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John Hartnett, Mike Tobar, Rhys Povey, Joerg Jaeckel The 5th Patras Workshop on Axions, WIMPs and WISPs DURHAM UNIVERSITY

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Michael E. Tobar ARC Australian Laureate Fellow School of Physics University of Western Australia, Perth Frequency Standards and Metrology Research Group Frequency Standards and Metrology Precision Microwave Oscillators and Interferometers: From Testing Fundamental Physics to Commercial and Space Applications

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High-Precision Oscillators, Clocks and Interferometers Generating and measuring frequency, time and phase at the highest precision Space

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Research Testing fundamental physics 1. Lorentz Invariance 2. Rotating cryogenic oscillator experiment 3. Odd parity magnetic MZ Interferometer experiment 4. Generation and detection of the Paraphoton Commercial Applications 1. Microwave Interferometer as a noise detector 2. Sapphire Oscillators (room temperature and cryogenic) Atomic Clock Ensemble in Space (ACES) Mission 1. Australian User Group 2. Long term operation of high precision clocks Astronomy 1. Cryogenic Sapphire Oscillators better than H-masers 2. With MIT, image black hole at the centre of the Galaxy 3. Within Australia -> SKA and VLBI timing

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Whispering Gallery modes WGE(H) mnp Vertically stacked TM 0np (n = 0,1; p = 0,1,2,3) Vertically stacked TE 0np (n = 0,1; p = 0,1,2,3) Vertically stacked

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WGE 16,0,0

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HEMEX Whispering Gallery Mode Sapphire resonator WGH 16,0,0 at 11.200 GHz

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Cavity mounted inside inner can

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19 11.83 copper nut 51.00 80 30 50 sapphire copper clamp silver plated copper cavity primary coupling probe secondary coupling probe 10 8

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TE mode: E θ field

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TM 010 TE 011

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Paraphoton wavenumber Cavity resonance frequency

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Resonance Q-factor coupling Paraphoton mass |G|~ 1

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Assuming P em = 1 W, P det = 10 -24 W, Q ~ 10 9, χ ~ 3.2 × 10 -11 Probability of Detection

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For 6 pairs of Niobium cylinders (stacked axially) with 2 GHz < ω 0 /2π < 20 GHz and ω 0 k 0 Microwave cavities Q~10 11, ….6 orders of magnitude better than Coulomb experiment

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k γ = paraphotonk 0 =ω 0 /c (resonance)k γ 2 =ω 2 – m γ 2

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Q =Rs/G G=Geometric factor & Rs = surface resistance G [Ohms] Freq [Hz] 10 GHz mode T ≤ 4 K Niobium Q~ 10 9

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In sapphire very high Q ~ 10 9 without Niobium ? G for high m seems small, need to confirm, as numeric integral needs to be checked

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Assuming detection bandwidth f = 1 Hz receiver temperature T = 1 K (very good amp) thermal noise power kT f = -199 dBm Power@1paraphoton per second S/N = 1 freqhf/sdBmSeconds 10 GHz6.63E-24-2022 1 GHz6.63E-25-21221

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Isolation will be the biggest problem Microwave leakage Unity coupling probes to cavities No reflected power Tuning High Q resonances exactly to the same frequency

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