a gravitational wave interferometer at 5ghz l. piccirillo, g. pisano – jodrell bank a.m.cruise –...
TRANSCRIPT
A Gravitational Wave Interferometer at 5GHz
L. Piccirillo, G. Pisano – Jodrell Bank
A.M.Cruise – Birmingham
• Strong science cases- well understood technology– Pulsar timing ~10-8 Hz – LISA/DECIGO 10-4 – 10-2 Hz – Advanced LIGO 102 – 5×103 Hz
• Emerging science cases- new technology– Microwave Frequencies 108 – 1010 Hz– IR and Optical Frequencies 1012 – 1015 Hz
First Detections?
Gravitational Wave Frequency Ranges
Cardiff - 12 Jul 2011 2Lucio Piccirillo - AMALDI 9 & NRDA
• Early Universe– Garcia-Bellido, Easther, Copeland, Leblond, etc
• Kaluza-Klein modes from Black Holes in 5-D gravity– Seahra, Clarkson and Maartens, Clarkson and
Seahra
• EM-GW mode conversion in magnetised plasmas– Servin and Brodin
Possible Sources at Very High Frequencies ?
See poster by Cruise, Pisano and PiccirilloCardiff - 12 Jul 2011 3Lucio Piccirillo - AMALDI 9 & NRDA
• Laser interferometers lose sensitivity as increases
• Use Graviton to Photon conversion in B Field
• De Logi and Mickelson (1977)
• Cross section for g
Graviton, g
Virtual Photon( Static Magnetic Field , B)
Photon,
3
228
c
LGBSpin states of g, B and
Detector Possibilities
B is magnetic field, L is path length
Cardiff - 12 Jul 2011 4Lucio Piccirillo - AMALDI 9 & NRDA
• Cross Section is small due to G/c3 factor but this is per incoming graviton
• Flux of gravitons is large due to c2/G factor
• Signal Power is
22 2 1
16 gwgw
cPhoton Flux h
G
2 2 2 2 2
0
1
8EMW gwP B L K h cSin
What are the fluxes ?
Cardiff - 12 Jul 2011 5Lucio Piccirillo - AMALDI 9 & NRDA
Conversion GW e.m waves
Inverse-Gertsenshtein effect
Cardiff - 12 Jul 2011 6Lucio Piccirillo - AMALDI 9 & NRDA
• Need smart transducer
GW EMW waveguides LNA detection
• With EMW’s. we can use standard interferometric
techniques
• Correlation receiver for a single baseline GW
detector
Conversion GW e.m waves
Cardiff - 12 Jul 2011 7Lucio Piccirillo - AMALDI 9 & NRDA
Instrument angular-acceptance/beam
• First tests at Birmingham create EMW’s completely inside
single mode waveguide- simple geometry
• New detector requires GW-EMW conversion outside
modified waveguide and at many anglesCardiff - 12 Jul 2011 8Lucio Piccirillo - AMALDI 9 & NRDA
New instrument concept
Conversion volume
g – waves e.m.- waves
Collectionpart
Detectionpart
single-mode RF
Magnets & waveguideWaveguide
taper
Cryo LNA
Correlator
Cardiff - 12 Jul 2011 9Lucio Piccirillo - AMALDI 9 & NRDA
Collection part
Single-modeoutput
Conversion volume
Collection part
Finite-element e.m. modelling (HFSS)
MagnetsStandard single mode waveguide
Tall waveguide
Plane-waves / modesfrom different
directions in input
Cardiff - 12 Jul 2011 10Lucio Piccirillo - AMALDI 9 & NRDA
New Detector
• Partial list of problems:– Conversion plane-wave waveguide modes– Waves from different directions Mismatch with the
main waveguide mode– Gradient of e.m. intensity along conversion volume– Magnetic field projection effects– Difference in waveguide phase-velocity– Multiple reflections inside the waveguide structure– Etc…
Cardiff - 12 Jul 2011 11Lucio Piccirillo - AMALDI 9 & NRDA
Angular-acceptance: Modes mismatch
Incident radiation from different directions
Variable response with angle and frequency
5.00 GHz5.25 GHz
Cardiff - 12 Jul 2011 12Lucio Piccirillo - AMALDI 9 & NRDA
GW Correlation Receiver
Correlator
• Sensitivity increase• Narrower beam in the z direction• …
Cardiff - 12 Jul 2011 13Lucio Piccirillo - AMALDI 9 & NRDA
20 K
LIA
LIA
900LPF
LPF
PS1
PS2
LO 7GHz
BPF
BPF
VideoAmp.
VideoAmp.
PS waveform generator
IN1
IN2
Cryo LNAC-band (5 GHz)
RC cos
RC sin
Re Im
USB (LO + Si)(12 GHz)
LSB (LO - Si)(2 GHz)
LO (7 GHz)
Signal Si
(5 GHz)
LPF BPF
IF1
IF2
Correlation receiver circuitry
Cardiff - 12 Jul 2011 14Lucio Piccirillo - AMALDI 9 & NRDA
X
s s
antennab
)cos(2 tVV ])(cos[1 gtVV
2/])2cos()[cos(21 gg tVV
2/)]/2cos([2/])cos([ 2121 cVVVVR gc sb
multiply
average
A small (but finite) frequency width, and no motion. Consider radiation from a small solid angle d, from direction s.
Cosine output
Correlation receiverB’ham/M’cr GW prototype experiment
cg /sb
Cardiff - 12 Jul 2011 15Lucio Piccirillo - AMALDI 9 & NRDA
Synthesizing beams…
Transit of a point-like source
Cardiff - 12 Jul 2011 16Lucio Piccirillo - AMALDI 9 & NRDA
Sensitivity ( Provisional )
Cardiff - 12 Jul 2011 17Lucio Piccirillo - AMALDI 9 & NRDA
Ideas for the (not so distant) future
• Amplifier is the low noise element (HEMT is state of the art)• Amplifiers have an intrinsic noise limit (Tmin = hν/k) due to uncertainty principle• Bolometric detectors (thermal detectors) are classical detectors and not limited by quantum mechanics• Bolometric interferometry (adding interferometry) can improve the minimum noise by a substantial factor (at least 1 order of magnitude)
Bolometric interferometry will allow to explore the 10 GHz – 1 THz GW region with aperture synthesisCardiff - 12 Jul 2011 18Lucio Piccirillo - AMALDI 9 & NRDA
Conclusion
• In addition to the obvious sources at LIGO and LISA frequencies there may be GW radiation at microwave although the sources are speculative
• The prototype detectors using the graviton to photon conversion are relatively cheap to build
• The Jodrell – Birmingham collaboration is studying the design a single baseline interferometer operating at 5GHz.
• The aim is to design and build an aperture synthesis array for Microwave Frequencies GWs
• The detector will locate sources in the sky
Cardiff - 12 Jul 2011 19Lucio Piccirillo - AMALDI 9 & NRDA
Thank you!
Questions?
• We generate the ‘sine’ pattern by inserting a 90 degree phase shift in one of the signal paths.
X
s s
antennab
cg /sb
)cos(2 tVV ])(cos[1 gtVV
2/])2sin()[sin(21 gg tVV
2/)]/2sin([2/])sin([ 2121 cVVVVR gs sb
multiply
average
90o
Making a SIN correlator
Cardiff - 12 Jul 2011 21Lucio Piccirillo - AMALDI 9 & NRDA
We now define a complex function, V, to be the complex sum of the two independent correlator outputs:
where
This gives us a relationship between the source brightness, and the response of an interferometer:
This expression can be inverted to recover I(s) from V(b).
iSC AeiRRV
C
S
SC
R
R
RRA
1
22
tan
dsIiRRV ciSC e /2)()( sbb
Define the Complex Visibility
Cardiff - 12 Jul 2011 22Lucio Piccirillo - AMALDI 9 & NRDA
• Formally identical to single baseline radio interferometer
• Stable, low-noise solution
• Re-use existing radio hardware at Jodrell Bank
• Multiply the two GW detector outputs
• The averaged signal is independent of the time t, but is dependent on the lag, g – a function of direction – and hence on the distribution of the brightness.
• To determine the dependence of the response over an extended object, we integrate over solid angle.
dcIRC )/2cos()( sbs
Correlation receiverB’ham/M’cr GW frequency detector
Cardiff - 12 Jul 2011 23Lucio Piccirillo - AMALDI 9 & NRDA