Tune-out wavelength spectroscopy: A new technique to characterize atomic structure. Cass Sackett UVa

Transcription

1 Tune-out wavelength spectroscopy: A new technique to characterize atomic structure Cass Sackett UVa

2 Outline Atomic parity violation experiments why they are important but stalled Tune-out spectroscopy what it is, how we do it Results and comparison to theory Next steps progress so far

3 Atomic parity violation S states in atoms have even parity ψ r = ψ(r) Transition ns n S ~ ns d n S = 0 forbidden! d = er Rubidium: 6S 497 nm 5S

4 Atomic parity violation Electron interacts with nucleus weak interaction violates parity mixes P character into S states allows transition! + Measure transition rate get strength of weak interaction 6S 5S

5 Fundamental symmetries Weak interaction violates CP symmetry So does the universe overall too much to explain via Standard Model Study symmetry violations look for surprises

6 Weak interaction Measure energy-dependence of weak interaction Steady improvements Except for atomic result, from 1995

7 Interpreting APV Measure transition rate, relate to weak interaction A PNC = n =5 6S 1/2 d n P 1/2 n P 1/2 H PNC 5S 1/2 E 5S E n P 1/2 + 6S 1/2 H PNC n P 1/2 n P 1/2 d 5S 1/2 E 6S E n P 1/2 n P 1/2 H PNC ns 1/2 : gives interaction strength ns 1/2 d n P 1/2 : dipole matrix elements

8 Interpreting APV Need precise dipole matrix elements Principle: 5S d 5P measure accurately Intermediate: 5S d np and 6S d np for n 12 calculate accurately Tail: 5S d np and 6S d np for n > 12 estimate 7P 6P 6S 5P 5S Also some additional corrections, calculated

9 Error contributions Contributions to PNC error: Terms Rel. contribution Uncertainty Principle Intermediate Tail Other Total experiment uncertainty: Limited by theory, mostly tail contribution

10 How to improve? Measure dipole matrix elements especially high-n tail Hard to do directly infinitude of states difficult to calibrate measurements

11 Measuring matrix elements Shine laser on atom detuned from any transition Get energy shift U = 1 α E2 αi 2 α = electric polarizability E = electric field I = laser intensity α depends on laser frequency ω Large for laser close to resonance

12 Measuring matrix elements 7P 6P 780 nm 5P 5S Polarizability of 5S ground state α ω n 5 J=1/2,3/2 np J d 5S 1/2 2 E nj E 5S E nj E 5S 2 ω 2 + α core Similar to PNC expression

13 Measuring matrix elements Measure α directly? One way: atom interferometer Splitting laser Bose condensate Splitting laser Split wave function: 0.1 mm 2ħk p = 0 +2ħk 2ħk m = 1.2 cm/s

14 Atom interferometer Could measure α directly One way: atom interferometer Wave packets Let packets propagate

15 Atom interferometer Could measure α directly One way: atom interferometer Wave packets Shine laser on one packet Phase shift φ stark = Ut ħ Stark beam

16 Atom interferometer Could measure α directly One way: atom interferometer Reverse momentum of packets 2ħk p = 0 +2ħk

17 Atom interferometer Could measure α directly One way: atom interferometer Packets return to starting point

18 Atom interferometer Could measure α directly One way: atom interferometer Recombine with laser: Interference: Fraction of atoms returned to p = 0 is cos 2 φ stark 2ħk p = 0 +2ħk

19 Atom interferometer Could measure α directly One way: atom interferometer Let wave packets separate Interference: Fraction of atoms returned to p = 0 is cos 2 φ stark

20 Atom interferometer Fit α = atomic units at nm 3% error, from intensity calibration Know 5P d 5S 2 to 0.1% from lifetime Need ~10 5 precision to extract all contributions to α

21 Measuring matrix elements Polarizability of 5S ground state α ω α core + n 5 J=1/2,3/2 np J d 5S 2 E nj E 5S E nj E 5S 2 ω 2 7P 6P 5P Find another method? 5S

22 Tune-out measurement In between resonances, α passes through 0 Location of zero doesn t depend on laser intensity Call λ 0 = tune-out wavelength

23 Tune-out measurement Use same atom interferometer technique Measure slope α > 0 α < 0 I/I max I/I max

24 Tune-out measurement Find λ 0 = nm our result 60 better than previous exp. 8 better than subsequent

25 Compare to theory Measurement doesn t directly give matrix elements Use theory to extract information α = α core + n 5 J=1/2,3/2 d 2 nj ω nj ω nj = E npj E 5S1/2 ω nj 2 ω 2 d nj = np J d 5S 1/2 Contributions: α = α prin + α int + α tail + α core 5P states n = 6 to 12 n > 12 core electrons

26 α (au) Compare to theory Calculate contributions for λ = λ 0 (M. Safronova): ± α prin 1.89 ±.02 α int 0.1 ± 0.1 α tail α core ± 2 Value Error Experiment says sum = 0 ± 0.1 au

27 Compare to theory Measurement specifies α prin = 5P contributions Mainly ratio d 2 2 3/2 /d 1/2 Theory for ratio much more accurate than individual d s d 1/2 d 3/2 Confirmed by tune-out measurement 2 d 3/2 2 d 1/2 Theory Exp Tuneout

28 α (au) Compare to theory Original theory: ± α prin 1.89 ±.02 α int 0.1 ± 0.1 α tail α core ± 2 Value Error

29 α (au) Compare to theory With tune-out constraint: ± α prin 1.89 ±.02 α int 0.1 ± 0.1 α tail α core ± 0.2 Value Error Can we get more information? Especially for tail?

30 More measurements More tune-out wavelengths near other P states 7P 6P 5P 420 nm 5S Two more data points Also two new parameters d 6,1/2 and d 6,3/2 Not a solution

31 More measurements Another degree of freedom: light polarization Atoms prepared in m = 1/2 Coupling depends on polarization σ + polarization P 3/2 m = 3/2 1/2 1/2 3/2 P 1/ α lin polarization σ polarization S 1/2 m = 1/2 λ

32 Polarization effects Two components to polarizability: α = α 0 + vα 1 scalar vector v = degree of circular polarization α 0 0 = α core + n 5 2 ω n1/2 2 d n3/2 ω n3/2 ω 2 n3/2 ω 2 + d n 1/2 ω 2 n1/2 ω 2 α 1 1 = α core + n 5 2 ω 2 d n3/2 ω ω 2 n3/2 ω 2 2d n 1/2 ω 2 n1/2 ω 2

33 Polarization effects Measuring α 0 and α 1 gives two data points per λ 0 different dependence on matrix elements Measure near 5P and 6P states: three tune-out wavelengths six polarizabilities seven unknowns (all normalized to d 5,1/2 ): d 5,3/2 d 6,3/2 d 0 6,1/2 α core 1 α core 0 α tail 1 α tail 0 Measure α core using Rydberg atoms

34 Rydberg measurement Electron in high-n, high-l state does not penetrate core 0 Energy shifted by polarizability of core α core Rydberg electron Rb + Collaborating with TFG to measure for Rb Microwave spectroscopy on 18f to 18g transition:

35 Polarization effects Measuring α 0 and α 1 gives two data points different dependence on matrix elements Measure near 5P and 6P states: three tune-out wavelengths six polarizability constraints six seven unknowns (all normalized to d 5,1/2 ): d 5,3/2 d 6,3/2 d 0 6,1/2 α core 1 α core 0 α tail 1 α tail

36 Polarization measurements Need precise control of light polarization ~10 5 Distorted by vacuum window ~10 3 Stark laser Atoms

37 Polarization measurements Minimize errors using circularly polarized light: v parameter = ±1 = max or min deviations 2 nd order in distortion effect ~10 6 Establish circular polarization using atoms 3/2 1/2 1/2 3/2 P 3/2 P 1/2 σ + S 1/2 m = 1/2

38 Polarization control Apply circular polarized light to atoms α = α 0 + vα 1 Vary v using magnetic field v ~ amount of circ polz B v = 1 v = 0 Stark laser v = 1

39 Polarization control Need to ensure that B is behaving as expected Use same trick with microwave spectroscopy B resonance B Microwaves

40 Polarization control Need to ensure that B is behaving as expected Use same trick with microwave spectroscopy B Initial resonance B After tuning Microwaves

41 Expected results Completing polarization and B-field characterization Measure 5P states soon, then 6P states Monte Carlo model: For expected meas. accuracy, get α tail to 0.01 au ~10 better than current theory Resolve parity violation bottleneck?

42 Impact Issues: Measure with Rb, parity exp with Cs Tail contribution not exactly same for α, PV exps Provide benchmark for theory Test methods, learn what works Motivate PV experiment in rubidium? A PV Z 3, 3 bigger in Cs But new experiment more than 3 better?

43 Conclusions Details of atomic structure needed for better PV exp. Obtain with tune-out spectroscopy Other applications: Atomic clocks EDM experiments Precision atom trapping/quantum computing

44 Conclusions Illustrate how AMO experiment involve many pieces New result will be based on advances in: atom trapping, BEC, lasers, spectroscopy, atomic theory,...? Many contributions from many people

45 Credits Grad students: Adam Fallon Seth Berl Eddie Moan Zhe Luo Undergrad: Yeshwanth Somu Theory: Marianna Safronova Funding: NSF, NASA