Detecting Gravitational Waves with Superconducting Cavities

 Warren Schappert

TD/SRF 

FermilabTuesday, September 22, 2015

10:30 am

Curia II (WH2SW)

2

Laser Vibrometry for ILC Cryomodules• In 2007 the TD/I&C department was

tasked to measure vibrations of the quadrupole in the first ILC type cryomodule, CM1

• Spec <1 nm

• Considered two different types of sensors

• Geophones are low-cost (~$50) nm level vibration sensors but measure only velocity

• Laser vibrometers can directly measure displacement but are much more expensive (>$20k)

Vibration Measurements (Animesh Jain, BNL);http://agenda.linearcollider.org/event/4562/session/9/contribution/18/material/slides/0.pdf

Research Techniques Seminar – September 22, 2015 3

Limits Interferometer Sensitivity• Most commercially available displacement

sensitive interferometers are limited to precisions of 0.1 m/Hz1/2

• for example by gain mismatches between the two phase measurement channels

http://resources.renishaw.com/en/details/white-paper-homodyne-and-heterodyne-interferometry--5653

4

LIGO• The most sensitive

interferometer extant is LIGO

• Gravitational wave detector with facilities in Hanford,WA and Livingston, LA

• Michelson interferometer with 4km long arms

• Displacement sensitivity of 10-18 m

http://www.ligo.org/multimedia/gallery/lho.php

5

Gravitational Radiation• Gravitational radiation predicted by

General Relativity• Ripples in the curvature of space-time that

propagate as tensor waves

• Indirect evidence in seen in decay rate of binary pulsars by Hulse and Taylor

• No direct observation of gravitational waves to date

https://en.wikipedia.org/wiki/Gravitational_wave

Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other

6

Detecting Gravitational Waves

• Distortion of space-time curvature induced by gravity waves leads to oscillations of a ring of test masses arranged in a circle in a plane transverse to the direction of propagation

• Two possible polarizations• GW waves may be detected if the

exquisitely small induced strains can be measured

7

The Birth of GW Detection• Early claims of direct detection using a

resonant bar detector by Weber have been discredited but his work sparked interest in the field

http://www.nytimes.com/2000/10/09/us/joseph-weber-dies-at-81-a-pioneer-in-laser-theory.html

''He is regarded universally as the father of this field of gravitational wave detection,'' said Dr. Kip Thorne, a professor of theoretical physics at the California Institute of Technology. ''Joe embarked on this in an era when nobody else in the world was thinking about these things.''

http://www.physics.umd.edu/GRE/GWdetect.htm

8

The LIGO Interferometer• Michelson interferometer

• 4km arms• 6W Nd YAG Laser (1064 nm) • Fabry-Cavity in each arm to increase

sensitivity

• Gravitational wave should cause relative extension/contraction of the two arms leads to relative phase shift

• Imperfect cancellation at the null port should result in a signal modulated at two times the frequency of the gravitational wave

9

LISA Satellite Interferometer

• Proposed long base-line interferometer on-board satellites

• Cancelled by NASA in 2011 due to funding

• $2.4B total cost

• LISA Pathfinder scheduled for launch in November 2015

• Single spacecraft with one of the LISA/eLISA interferometer arms shortened to about 38 cm, so that it fits inside a single spacecraft

10

Interferometer Sensitivity Limits

• LIGO has published extensive comparisons of measured detector noise to predictions that include a variety of noise sources

• Fundamental physical limit at high frequencies from shot noise

11

Interferometer Shot Noise Sensitivity

• Given the photon wavelength, input power, and mean photon lifetime in the detector, calculating the shot-noise sensitivity limit is straightforward

• Dimensionless strain limit can be re-expressed in terms of the noise and the loaded quality factor of the cavities in the interferometer arms

• QL normally interpreted in terms of fractional energy loss per cycle

• QL can equally be interpreted as phase advance of over the mean photon lifetime in the apparatus

• Leads to a very simple physical picture can be used as a basis for comparison of candidate GW detectors

𝜑𝑆𝑁=√ h𝑐𝜆𝑃h𝑆𝑁=𝜑𝑆𝑁

𝜆2𝜋 𝐵𝐿

Dimensionless Strain Sensitivity

Shot Noise

Bounce Factor 𝑐2𝜋 𝐵𝐿

=1

4 𝜋𝜏

h𝑆𝑁=12

𝜑𝑆𝑁

𝑄𝐿

Equivalent Strain Sensitivity in Terms of QL

Loaded Cavity Quality Factor 𝑄𝐿=𝜔𝜏

http://pages.uoregon.edu/rayfrey/intro/coyne95.pdf)

⟨𝜑 ⟩= ⟨∫𝜔𝑑𝑡 ⟩=𝜔𝜏=𝑄𝐿𝛿𝜑

An SRF Interferometer as a GW Detector?• Example

• Mach-Zender interferometer with single-cell 1.3 GHz SRF cavities in each arm

• Modest cavity operating parameters

• NOT an optimized GW detector design

• Strawman intended only to evaluate the feasibility of the concept

• Direct microwave analog of LIGO• GW radiation causes relative

contraction and expansion of the two arms

• Differential phase shift leads to non-null signal at output port

SRF Cavity

SRF Cavity

Null Port∆

∑Combiner

Power Port

SplitterAmplifier

13

Shot Noise Sensitivity Comparison• Very different operating regimes

• Frequency: x10-5

• QL: x10-3

• : x103

• Shot noise limit not so different (x30)

• SRF cavity operating parameters selected for reasons that will be justified later

• Longer SRF cavity lifetime will reduce the sensitivity for GW frequencies above 1 Hz

Physical ConstantsSpeed of Light/c (m/s):                       3e+008Planck Constant/hbar (m^2.kg/s):           1.05e-034                                                  SRF        LIGOCavity ParametersFrequency (Hz):                             1.3e+009   2.82e+014Wavelength (m):                                0.231   1.06e-006Q_L:                                          1e+010    1.7e+012Effective Length (m):                           0.01      4e+003Cavity Impedance (Ohms):                         116         377Half Bandwidth (Hz):                           0.065        82.8Mean Photon Lifetime (s):                       1.22    0.000961 Power ParametersInput Power (W):                              0.0631         4.5Input Power (dBm):                                18        36.5Recycling Gain:                                    1          60Reactive Power (W):                        1.45e+010   1.22e+005Stored Energy (J):                             0.485        1.63Gradient (MV/m):                                6.77        16.5Output Power (W):                             0.0631         270 Shot NoisePhoton Energy (J):                         8.62e-025   1.87e-019Number of Photons in the Cavity:           5.63e+023   8.73e+018Output Photons per Second:                 7.32e+022   1.45e+021Output Fractional Shot Noise (Hz^(-1/2)):   3.7e-012   2.63e-011Mean Photon Integrated Phase (radians):       1e+010    1.7e+012Shot Noise Strain Sensitivity Limit:        3.7e-022   1.55e-023

High Q SRF Cavities

• Extensive research on high Q SRF cavities• CERN

• Nb Film Sputtered on Cu• Cornell

• Pure Nb with HF rinsing• Fermilab

• Pure Nb with N doping

• Intrinsic quality factors, Q0, of 2x1010 up 1012 can be achieved at moderate gradients

• Lower heat load will improve stability

• Operating with QL 109 -1010 should be quite very feasible

• ~1-10 Hz upper limit on frequency of gravitation radiation

Superconducting niobium cavities, a case for the film technologyhttp://www.sciencedirect.com/science/article/pii/S0168900201001656

Nb Sputtered on CuSingle Cell 1.5 GHz TM010

15

Microwave Phase Noise Measurement Limits• LIGO can measure phase

differences to between 10-9 and 10-11 rad/Hz1/2

• Current limits to real-time microwave phase noise measurements comparable (Rubiola): 10-9 rad/Hz1/2 with 18dBm input signals

• “obtained in a relatively unclean electromagnetic environment, and without using a shielded chamber”

• Room for further improvement according to authors Enrico Rubiola∗ Vincent Giordano†

Advanced bridge (interferometric) phase and amplitude noise measurements;

Review of Scientific Instruments vol. 73 no. 6 pp. 2445–2457, June 2002;

http://arxiv.org/pdf/physics/0503015.pdf

16

Sub-Hz Gravitational Sources?

Nicholas Hunter JonesNovel Approaches to Newtonian Noise Suppression in Interferometric

Gravitational Wave Detectionhttp://dspace.mit.edu/bitstream/handle/1721.1/65529/746874370-MIT.pdf?sequence=2

• Frequency band below 10 Hz contains numerous potential sources of gravitational radiation

• In-spirals of black-hole and white-dwarf binaries expected to emit at levels well above LIGO sensitivity limits but coalesce before they emit a frequencies in the LIGO frequency band

• LISA which would have been sensitive to low-frequency GW radiation was cancelled

17

Component Noise Sources• Shot noise is a fundamental physical

limit but other noise sources may dominate in particular bands

• LIGO 4-stage pendulum isolation system limits sensitivity at GW frequencies below 10Hz

• Seismic noise expected to be much less important for a compact SRF interferometer

• Depends strongly on how the cavities are mounted

• Phase noise expected to dominate at low frequencies

• Estimates based on Rubiola’s papers

• Calculations have not been checked independently

18

Cavity Stability

• Relative frequency stability of cavities over periods of 0.1 and 1000 seconds will be critical to successful detection

• Relative detuning could wash out any gravitational signal

• Superconducting Cavity Stabilized Oscillator• 8.6 GHz Nb cavity• Q0>1011 at 1.2K• “In the laboratory, it is possible to reduce the temperature-

induced fractional frequency drift to df/f =10-18“ (absolute NOT relative)

• Mechanical mounting is critical• “ Early versions of the cavities were supported at their ends,

leading to a significant acceleration sensitivity. If a cavity is supported at its mid-plane, however, the effect can be reduced substantially.”

• 10 nK temperature control

19

Towards an Optimized GW Detector Design

• SRF interferometer described here is NOT intended to represent an optimized GW design

• Strawman intended only to evaluate the feasibility of the concept

• Numerous options to be optimized for performance• Cavity type• Number of cavities• Physical orientation• Operating frequency• RF mode• Operating temperature• Wall thickness• Material• Mechanical mounting and support structure• RF system• …

20

Limits to Terrestrial Detection

• Review by B.F. Schutz (1997 Alpbach Summer School) emphasizes the difficulty of overcoming terrestrial backgrounds at GW frequencies below 1 Hz.

• Recent PRD article describes 3 proposed detectors (MANGO) with dimensionless sensitivities of 10-20 Hz-

1/2 or better at 0.1 Hz• Emphasize the technical challenges are

considerablePHYSICAL REVIEW D 88, 122003 (2013)

Low-frequency terrestrial gravitational-wave detectorsJan Harms,1 Bram J. J. Slagmolen,2 Rana X. Adhikari,3 M. Coleman Miller,4,5 Matthew

Evans,6

Yanbei Chen,7 Holger Mu¨ ller,8 and Masaki Ando9,10

21

Capital and Operational Costs

• Cost of a SRF microwave interferometer is expected to be relatively modest when compared to laser interferometers (~$300M/yr) or satellite missions (>$1B)

• Fermilab VTS operational budget of ~1M/yr provides a benchmark for comparison

• Low cost opens the possibility of multiple detectors at various locations around the country or around the world

• Cross-correlations of data from different detectors could be used to enhance signals and suppress noise

22

Spatio-Temporal Spectral Analysis• Variety of spectral estimation techniques that

may be used to improve sensitivity, directivity and rejection of unwanted signals, MVDR, Linear Prediction, Maximum Entropy, Adaptive Beamforming, Super-resolution, STAP, MUSIC…

• May be applied in either the spatial or time domain• Common in military applications (sonar, radar)• Now finding use in cellular base stations

• Related techniques are (almost certainly) being employed for GW detection in the time domain

• Multiple detectors would allow use of these techniques in the spatial domain as well THE USE OF ADAPTIVE ARRAYS FOR WIRELESS BASE STATION

Hung Nguyen

23

MVDR Beamforming

Though the MVDR/Capon beamformer can achieve better resolution than the conventional (Bartlett) approach, but this algorithm has higher complexity due to the full-rank matrix inversion. Technical advances in GPU computing have begun to narrow this gap and make real-time Capon beamforming possible. [1]

Conventional (Bartlett) beamformer[edit]The Bartlett beamformer is a natural extension of conventional spectral analysis (spectrogram) to the sensor array. Its spectral power is represented by

The angle that maximizes this power is an estimation of the angle of arrival.

MVDR (Capon) beamformer[edit]The Minimum Variance Distortionless Response beamformer, also known as the Capon beamforming algorithm, has a power given by

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6570524

24

Pound-Drever-Hall

• Pound-Drever-Hall technique routinely used to lock lasers to optical cavities

• Including LIGO

• Based on techniques developed by Pound in the 1950s

• Frequency modulation of drive signal induces side bands

• Magnitude and phase symmetry of the sidebands can be used to monitor the cavity frequency with very high precision

• May provide an alternative approach to interferometry

25

SRF Cavities at Fermilab• Since Helen Edwards first became involved

with the superconducting TESLA collider collaboration in the 1990s Fermilab has made a major investment in superconducting RF technology

• Capabilities and facilities here can only be matched at a handful of other institutions around the world

• DESY, JLab, KEK, Argonne, Cornell, BNL…

• Fermilab TD has the expertise and facilities to take a raw sheet of niobium and turn it into a high performance superconducting cavity V. Yakovlev, Division Head's Programmatic Internal Self assessment of TD-SRFD Department

26

SRF GW Detectors

• CERN group built SRF detector using two coupled cavities as a parametric oscillator

• Two coupled cavities with two modes

• Excite one mode• GW will transfer energy into

second mode

27

Summary I

• Sensitivity limit of an interferometer to dimensionless strain is determined by the ratio of the phase noise at the null port of the to the loaded quality factor of the cavities in the interferometer arms

• Microwave cavities can achieve Q0s approaching 1011 or better.• Microwave phase noise can be measured to 10-9 rad/Hz1/2 or better in real time

• Sensitivity of a SRF microwave interferometer will most likely be limited by vibration and temperature/pressure stability of the cavities rather than any fundamental physical limit (e.g. shot noise)

• Mid-term (0.1s to 1000s) frequency stability of 10-18 will be EXTREMELY challenging• Level has already been demonstrated in SCSO cavities

• But it will still be EXTREMELY challenging

28

Summary II

• SRF interferometer will be sensitive to lower frequency (<10 Hz) GW radiation than large laser detectors

• Compact size of a SRF interferometer eliminates need for mirror isolation systems required by large laser interferometers together with the attendant low frequency noise

• Upper frequency limit will be determined by the mean photon lifetime (1-10 Hz)• Low frequency limit will likely be determined by terrestrial backgrounds (>0.1 Hz)

• Relatively modest expected capital and operating costs (~1M/yr/interferometer) may open possibility of deploying multiple detectors

• Data from multiple devices might be cross-correlated to extend the low frequency limit for example

29

Summary IV• Physics case for such a device is unquestionable if the technical challenges can be met

• Numerous interesting GW sources expected the 0.1 to 10 Hz range• Band is not covered by current terrestrial or planned space-borne detectors

• Some of the most daunting technical challenges (e.g. 10-18 frequency stability) have already been met elsewhere (e.g SCSO)

• Difficulties will still be considerable and must not be underestimated• Strong physics case justifies a strong effort to meet those challenges

• Further progress on will require a much more structured effort

• Fermilab is uniquely positioned to construct and operate such a device• Huge investment at FNAL in SRF technology over the last twenty years

• TD/SRF extensive experience with cavity design, processing, operation• AD/LLRF experts in low-phase noise RF electronics

• Only a handful of other institutions, (DESY, JLab, KEK, Cornell, Argonne..) have comparable capabilities

• If this concept can be developed to fruition it may offer an opportunity to leverage some of the SRF investment to address one of the outstanding fundamental questions of experimental physics

30

Acknowledgements

• I would like to thank everyone that have provided insight, guidance and assistance including

• Vyatcheslav Yakovlev• Aaron Chou• Brian Chase• Dmitri Sergatskov• Dave Harding• Timergali Khabibouline• Yuriy Pischalnikov• Jermiah Holzbauer