Search for Time-Variation of the Electron-Proton Mass Ratio (μ) with ...

Search for Time-Variation of theElectron-Proton Mass Ratio (μ) withmilliKelvin Trapped Molecular IonsBrian OdomEnrico Fermi InstituteAbstractMost extensions of the standard model predict that if the fundamental constants vary with time,the electron-proton mass ratio should change 30-40 times more rapidly than the fine structureconstant. However, in current model-independent laboratory searches, sensitivity to timedependenceof the electron-proton mass ratio lags behind that of the fine structure constant bytwo orders of magnitude. I present a proposal to improve sensitvity to time-variation of theelectron-proton mass ratio using spectroscopy on milliKelvin trapped molecularions. Specifically, the molecular ions of interest have a long-lived electronic state nearlydegenerate with a highly-excited vibrational level of the electronic ground state.

Leading (Model-Independent) ResultsFine structureconstantαQuasar absorption lines:For Cs μwaveclockΔ ν

Sympathetic Cooling of Molecular Ions to ~ 10 mK(already demonstrated in Schiller and Drewsen groups)HD + cooled to 20 mK by Be + (cloud shapes well understood)Blythe, Roth, Frohlich, Wenz and Schiller, PRL 95, 183002 (2005):• Cooling is better with smaller clouds,down to 2x atomic ion temperature• Crystal can be turned off, unwantedions ejected, then recrystallizedSee also• Drewsen et al for MgH +• Schiller et al for mass 410 “Alexa Fluor 350”

Sensitivity of Molecular Vibrations to ΔμSensitivity of interval:∂Ω / ΓFOM 1 ≡ × 10∂μ/μ−15( number of line widths shifted,in response to Δμ / μ = 10 −15 )Monitoring the nth vibrational harmonic oscillator state:E ≈nω∝nnvibμ − 1/2FOM 1Maximize FOM 1 by monitoring:• a high-n level• of a tightly bound oscillator—large ω vib• with narrow linewidth=12nω vibΓ

Limitations of FOM 1Some systematics, such as clock instability or dopplershift, impose fractional frequency errorConsider monitoringΩ =Ω= nω∝vibEnA fractional uncertainty( )−15σ ΔΩ / Ω = 1×10 imposes( )−15σ Δ μ/ μ = 2×10regardless of whether FOM 1 isincreased by using a higher nA larger FOM 1 doesn’t always help. Wewould like precision enhancement.n−E01/2μ −

Precision Enhancement, FOM 2Exploit a DegeneracyAngstmann, Dzuba, Flambaum, Nevsky, Karshenboim, J Phys B, 39 (2006)Nguyen, Budker, Lamoreaux, Torgerson, PRA, 022105 (2004)DeMille, Sainis, Sage, Bergeman, Kotochigova, Tiesinga, arXiv:0709.0963Consider monitoringσσΔΩ / Ω = 1×10( )−15Δ μ/ μ = 2×10( )−18Ω =E −E′−3With a degeneracy of Ω= 10 En,a fractional uncertaintyMuch better!now imposes• Molecular complexity is definitely a good thing here• A long-lived state is needed• Added benefit: effect of clock’s dependence on α, μ suppressedn

Vibrational / F.S. Degeneracy ProposalFlambaum, and Kozlov, PRL 99, 150801, (arXiv posted May 2007)Approach: exploit degeneracy between low-n level and spin flip.Ion trap suggested for charged species.shift sens. prec. enh. reachSensitivity: decentPrecision enhancement: goodRange of molecules: goodAdvantage: ion trap

Cesium ProposalDeMille, Sainis, Sage, Bergeman, Kotochigova, and Tiesinga, arXiv:0709.0963 Sept. 2007Approach: exploit degeneracy between high-n leveland electronic level, in laser-coolable speciesSensitivity: goodPrecision enhancement: goodto excellentRange of molecules: noneAdvantage: cesium technology,both FOMs good

This ProposalApproach: exploit degeneracy between high-n leveland electronic level, in ion trapshift sens. prec. enh.reachSensitivity: good to excellentPrecision enhancement: goodto excellentRange of molecules: largeAdvantage: top scores in allcategories

Comparison with Cs ProposalIn favor of Cs proposal:Atomic Cs technology is well-developedIn favor of this proposal:More general technique—choose from entire periodic table• Better figures of merit• Study of multiple molecules

Systematics & Ultimate ReachInitial work will be on large cloud, but here we estimate reach ofultimate single-molecule experiment, based on current ion clocksFor the case of Se 2+ (0.17 Hz shift for Δμ/μ = 10 -15 ) :EffectShift (μHz)Uncertainty (μHz)σ(Δμ/μ) ∗ 10 -191 st -order Doppler00.000 1~02 nd -order Doppler0.0020.002~0Quadratic Zeeman, DC1000504Quadratic Zeeman, AC100503Electric Quadrupole01006Stark, micromotion50503Stark, blackbody~0~0~0Stark, light shift???• Note that 100 μHz accuracy is already achieved in NIST 7-Hg-ion μwave clock•1 st and 2 nd -order Doppler shifts are very small due to μwave spectroscopy in trap• μwave spectroscopy also allows large trap and low AC fields, reducing systematics• Cryogenic operation is required to obtain a low blackbody stark shift

Comparison of ProposalsIon trap, high Eby direct driveLattice, mediumE by direct drivefreq. shift sens. prec. enh. reachIon trap, low Ewith degeneracyFountain, mediumE with degeneracyIon trap, high nwith degeneracy(Spontaneous emission lifetimes not yet calculated, but can be > 1 s)This proposal allows sensitivity to Δμto potentially pass current limits on Δα

Conclusions• Linear rf-trap, allows for great μwave clocks• Entire periodic table is the playground for Δμ• Deep potential wells• Accidental degeneracies• Orders of magnitude sensitivity improvement to Δμ• In search of the right physical-chemist• New area of research—expect other applications• Parity violation studies• Low-temperature chemistry• …