Quantum mechanics on giant scales

Transcription

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

2 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

3 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 h GW h GW! L " L ~ 10 # 21 "

4 GW detector at a glance Mirrors hang as pendulums Quasi-free particles Respond to passing GW Filter external force noise! L " hgw L # 21 " 10 $ 4000 # 18 ~ 10 meters 4 km 20 kw Optical cavities Mirrors facing each other Builds up light power 10 W Lots of laser power P Signal! P Noise! P

5 WA LIGO: Laser Interferometer Gravitational-wave Observatory 4 km 3030 km (±10 ms) MIT Caltech NSF LA 4 km

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

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

8 Origin of the Quantum Noise Vacuum fluctuations

9 Quantum states of light! Heisenberg Uncertainty Principle X 1 and X 2 associated with amplitude and phase! Coherent state (laser light)! Squeezed state! Two complementary observables! Make on noise better for one quantity, BUT it gets worse for the other X 1 X 2

10 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 Laser X % X 1 Shot Arbitrarily noise limited below! X (number shot of noise photons) 1/2 % X % Vacuum fluctuations Squeezed vacuum X 1

11 Quantum Enhancement Squeezed state injection

12 Squeezing injection in Advanced LIGO Laser GW Detector SHG Squeezing OPO source Squeeze Source GW Signal Faraday isolator Homodyne Detector

13 Advanced LIGO with squeeze injection Radiation pressure Shot noise

14 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

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

16 Squeezing injection in a prototype interferometer 2.9 db or 1.4x 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)

17 Radiation pressure The other side of the quantum optical coin

18 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

19 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 N " kt B eff Colder oscillator!& eff Stiffer oscillator

20 Reaching the quantum limit in macroscopic mechanical oscillators! Large inertia requires working at lower frequency (& osc! 1/!M osc )! To reach B kt N " "!& 1! For small '-oscillator & osc = 10 MHz and T = 0.5 mk! For larger objects & osc = 1 khz and T = 50 nk below room temperature!

21 Mechanical vs. optical forces! Mechanical forces # thermal noise! Stiffer spring (& m ") # larger thermal noise! More damping (Q m #) # larger thermal noise! Optical forces do not affect thermal noise spectrum S F ( m 4 B m k T Q & Fluctuation-dissipation theorem Connect a high Q, low stiffness mechanical oscillator to a stiff optical spring # DILUTION True for any non-mechanical force ( non-dissipative or cold force ), e.g. gravitation, electronic, magnetic

22 The optical spring effect and optical trapping of mirrors

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

24 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 radiationpressure exerts a restoring force on mirror! Time delay in cavity response introduces a viscous anti-damping force x P

25 Optical springs and damping 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 Anti-restoring Cavity cooling Damping Restoring Optical spring Anti-damping

26 Classical Experiments Extreme optical stiffness Stable optical trap Optically cooled mirror

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

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

29 External vibration isolation 10 W, frequency and intensity stabilized laser

30 ! 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 Extreme optical stiffness Displacement / Force 5 khz $K = 2 x 10 6 N/m Cavity optical mode # diamond rod Phase increases $ unstable Frequency (Hz)

31 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 P c /P sc = 20! Independently control spring constant and damping Stable! T. Corbitt et al., Phys. Rev. Lett 98, (2007)

32 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, (2007)

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

34 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 = T eff = 6.9 mk N = 10 5 T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, (2007)

35 Quantum measurement in gravitational wave detectors

36 Even bigger, even cooler! Initial LIGO detectors much more sensitive # operate at 10x above the standard quantum limit SQL! 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

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

38 Cooling the kilogram-scale mirrors of Initial LIGO T eff = 1.4 'K N = 234 T 0 /T eff = 2 x 10 8 M r ~ 2.7 kg ~ atoms & osc = 2 ) x 0.7 Hz LIGO Scientific Collaboration

39 Other cool oscillators

40 NEMS # 10 #12 g Some other cool oscillators Toroidal microcavity # 10 #11 g Micromirrors # 10 #7 g AFM cantilevers # 10 #8 g SiN 3 membrane # 10 #8 g LIGO # 10 3 g Minimirror # 1 g

41 Next steps Marching on toward the quantum limit

42 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

43 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

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

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

46 end mirror (1 gm) 10 kw Present status laser source 1 W input mirror (250 gm) BS squeezed light (vacuum)

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

48 Present status 4x Scattered light?

49 Closing remarks

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

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

52 LIGO Quantumness SQL N = 234 N = 1

53 And now for the most important part

54 Cast of characters MIT! 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

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