Laser interferometric gravitational wave detectors The search for the elusive wave Nergis Mavalvala (LIGO Scientific Collaboration) NYUAD, Jan 2010

Outline Gravitational waves (GWs) Sources Detectors (Sampling of) astrophysical searches Next generation detectors Confronting quantum measurement limits Detectors in space

Gravitational wave (GW) basics Gravitational Waves are a prediction of general relativity “Ripples in spacetime fabric” traveling at speed of light Stretch and squeeze the space transverse to direction of propagation Strain Emitted by aspherical accelerating masses Like tides  for objects that are free to move, GWs change lengths by fractional amounts Like tides  GWs change lengths by fractional amounts

Astrophysics with GWs vs. Light Very different information, mostly mutually exclusive Difficult to predict GW sources based on EM observations Light GW Accelerating charge Accelerating mass Images Waveforms Absorbed, scattered, dispersed by matter Very small interaction; matter is transparent 100 MHz and up 10 kHz and down

Astrophysical sources of GWs Ingredients Lots of mass (neutron stars, black holes) Rapid acceleration (orbits, explosions, collisions) Colliding compact stars Merging binaries Supernovae The big bang Earliest moments The unexpected GWs neutrinos photons now

Gravitational waves -- the Evidence Hulse & Taylor’s Binary Neutron Star System (discovered in 1974, Nobel prize in 1993) PSR 1913 + 16 Two neutron stars orbiting each other at 0.0015c Compact, dense, fast  relativistic system Emit GWs and lose energy Used time of arrival of radio pulses to measure change in orbital period due to GW emission Change in orbital period NS rotates on its axis 17 times/sec. Reaches periastron (minimum separation of binary pair) every 7.75 hours. Systematic variation in arrival time of pulses. Variation in arrival time had a 7.75 hour period  binary orbit with another star. Pulsar clock slowed when traveling fastest and in strongest part of grav field (periastron). Figure shows decrease in orbital period of 76 usec/year. Shift in periastron due to decay of orbit. Y-axis = change in orbital period relative to 1975 measurement Define periastron as measure of orbital period Exactly as predicted by GR for GW emission Years

In our galaxy (21 thousand light years away, 8 kpc) Strength of GWs Hulse-Taylor binary pulsar at the end of its lifetime (100 million years from now) In our galaxy (21 thousand light years away, 8 kpc) h ~ 10-18 In the Virgo cluster of galaxies (50 million light years away, 15 Mpc) h ~ 10-21 M r R

Interferometric detectors Laser Photodetector GW from space Laser Photodetector 1000 times smaller than the nucleus of an atom

Measurement and the real world How to measure the gravitational-wave? Measure the displacements of the mirrors of the interferometer by measuring the phase shifts of the light What makes it hard? GW amplitude is small External forces also push the mirrors around Laser light has fluctuations in its phase and amplitude

GW detector at a glance Seismic noise Ground motion (natural and anthropogenic) Vibration isolation 20 kW Thermal noise Vibrations due to finite temperature Low mechanical dissipation Shot noise Operate on dark fringe High circulating power 10 W

10 kg Fused Silica 25 cm diameter 10 cm thick < lambda/5000 over beam diameter

Some (small) numbers Sensitivity: 10-19 m/√Hz at 150 Hz 10-10 rad/√Hz at 150 Hz Actuation range: ~100 µm (tides) Stabilization of 4 km arms: 10-13 m rms Laser intensity noise (RIN): ≤10-8 /√Hz at 150 Hz Frequency noise: ≤ 3×10-7 Hz/√Hz at 150 Hz Angular Control: ≤ 10-8 rad rms Angular Sensing: 10-14 radians/√Hz at 40 Hz Input beam jitter: ≤4×10-9 rad/√Hz at 150 Hz Mechanical loss angle: suspension ≤10-6 optical coatings ≤10-4 substrate ≤10-6

Initial LIGO (2005 to 2007) Initial LIGO Seismic noise Thermal noise Ground vibrations Initial LIGO Thermal noise Damped pendulum Shot noise Photon counting SQL: h(f) = sqrt(8*hbar/M)/Omega/L Sounds – 200 Hz, 440 Hz, 1 kHz, 10 kHz Standard Quantum Limit

Global network of detectors GEO VIRGO LIGO TAMA AIGO LIGO Detection confidence Source polarization Sky location LISA

Gravitational-wave searches Instrument and data

Science runs and sensitivity 1st Science Run Sept 02 (17 days) S2 2nd Science Run Feb – Apr 03 (59 days) S3 3rd Science Run Nov 03 – Jan 04 (70 days) Strain (sqrt[Hz]-1) LIGO Target Sensitivity S5 5th Science Run Nov 05 onward (1 year integrated) S4 4th Science Run Feb – Mar 05 (30 days) Frequency (Hz)

Science runs and Sensitivity

Astrophysical searches Coalescence of binary compact objects (neutron stars, black holes, primordial BH) Core collapse supernovae Black hole normal mode oscillations Neutron star rotational instabilities Gamma ray bursts Cosmic string cusps Periodic emission from pulsars (esp. accretion driven) Stochastic background (incoherent sum of many sources or very early universe) Expect the unexpected! Transient Campanelli et al., Lazarus Project GWs neutrinos photons now High duty cycle

Sampling of current GW searches Stochastic Background

Cosmological GW Background 385,600 10-22 sec 10+12 sec Waves now in the LIGO band were produced 10-22 sec after the Big Bang WMAP 2003

Stochastic GW background What’s our Universe made of? Elements in the early Universe 10-5 10-6 Dark matter 23% Initial LIGO (2 year data) Atoms 4% Speculative structures (cosmic strings) 10-8 Energy density in GWs GWs ?? 10-9 Advanced LIGO (1 year data) S4 Sensitivity scales as sqrt(BW*T_int) for Omega, or fourth-root(BW*T_int) for strain. S5 Nature result = 6.9e-6 (Nature 460, 990-994, 2009) Dark energy 73% 10-13 Inflation f ~ 100 Hz

Example of current GW searches Binary Inspirals

Gamma-ray Bursts GRB 070201 Looked for a GW signal in LIGO Short, hard gamma-ray burst Consistent with being in M31 Leading model for short GRBs: binary merger involving a neutron star Looked for a GW signal in LIGO Searched for both inspiral and burst signals No plausible GW signal found Abbott et al., Ap. J 681, 1419 (2008) Conclusion: it was most likely an SGR giant flare in M31 Mazets et al., Ap. J 680, 545 (2008) Ofek et al., Ap. J 681, 1464 (2008) This is the improved position localization, using Konus-Wind, INTEGRAL and MESSENGER Leading model for short hard GRBs: binary merger involving a neutron star (found in giant elliptical galaxies, too old (> 5 Gyr to be supernovae). SHBs in non-star-forming region or gaint ellipticals which contain large population of LMXBs that accrete and merge. Core collapse in young, star forming regions. Significance of extragalactic SGR giant flares as origin of some short hard GRBs The LIGO result is mentioned in these papers as evidence against a merger Ofek et al.: “Given the properties of this GRB, along with the fact that LIGO data argue against a compact binary merger origin in M31, it is an excellent candidate to have been an extragalactic SGR giant flare…. However, we cannot rule out the possibility that it was a short-duration GRB in the background.” Mazets et al.: Title of paper (paraphrased) is: “A giant flare from an SGR in M31” IPN 3-sigma error region from Mazets et al., ApJ 680, 545

Search for Binary Inspirals Number of galaxies Distance (~50 Mly) Initial LIGO Sources Binary neutron stars (~1 – 3 Msun) Binary black holes (< 30 Msun) Primordial black holes (< 1 Msun) Search method Look for “chirps” Limit on rate at which NS are coalescing in galaxies like our own BBH BNS Here shown is inspiral range – averaged over all sky BNS inspiral horizon distance – two 1.4 Msun NS optimally oriented, SNR =8 For binary black hole searches the effective distance is for two 5 Msun BHs optimally oriented with SNR =8. 50 Mly is about 15 Mpc. So units of the Kalogera graph is distance to Virgo cluster. The S5 results are quoted in terms of blue solar luminosity, L_10. The MW has ~1.7*L_10. The rate of compact binary coalescences is expected to be proportional to be the blue light luminosity of a galaxy. L_10 is 10^10 times the blue solar luminosity. The S5 result is < 0.039 per year per L10 or 0.039*1.7 = 0.066 per year per MWEG. S5  R < 0.066 per year per MW-like galaxy 24 galaxies like our Milky Way S4

Next generation detectors Advanced LIGO

Ultimate limits ? Seismic gravity gradient When ambient seismic waves pass near and under an interferometric gravitational-wave detector, they induce density perturbations in the Earth, which in turn produce fluctuating gravitational forces on the interferometer’s test masses. Human gravity gradient The beginning and end of weight transfer from one foot to the other during walking produces the strongest human-made gravity-gradient noise in interferometric gravitational-wave detectors (e.g. LIGO). The beginning and end of weight transfer entail sharp changes (time scale τ∼20 msec) in the horizontal jerk (first time derivative of acceleration) of a person’s center of mass.

Beyond Initial LIGO Shot noise Quantum radiation pressure noise

Advanced LIGO improvements Seismic noise Active isolation system Mirrors suspended as fourth (!!) stage of quadruple pendulums Thermal noise Suspension  fused quartz; ribbons Test mass  higher mechanical Q material; more massive (40 kg) Optical noise Laser power  increase to ~200 W Optimized interferometer response  signal recycling

Origin of the Quantum Noise Vacuum fluctuations Quantum nature of light

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

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) 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

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? My favorite way A tight hug

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 Input Interferometer Laser GW Detector SHG Faraday isolator The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. an optical parametric oscillator. OPO Homodyne Detector Squeeze Source GW Signal

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 quantum noise Quantization of mirror states?

Optical cooling and trapping of mirrors Low mass movable mirror Detuned optical cavity with high circulating laser power Radiation pressure Restoring force (trap) Damping force (cool) Quantum states of mirrors Path to observing quantum states for mirrors

Optically trapped and cooled mirror Optical fibers 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. 1 gram mirror T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, Phys. Rev. Lett 99, 160801 (2007)

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

Space observatories LISA DECIGO

LISA (mid to late 2010’s)

Opportunities Most sensitive GW telescopes with user community of few 100 scientists Advanced LIGO has hardware (and software/pipeline) contributions from international partners R&D for third generation detectors needs to be done now Gravity gradients Underground observatories? Active cancellation? Optics and quantum nondemolition techniques High laser power systems (Non)linear optics Thermal noise mitigation Super-materials? Cryogenic operation The LIGO Scientific Collaboration: www.ligo.org

When the elusive wave is captured… Tests of general relativity Waves  direct evidence for time-dependent metric Black hole signatures  test of strong field gravity Polarization of the waves  spin of graviton Propagation velocity  mass of graviton Astrophysics Predicted sources: compact binaries, SN, spinning NS Inner dynamics of processes hidden from EM astronomy Dynamics of neutron stars  large scale nuclear matter The earliest moments of the Big Bang  Planck epoch Precision measurement below the quantum noise limit

The End

Photon counting statistics Radiation pressure noise Beyond initial LIGO Shot noise Photon counting statistics Radiation pressure noise Fluctuating photon number exerts a fluctuating force