and quant. rp with 5 W of input power

Thermal noise, be vanquished! All glass suspension Bonded with vacseal Glass fibers drawn in-house Large “ears” to isolate mirror from fiber bending point Many iterations on assembly and handling 18 hours

Present status 4x Scattered light?

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

LIGO Quantumness N = 234 SQL N = 1

And now for the most important part…

Cast of characters MIT Collaborators Thomas Corbitt Christopher Wipf Timothy Bodiya Sheila Dwyer Nicolas Smith Edith Innerhofer MIT LIGO Lab Collaborators Yanbei Chen and group Stan Whitcomb Daniel Sigg Rolf Bork Alex Ivanov Jay Heefner LIGO Scientific Collaboration

The End Gravitational wave detectors Quantum nature of light Quantum states of mirrors

Trapping and cooling Dynamic backaction cooling Stable optical trap with two colors Stiff! Stable! T. Corbitt et al., Phys. Rev. Lett 98, 150802 (2007)

Entanglement Two systems are entangled when their individual states cannot be recovered separately Correlate two optical fields by coupling to mechanical oscillator Quantum state of each light field not separable (determine by measuring density matrix) Quantify the degree of non-separability using logarithmic negativity Entanglement C. Wipf, T. Corbitt, Y. Chen, and N. Mavalvala, New J. Phys./283659 (2008)

Cavity cooling 200x 1012x Cornell,CU UCB