1. Can dT CMB /dt be Measured? R. V. Duncan University of New Mexico, and Caltech Quarks to Cosmos Workshop Airlie Center, May 23, 2006 Work sponsored by NASA, and by and equipment loan from Sandia National Labs Acknowledge helpful discussions with Prof. George Seidel (Brown) and Prof. Philip Lubin (UCSB)

2. Why? Fundamental test of cosmological theories Hubble’s Law: v = H D –H is very uncertain, 45 – 90 km/s per Mpc –T -1 dT/dt ~ D -1 dD/dt = v / D = H, hence a direct measurement of Hubble’s Constant. Vastly improved long-baseline stability for all space radiometry applications –Quasar / Black Hole / etc. radiation variation –Anisotropy stability studies Anticipate dT CMB /dt ~ 200 pK/year

3. An Exceptionally Hard Experiment Photon Collection from a faint 2.7 K source: To resolve  T/T ~ 10 -11 requires Averaging time ~ one month Foreground Sources: Hubble Ultra - Deep Field: SW of Orion in Constellation Fornax, chosen for sparce foreground sources. 0.05 arc degrees Metrology: BB stable to within 100 pK over decades!

4. New Ultra-Stable Platform C. J. Green, D. A. Sergatskov, and R. V. Duncan, J. Low Temp. Phys. 138, 871 (2005). 1 2

5. 1. Paramagnetic Susceptibility Thermometry Magnetic flux is trapped in a niobium tube A paramagnetic substance with T > T c is thermally anchored to the platform M = H  (T)  [(T – T c )/T c ] -  so small changes in T create large changes in M Gifford, Web, Wheatley (1971) Lipa and Chui (1981) PdMn: Klemme et al., JLTP 116, 133 (1999) Nelson, Sergatskov, & Duncan, JLTP 127 173 (2002) H Pd Mn

6. PdMn0.9% Thin Film Magnetic Susceptibility Thermometry See R.C. Nelson et al., JLTP (2002) For thermometry, See Duncan et al., 2 nd Pan Pacific Basin Workshop, 2001. Thin film sensitivity vs. T and HNo hysteresis was observed

7. Fundamental Noise Sources Heat fluctuations in the link one independent measurement per time constant  = RC (noise) 2   / C  (  T Q ) 2  = 4Rk B T 2 so  T Q  √R and  T Q  T See: Day, Hahn, & Chui, JLTP 107, 359 (1997) Thermally induced electrical current fluctuations mutual inductance creates flux noise  (  ) 2   T N 2  r 4 / L  M =  / s, s ≈ 1    so  M    √T SQUID noise  (  SQ ) 2  1/2 ≈ 4    √Hz with shorted input external circuit creates about three times this noise level so  ≈ 12    √Hz and  SQ ≈ 12 pK/√Hz T, C T bath R r N  L

8. Heat Fluctuation Noise Across the Link R = 40 K/W  (  T Q ) 2  = 4Rk B T 2 so  T Q = 0.10 nK/√Hz 3 dB point at 10 Hz, suggesting  ≈ 50 ms (collaboration with Peter Day)

9. HRT Time Constant Method: Controlled cell temperature with T1 Pulsed a heater located on T2 Cell in superfluid state Contact area of only 0.05 cm 2 Rise time ~ 20 ms Decay time = 48 ms Collaboration with Peter Day

10. Reduce the Heat Fluctuation Noise Reduce R from 40 to 0.25 K/W Now  T Q ≈ 7 pK/√Hz Minimize  T M with a gap to reduce mutual inductance to the SQUID loop  is PdMn thickness = 0.76 mm r 4  4 r  3 r 3 /(4  3 ) ≈ 18

11. The Cryostat

12. Typical Noise Spectrum, T = 1.6 K Data: 30 min. at 10,000 points / s FFT: MATLAB ‘pwelsh’  T  25 pK/√Hz

13. Thermally Driven Electric Current Fluctuations Thermal current fluctuations:  = 38   /(Hz K) 1/2 √  SQUID circuit noise:  SQ = 12.5   /√Hz

14. 2. RF-biased Josephson Junctions for Heater Control V n = n (h/2e) f h/2e =  o = 2.07  V/GHz f = 94.100000000 GHz R el = 1,015  P n = V n 2 / R el = 37.3 n 2 pW

15. Standoff vs. Josephson Quantum Number R el = 1,015  R so = 4,456 K/W T cool T R so

16. n = 7 n = 10 n = 0 A New ‘Fixed-Point’ Standard T = T – 125  K

17. Conclusions Fundamental noise sources in PST identified and reduced Lowest noise  25 pK/√Hz at 1.6 K New rf-biased Josephson junction heater controller developed Technology in place now to develop a BB reference standard more stable than the CMB temperature (< 200 pK/year drift) in a weightless lab, provided that T does not vary with the cosmic expansion

19. PdMn0.9% Thin Film Magnetic Susceptibility Thermometry See R.C. Nelson et al., JLTP (2002) For thermometry, See Duncan et al., 2 nd Pan Pacific Basin Workshop, 2001. Thin film sensitivity vs. T and HNo hysteresis was observed

20. New Data, PdMn0.4%, 6.67  m thick films T c =1.17 ± 0.01 K  = 1.41 ± 0.01 Data by… Ray Nelson Colin Green Dmitri Sergatskov R. V. Duncan