Determining the Fine Structure Constant with Bose-Einstein Condensate Interferometry

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1 Determining the Fine Structure Constant with Bose-Einstein Condensate Interferometry Eric Cooper, Dan Gochnauer, Ben Plotkin-Swing, Katie McAlpine, Subhadeep Gupta August 16, 2017 S

2 Outline S Introduction S Fine Structure Constant S Bose-Einstein Condensate Interferometry S Discussion of REU project work S Helping choose a direction for future work S Analyzing experimental timing precision S Building frequency generator needed for the future experiment

3 The Fine Structure Constant,α S Dimensionless combination of fundamental constants α = 1 4πε 0 e 2!c S Strength of electromagnetic coupling in QED S Magnitude of relativistic corrections in atomic physics undoubtedly the most fundamental pure (dimensionless) number in all of physics. -David Griffiths all good theoretical physicists put this number up on their wall and worry about it -Richard Feynman

4 Best Measurements ofα S Electron g 2 S 0.25 ppb (Harvard 1 ) S Calculation requires >10,000 Feynman Diagrams S Atom Recoil S 0.7 ppb (France 2 ) S 0.1 ppb (Our goal) 1E+00 1E-03 1E-06 1E-09 1E-12 Contributions to Electron g 2 Contribution Uncertainty Experimental Uncertainty S Comparison tests QED 1 R. Bouchendira, et al. PRL (2011) 2 D. Hanneke, et al PRL (2008) Adapted from Alan Jamison 2014 thesis

5 Atom Recoil Measurements Yb #! 2 % $ 2m p =!k Time-dependent Schrödinger Equation: 2 & x 2 +V(x) (ψ =! ' i ψ = e i(kx ω rect) t ψ (!k)2 2m Yb =!ω rec

6 Using ω rec to Measureα S Recoil frequency combines with precisely known constants to give an expression forα. α 2 = 4π R c! m e (!k) 2 2m Yb =!ω rec α 2 = 8π R c m Yb m e ω rec k ppb 1.3 ppb 0.1 ppb Our Goal: 0.1 ppb

7 Measuring ω rec with Atom Interferometry S Diffraction by standing waves of light gives precise momentum kicks with photon pairs S Final atomic interference pattern allows precise measurement of phase. ω rec φ T = ΔE! Time 0 T T ~10ms Horizontal Position Splitting Pulse Yb Mirror Pulse Readout Pulse φ=0.408

8 Precision of Atom Interferometry S Uncertainty in recoil frequency due to uncertainty in phase and time: ω rec φ T S N = 1 Horizontal IFM: S Precision in increase φ Δφ " Δω $ rec # ω rec % ' & 2 " = Δφ % $ ' # φ & is limited so it is necessary to 2 " + ΔT % $ ' # T & Δφ φ 10mrad 930rad =

9 Increasing Phase Evolution S Total phase proportional to square of number of recoils, 2N φ = ω rec (2N) 2 (2T ) S Have successfully accelerated up to N = 28 S Lose evolution time φ max 120, 000 N = 20 Δφ / φ Time 0 Acceleration Pulses ~10ms T T Horizontal Position Splitting Pulse Yb Mirror Pulse Readout Pulse

10 My REU Project Analyzing means to further increase φ Building programmable frequency generator for future setup Measuring precision for ΔT/T S

$Next Steps to Increase Phase Horizontal Diffraction Add vertical launch (2 Time) Vertical Diffraction Add vertical$

11 Next Steps to Increase Phase Horizontal Diffraction Add vertical launch (2 Time) Vertical Diffraction Add vertical launch (20 Time) Better 0.5 mm 10 cm Δφ / φ Need ΔT 2 ps for 0.1ppb Δφ / φ Need ΔT 20 ps for 0.1ppb

12 Planning for a Vertical Geometry S Begin with vertical launch to achieve 200ms of freefall S Now needδt 20 ps S Compensate standing waves for effects of gravity ~10 cm Vertical Position Bloch Oscillation Launch Splitter + Acceleration Mirror deceleration + readout 100 ms 100 ms 0 Time ~300 ms

13 Making Diffraction Beams fall with Gravity S As atoms fall, Doppler shifts disturb standing waves f 0 f 0 v λ S Need to adjust frequencies at a rate of g /λ = khz/ms S Use Direct Digital Synthesizer (DDS) to produce frequency sweeps Yb f 0 Yb v f 0 + v λ

14 How to chirp beams with a DDS Upward Beam: f 0 + g +δ Downward Beam: f 0 g δ DDS 4 Gravity Controller Ramp up: Bloch oscillations Ramps down: Gravity 200 MHz + g L-pass H-pass L-pass H-pass DDS 1 Profile Mode 8 modes: 200 MHz + δ fine DDS 2 Profile Mode DDS 3 Profile Mode 5 modes: 200 MHz + δ coarse 5 modes: 200 MHz δ course δ coarse = 0, +5hk, -47hk, +53hk, -95hk, +101hk, -143hk δ fine = 6hk* n (n = [0,7]) δ=δ coarse + δ fine (Through N = 73)

15 Building a Direct Digital Synthesizer Fixed 30dB amplifier Variable Gain Amplifier Arduino Software Controls Cesium Frequency Standard Input DDS Board

16 Testing the DDS S DDS Sweep compensates for gravity with accuracy limited by knowledge of g Frequency Sweep Endpoint (khz) S Timing device used for testing found to 40 be stable to within ps 0 DDS Gravity Frequency Sweep Slope = khz /ms g/λ = (2) khz/ms Error Bars = 10 7 σ Ramp Up Time (ms)

17 Analyzing Timing Stability S Discovered for ppm systematic error in timing S Found 100 ns errors at repeatable timings

18 Corrected Timings S Corrected for ppm systematic error in timing S Compensated for 100 ns errors at repeatable timings S Remaining timing jitter statistical S ΔT 20 ps possible after 2500 shots (10hr) RMSE = 0.80 ns

Conclusions and Next Steps S New DDS setup built and ready for

systematic timing variations S Vertical setup is promising for 0.

Thanks To: Dan Gochnauer Ben Plotkin-Swing Katie McAlpine Prof.

19 Conclusions and Next Steps S New DDS setup built and ready for integration into the experiment S Discovered and corrected systematic timing variations S Vertical setup is promising for 0.1 ppb level measurements of the fine structure constant Many Thanks To: Dan Gochnauer Ben Plotkin-Swing Katie McAlpine Prof. Deep Gupta REU Program Gray Rybka, Subhadeep Gupta Linda Vilett Cheryl McDaniel

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