Cross-spectral measurement techniques for axion cavity searches

1. Faculty of science Cross-spectral measurement techniques for axion cavity searches stephenparkeR Workshop on Microwave Cavity Design for Axion Detection August 26th, 2015 Lawrence Livermore National Laboratory, USA

2. Outline • Fundamental principles of cross-correlation • Improving the resolution of thermal cavity noise spectrums with cross-correlation measurements • Cross-correlating two cavities in an axion/WISP search • Low & High frequency cavity-based axion searches Stephen.Parker@uwa.edu.au

3. Cross-Correlation Compute the cross-spectrum of two signalsUncorrelated signals are rejected Correlated signals are retained Generally deal with white noise. Built-in function of most VSA(FFT) Or digitizer devices No additional measurement time Stephen.Parker@uwa.edu.au

4. Taken from arXiv:1003.0113v1 Cross-Correlation Basic Schematic <YX*> <(C+B) x (C+A)*> <CC*> + <CA*> + <BC*> + <BA*> Stephen.Parker@uwa.edu.au

5. Cross-correlation: rejection of uncorrelated noise Basic experiment to demonstrate how uncorrelated noise is rejected. 2 nominally identical amplifiers Inputs terminated with 50 ohm loads Outputs recorded on 2 channels of FFT in frequency range outside of flicker noise regime Single channel spectrums and cross-spectrum recorded for different averages. 2 channels – noise is rejected proportional to rt(2m). But, typically measuring some DUT, power split by rt(2) between channels Limitation: isolation between the 2 channels. Stephen.Parker@uwa.edu.au

6. Cross-correlation: rejection of uncorrelated noise Single channel: Mean is constant Error (std-dev) scales with rt(m) Stephen.Parker@uwa.edu.au

7. Cross-correlation: rejection of uncorrelated noise Single channel: Mean is constant Error (std-dev) scales with rt(m) Cross-spectrum: Mean scales with rt(2m) Error (std-dev) is constant relative to mean Stephen.Parker@uwa.edu.au

8. Cavity enables resonant enhancement of converted photon signal. Measure power to constrain axion-2photon coupling. The Axion Haloscope – Quick Recap & Overview Excellent sensitivity (real discovery potential) Can reveal some astrophysics Relatively cheap ρa – Axion density ma – Axion mass B0 – Magnetic field strength V – Cavity volume C – Form factor (E.B overlap) Q – Cavity quality factor (or axion Q) Stephen.Parker@uwa.edu.au

9. Cavity thermal noise + Amplifier noise = measurement system noise Axion haloscope primary noise contributors PSD = + Frequency Assuming low noise L.O. & mixer Stephen.Parker@uwa.edu.au

10. Define our SNR / “figure of merit” SNR = m = number of averages Signal / S.D. In this context, reduction of level of systematic noise functionally equivalent to reducing overall statistical measurement error Stephen.Parker@uwa.edu.au

11. Improving resolution of intrinsic cavity noise Initial motivation - measuring intrinsic noise of cryogenic BAW quartz resonators Stephen.Parker@uwa.edu.au

12. Improving resolution of intrinsic thermal cavity noise - SNR Single channel haloscope SNR = If PA1 >> PC then equivalent to single channel haloscope SNR = … no SNR benefit, but enhanced resolution of cavity noise in spectrum Stephen.Parker@uwa.edu.au

13. Cross-spectrum “proof-of-concept” measurement setup Sapphire-loaded copper cavity resonators Resonance at 9.3 GHz Room temperature Q of ~50,000 Thermally anchored / controlled in vacuum chamber ~60 dB gain in each channel Mixer conversion efficiency ~11 V/rt(W) L.O. = Agilent E8257C Recorded on HP89410A Stephen.Parker@uwa.edu.au

14. A brief detour on mixer phase difference conditions Amplitude Sensitive V R.F. L.O. Phase Sensitive I.F. Δθ “Ideal” conditions… Characterize by injecting modulated signal Thermal noise should be equally distributed between phase and amplitude So cannot “further improve” on cross-spectrum rejection by having one channel phase sensitive and the other amplitude sensitive… …Of course, always check and optimize your measurement system. Stephen.Parker@uwa.edu.au

15. (1000 averages) Improving resolution of intrinsic cavity noise - measurements Single channel SNR ~ 25σ Stephen.Parker@uwa.edu.au

16. (1000 averages) Improving resolution of intrinsic cavity noise - measurements Single channel SNR ~ 25σ Cross-spectrum SNR ~ 32σ PC ~ PA1 (single channel has not accounted for power splitting) Stephen.Parker@uwa.edu.au

17. Effectively combine two cavity outputs (put that rt(2) to good use) Immediate amplification allows for cavities to be well separated (test coherence length) Cross-correlating two cavities Stephen.Parker@uwa.edu.au

18. Relative phase of the two measurement channels shouldn’t impact the cross-spectrum Maximum sensitivity for both resonant frequencies overlapped, but in principle can work with relative detuning in the form of an effective Q-factor: Cross-correlating two cavities – relative phase & frequency f2 = f1 (1+x/2) Stephen.Parker@uwa.edu.au

19. Cross-correlating two cavities – SNR SNR = Rt(2) improvement due to addition of second cavity volume How does this compare to standard power-combining… Stephen.Parker@uwa.edu.au

20. Briefly: Power-summing cavities … SNR = N cavities Stephen.Parker@uwa.edu.au

21. Cross-correlating two cavities – SNR comparison For PA1 >> PC comparison reduces to N (traditional approach scales up better) For PA1 ~ PC or PC > PA1 then cross-correlation improves (assuming N = 2) Stephen.Parker@uwa.edu.au

22. Cross-correlating two cavities – experimental setup Same environment and setup as before Pair of nominally identical sapphire-loaded copper cavity resonators 9.3 GHz / Q ~ 50,000 Thermally anchored / controlled in vacuum chamber Frequency-tuned to overlap by adjusting temperature control set-points. Stephen.Parker@uwa.edu.au

23. Cross-correlating two cavities – measurements Single channel SNR = 14σ Stephen.Parker@uwa.edu.au

24. Cross-correlating two cavities – measurements Single channel SNR = 14σ Cross-spectrum SNR = 20σ 20 / 14 ~ rt(2) Stephen.Parker@uwa.edu.au

25. Cross-correlating two cavities – measurements Fit to data points: Single-channel = 0.44*rt(m) Cross-spectrum = 0.46*rt(2m) Starting SNRs are “small” (less than 1) Stephen.Parker@uwa.edu.au

26. Cross-spectrum wrap-up Cross-correlation can be used to: Enhance resolution of intrinsic thermal cavity noise Effectively combine two spatially well-separated cavities, with possible SNR improvements if measurement system is limited by cavity noise Can be used to scrutinize candidate signals and test coherence length Stephen.Parker@uwa.edu.au

27. Low and High frequency cavity axion searches What equipment do we have lying around…

28. Equipment – Dilution Fridges Stephen.Parker@uwa.edu.au

29. Magnet & readout LNF Cryo HEMTS ~10 K Noise temp (15 – 29 GHz) SQUID amps around 10 MHz 2-channel digitizer Keysight U5303A 7 T Magnet (10 cm bore) Stephen.Parker@uwa.edu.au

30. Pushing frequency lower in fixed diameter - Prototype Low frequency lumped LC 3D Cavity Applications 1) Measure RF Permittivity of Samples (MWA / SKA). 2) Low frequency Axions?? We proposed in 2013/14 Advantage: Large tuning range Lower frequency Disadvantage: Lose sensitivity ~13 cm B field E field ~40 cm Stephen.Parker@uwa.edu.au

31. Re entrant Vol=6.3 x 10-7 m3 Vol=6.3 x 10-5 m3

32. Stephen.Parker@uwa.edu.au

33. A cavity-based search for 26.6 GHz (110 μeV) CDM axions WHY? Stephen.Parker@uwa.edu.au

34. A cavity-based search for 26.6 GHz (110 μeV) CDM axions Claim that multiple J-J experiments observe anomalous Shapiro steps that are consistent with being caused by axions with mass Ma = 110 +/- 2 μeV. Should be checked via independent dedicated experiment. Relatively narrow mass-range means cavities could be appropriate method. BUT Need to check for local galactic axion density of ρa ~ 0.05 GeV/cm3 (compared to the usual assumption of ~ 0.45 GeV/cm3) Can we push ahead with this right now? Stephen.Parker@uwa.edu.au

35. Big problems with standard approach: loss of cavity volume, increased amplifier noise or other amplifier problems Higher frequency cavity-based axion searches Brute force solution: Compensate for loss in volume at high frequencies by looking at multiple frequencies simultaneously. Alternative to power-summing at one frequency and dealing with keeping all the cavities frequency-tuned / locked We’ll need an acronym or two… Stephen.Parker@uwa.edu.au

36. micrOwave Resonator Group Axion coNvertor O.R.G.A.N. ORGAN PIPE micrOwave Resonator Group Axion coNvertor PathfInder ProjEct Start with 1 cavity… Stephen.Parker@uwa.edu.au

37. TM0x0 mode family provides best overlap for E.B Note that product of form factor * volume is ~constant for TM0x0 modes for a set frequency Cylindrical Copper Cavities C * V (fractional, relative to TM010) For TM020, a 2cm diameter gives 26.6 GHz TM0x0 Stephen.Parker@uwa.edu.au

38. Cavity Tuning To check the full error range of 26.6 GHz signal, need ~4% frequency tuning 26.1 – 27.1 GHz Want a simple tuning solution that can be implemented on a physically small cavity in cryogenic environment. Stephen.Parker@uwa.edu.au

39. Cavity Tuning – “Squiggle” motor 20 mm travel Stephen.Parker@uwa.edu.au

40. Unperturbed TM020 ~ 0.13 Cavity Tuning - COMSOL C Post position (mm) Frequency GHz (TM020) Post position (mm) Stephen.Parker@uwa.edu.au

41. Oxidisation due to slight coldhead helium leak Cryogenic system – quick show & tell Stephen.Parker@uwa.edu.au

42. Cross-spectrum techniques can be used to enhance intrinsic cavity noise measurements or “combine” 2 spatially well-separated cavities • Reentrant cavity to drop frequency for fixed diameter • Experiment under construction to check claim of axion signal at 110 μeV (26.6GHz). • Possible future expansion to look over wider mass range. Summary Acknowledgements Ben McAllister, Daniel Creedon, Ken Foo, Eugene Ivanov & Michael Tobar Stephen.Parker@uwa.edu.au