Probing the Variation of Fundamental Constants with Polar Molecule Microwave Spectroscopy

Transcription

1 Probing the Variation of Fundamental Constants with Polar Molecule Microwave Spectroscopy Eric R. Hudson Yale University JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado at Boulder J.R. Bochinski H.J. Lewandowski Brian C. Sawyer Benjamin Lev Jun Ye

2 OUTLINE Background Importance of variation Why should fundamental constants vary? Current state of affairs Our experiment Producing cold, slow laboratory OH Measuring Λ-doublet transition frequencies Future work New experiment based on Th-229 nuclear transition

3 Why should we care if the fundamental constants vary? They re supposed to be constant Varying fundamental constants violate both Lorentz invariance and CPT symmetry.

4 Why should we think the fundamental constants could vary? Attempts to unify gravity predict (or allow for) space-time varying fundamental constants Physics Today 57, No. 10, 40 (2004). Why should they be constant? Interaction of matter and radiation with dark energy quintessence field leads to varying fundamental constants. Quintessence - photon interaction δ i α 0 Quintessence - electron interaction δ i m e 0 Physics Today 57, No. 7, 40 (2004).

5 Oklo Natural Nuclear Reactor Taken from: Currently 238 U ~ 99.3% and 235 U ~ 0.7% 2 billion years ago 235 U ~ 4% (typical reactor concentrations) Neutron capture cross-section for 149 Sm sensitive to Δα because of 97.3 mev resonance.

6 Oklo Reactor GSL 2006 Revised LT 2004 Two Solutions PNOPS 2005 Consistent with zero: Δα α 17 1(10 ) yr -1 OR Fuji et al., 2002 DD Δα/α X 10-7 over the last 2 Billion years (LT 2004) PRD (PNOPS 2005) arxiv: hep-ph/ (DD 1996) Nucl. Phys. B Fujii et al., AriXiv:hep-ph (GSL 2006) PRC

7 Atomic clock measurements Simple Idea: Measure atomic transition frequencies and see if they vary with time Problem: To measure a frequency you need a clock (i.e. another frequency) Solution: Use Cs hyperfine transition as a reference Optical transitions: ν i ~ Ry F i (α) Hyperfine transitions: ν j ~ α 2 (μ Cs / μ B )Ry F j (α) Relativistic Correction: F(α) ~ α N Fractional variation: d dt v ln v Optical Cs = ( N Optical N Cs & α 2) α d dt μcs ln μb N Cs = 0.8 N Hg+ = -3.2

8 Atomic clock measurements Several excellent experiments: 199 Hg + vs. Cs H vs. Cs 171 Yb + vs. Cs Rb vs. Cs Future: Sr, Yb, Ca, Al + Constraints are typically 2-D Stolen from Peik et al. Taken from PRL

9 Δα/α Status Oklo Analysis Δα/α x yr -1

10 Δα/α Status Atomic Clock Data: PRL Oklo Analysis Atomic Clock Data Δα/α x yr -1

11 Astrophysical measurements Quasar Absorption: Conceptually the same as atomic clock measurements. Quasars emit over a large spectrum Look for absorption from gas between the quasar and us Other possibilities from astrophysics: Non-zero Δα causes change to the CMB pattern. Look back to z ~ 1000, Δα ~ 10-3 PRD 60, Big Bang Nucleosynthesis Taken from: R.Srianand et al PRL,

12 Δα/α Status Atomic Clock Data: PRL Oklo Analysis Atomic Clock Data Δα/α x yr -1

13 Δα/α Status Dysprosium? Oklo Analysis Atomic Clock Data Quasar Data Quasar Data: PRL PRL Atomic Clock Data: PRL Re-analysis by different group yields a shift Later results show no shift. Mon. Not. R. Astron. Soc. 327, 1244 (2001) Δα/α x yr -1

14 Recap Modern epoch (and then some) consistent with zero Constraints are rapidly improving with no end in sight Early universe not so clear Lack of control of systematics in astrophysical measurements neccesitates the need for an ultimate check OH Mega-masers allow interrogation of the early universe AND have an ultimate check for systematics

15 Molecular structure: What is a molecule? Energy V e (R) Rb (S 1/2 ) + Cs (P 1/2 ) Electronic potentials ~ 300 THz (~ 1.5 ev) v = 0 V g (R) Rb (S 1/2 ) + Cs (S 1/2 ) J=1 J=0 Internuclear distance R Vibrational levels ~ THz Rotational levels ~ GHz Two levels for qubit

16 PA Primer: Electronic state labeling Heteronuclear diatomic molecules possess only axial symmetry - different good quantum numbers than for atoms J L Ω Λ S Σ N Ω = Λ + Σ J = Ω + N Electronic potentials are labeled as 2Σ+1 Λ Ω - Σ, Π, Δ,... states for Λ = 0, 1, 2,... (i.e., 3 Σ 1 state has Λ=0, Σ=1, Ω=1) Good quantum # s are Λ, Σ, Ω, J, m J (or just Ω, J, m J )

17 Using OH transitions to constrain α F = 2 F = 1 Hyperfine interactions ~ α 4 OH megamasers 2 Π 3/2 Lambda doubling ~ α 0.4 F= 2 F= 1 Allows for measurements of multiple transitions from the same gas cloud (Doppler shifts constrained and self check on systematics from closure) Previous uncertainly in laboratory based experiments is Hz, which leads to Δα/α ~ 10-5 O H High redshift z > 1 Darling, Phys. Rev. Lett 91, (2003). Chengalur et al., Phys. Rev. Lett. 91, (2003). Kanekar et al., Phys. Rev. Lett. 93, (2004). ter Meulen & Dymanus, Astrophys. J. 172, L21(1972).

18 Using OH transitions to constrain α 2 Π 3/2 F = 2 }Δ H+ α 4 F = 1 Δ Λ α 0.4 Astronomical observation: ω 11 = Δ Λ α o 0.4-1/2(Δ H+ -Δ H+ ) α o 4 + RS 11 ω 22 = Δ Λ α o /2(Δ H+ -Δ H+ ) α o 4 + RS 22 Lab measurement: ω 11 = Δ Λ (Δα + α o ) 0.4-1/2(Δ H+ -Δ H+ ) (Δα + α o ) 4 ω 22 = Δ Λ (Δα + α o ) /2(Δ H+ -Δ H+ ) (Δα + α o ) 4 F= 2 F= 1 }Δ H- α 4

19 First make the molecules : Sourcery Supersonic Expansion: -Cold molecules moving at a few 100 m/s.

20 Stark deceleration Second step: slow the molecules in to the rest frame of the lab + v v Conservative process, no cooling F net p + - p + - Phase space selection Phase space area linked to the deceleration angle (φ 0 ) - Phase space rotation (constant density) Energy Position Resembles a pendulum driven by a constant torque

21 Basic energy structure of OH 2 Σ 1/2Pump: 282 nm v = 1 Frank-Condon ~ 70% Detect: 313 nm Basics: -Discharge H 2 O in Xe -Ground State 2 Π 3/2 -λ doublet spacing ~1.7 GHz v = 1 -µ = 1.67D H 2 Π 1/2 v = 0 2 Π 3/2 v = 0 O μ

22 OH Molecues (linear scale) (a) 0.005x (b) (c) 5x (d) 5x (e) 5x Time (ms) (a) at skimmer (b) after hexapole (c) before 23 rd stage (d) before 51 st stage (e) trap region

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25 φ o = 0 o, 380 m/s Photon Counts (300 Records +) Time from Discharge [ms]

26 φ o = 0 o, 380 m/s φ o = 10 o, 312 m/s Photon Counts (300 Records +) Time from Discharge [ms]

27 Photon Counts (300 Records +) φ o = 0 o, 380 m/s φ o = 10 o, 312 m/s φ o = 20 o, 224 m/s Time from Discharge [ms]

28 3D Monte Carlo Simulation Results φ o = 0 o OH LIF Signal [arb.u.] Time from discharge [ms]

29 Experimental Set-up All metal detection area Slowed OH beam Decelerator Hexapole PMT Detection can Microwave cavity Excitation laser

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31 Hyperfine structure f F = 2 F = 1 m F = e F = 2 F = 1 m F = μ e ±2 = 2 x μ e ±1 Transition dipoles are different by a factor of two.

32 Double Rabi flopping Population in F = 2, f m f = ± 1 Time m f = ± 2 Total LIF signal

33 Rabi flopping (F =2 F =2) Population in initial state Molecular beam Microwaves on for VARIABLE time Microwave pulse length (μs) Detect population in initial state

34 Rabi flopping (F =2 F =2) Molecular beam Microwaves on for FIXED length Detect population in initial state Population Pulse mean sp eed [m/s]

35 Transition lineshape and center F' = 2 Population F = 2' F = 2 Transition 1 khz At fixed beam speed and pulse duration: Vary detuning 0.4 f center = ± 11.3 Hz f [Hz]

36 Ramsey Spectroscopy, Population f [Hz]

37 Ramsey Spectroscopy, Population f [Hz]

38 Ramsey Spectroscopy, Population f [Hz]

39 F = 2 F = 1 m F = F = 1 to F = 1 Transition F = 2 F = 1 m F = fc = -12 ± 72 Hz 1 1, P = -23 dbm + Population f [Hz]

40 Line Center Summary

41 Δα/α? This measurement will allow an order of magnitude improvement: Δα/α = 1 ppm over years» Same as atomic clocks if assume time derivative is linear» Can probe spatial changes Still waiting on astrophysical result... Over 100 hours of data taken on GBT, but analysis is bogged down by some terrestrial noise New data set from Arecibo being analyzed (N. Kanekar) The future is bright Because the frequency is in the cooled L-band no resolution limits yet New telescopes coming on-line in the next 10 years can approach our resolution with only a few hours of data collection

42 Using OH transitions to constrain α 2 Π 3/2 F = 2 }Δ H+ α 4 F = 1 Δ Λ α 0.4 Astronomical observation: ω 11 = Δ Λ α o 0.4-1/2(Δ H+ -Δ H+ ) α o 4 + RS 11 ω 22 = Δ Λ α o /2(Δ H+ -Δ H+ ) α o 4 + RS 22 Lab measurement: ω 11 = Δ Λ (Δα + α o ) 0.4-1/2(Δ H+ -Δ H+ ) (Δα + α o ) 4 ω 22 = Δ Λ (Δα + α o ) /2(Δ H+ -Δ H+ ) (Δα + α o ) 4 F= 2 F= 1 }Δ H- α 4 Dirty secrets: 1. ΔH + ΔH - reduces the effect of the α 4 term and Λ-doubling Use Satellite depends lines on α 0.4, so these transitions depend weakly on α. Use all 4 lines really just want to see something first 2. What about the other constants?

43 Measuring the Satellite Lines Satellite lines are much more sensitive to magnetic fields Main lines: ~ khz/gauss Satellite lines: ~MHz/Gauss In our experiment we could apply a very uniform field F' = 2 Population F = 2' F = 2 Transition f center = ± 11.3 Hz ν 12 = (15) Hz ν 21 = (10) Hz Δα/α = 30 ppb over years f [Hz]

44 Δα/α Status Quasar Data: PRL PRL Oklo Analysis Quasar Data Atomic Clock Data OH Projected Atomic Clock Data: PRL Δα/α x yr -1

45 Δα/α Status Quasar Data: PRL PRL Atomic Clock Data: PRL Oklo Analysis Quasar Data Atomic Clock Data OH Projected Δα/α x yr -1

46 Th-229 (Yale) Transition frequency is (probably) fantastically sensitive to constant variation: δω ω X q = m q δα δ Λ q QCD α, X s δx X q m = Λ s QCD X X V. Flambaum, arxiv:physics/ s s Linewidth is ridiculously small: < 100 μhz The greatest clock ever Figure taken from PRC ev 165 nm

47 Th-229 How do you optically observe a nuclear transition? Previous proposals (incomplete): Vapor cell-like experiments 1. Having Gas Discharge an optically Cell. accessible Excite the nuclear metastable transition nuclear is very state unique. via What inverse are the internal properties conversion it has that and electronic look for transitions decay of the don t? state: photons and alphas. 1. Less Inamura sensitive et al., to Hypefine it s environment Interactions than (2005). electronic transitions. 2. Trap Changes laser-cooled the nuclear Th 3+ spin and detect of the the atom. metastable state by monitoring the frequency of a hyperfine sensitive transition 3. of Decay the valence products electrons as you scan a laser hoping to excite the nuclear state. E. Peik, Europhys. Lett (2003) Put it in a solid to look for transitions (and do NMR spectroscopy or look for decay products)

48 Th-229 General Idea (first we just need to see the state): A few notes about detection: PMT VUV transmissive material doped with Th-229 Tunable 165 nm ± 10 nm H 2 Raman Cell Eventually you ll want a nice CW laser VUV comb 1. TIR makes solid angle of detection ~ 4π 2. PMTs are excellent here (QE ~ 40%!) 3. Use of monochromator and exploiting the long time scale should give excellent background discrimination. 4. NMR detection of the change in I is potentially background free. (Th 232 has I = 0) 5. Also look at decay spectrum.

49 Th-229 What are the possibilities for VUV transmissive materials? Readily available CaF 2 MgF 2 Th, ThF 3, or ThF 4? 3. LiF 4. Modified Fused Silica (157 nm photo-lithograpy)? Th Th +1 Th +2 Th +3 Ionization Energy 6.1 ev 11.5 ev 20 ev 28.8 ev Not so easy 1. Ce:LiSAF 2. Ce:LiCAF High transmission down to 110 nm Developed for tunable UV lasers around 300 nm based on Ce 3+. Crystal developed specifically to handle large amounts of UV power AND to maintain the Ce 3+ level structure! Would expect Th 3+ to not be modified so could verify its presence by strong absorption on the d f line (τ ~ 10 ns).

50 5s and 5p level shield 4f electron from crystal field Seems band gap is large Taken from: J. Crystal Growth 211 (2000) 302.

51 Cryst. Res. Technol (2001)

52 Th-229 Back of the envelope signal-to-noise calculation: Resonant cross-section: 2 λ Γ σ = 2 π Δ ω L Parameters: Γ = 2π (10 μhz) λ= 165 nm For Δω L = 1 cm -1, P = 10 μj, 10 ns pulse, 1 mm X 1 mm XTAL: N Excited = N Total σ N photons After one pulse: N Total Γ N Excited(t = 0) After Absorption: ~12 hrs: Γ Exp[ n N Excited (t σ = L 0) ] Th-229 Specific Activity: μg/μci 1 μci 10 μci (10 20 ppb 5 ) (10 ppb 6 ) 100 μci (10 2 ppm 7 ) 1 mci (10 20 ppm 8 )

53 Th-229 Possible flies : 1. Th-229: $50, 000 per mg 2. Fabrication of XTAL, Thorium is radioactive (7900 yr half life) nm laser system 4. Electron Bridge mechanism 5. Background from long-time scale fluorescence in crystal (?) 6. Forming of color centers, leading to more of #5. 7. Broadening due to Hyperfine coupling to electronic cloud and/or nuclear electric quadrupole moment