Status of Atomic Parity Violation Experiments Lorenz Willmann, Van Swinderen Insitute for Particle Physics and Gravity, University of Groningen Physics of Fundamental Interactions and Symmetries PSI2016 Oct. 16-20, 2016

Direct observation versus precision measurements Direct measurement Precision measurements F. Maas, Tuesday

Standard Model The Weinberg Angle

Ra+ Cs F. Maas, Tuesday

Running sin2 θW and Dark Parity Violation Possible P2 Q2-Range Bill Marciano

Cs APV Experiment Stark induced forbidden transition (C. Wieman et al. 1985-1996)

sin2(θW) = (1 – (MW/MZ)2) + rad. corrections + New Physics Weinberg Angle θW sin2(θW) = (1 – (MW/MZ)2) + rad. corrections + New Physics 5 4 3 Cs ≈ 3 % 5 2 1 Ra+ QW(p) eD-DIS

Physics Beyond the SM Extra Z’ boson in SO(10) GUTs: Additional U(1)’ gauge symmetry Does not affect ordinary Z and W physics Assume no Z-Z’ mixing Londen en Rosner (1986) Marciano en Rosner (1990) Altarelli et al. (1991) Bounds on MZ’ from APV (68% confidence level, ξ= 52°) With current Cs result Mz’> 1.2 TeV/c2 (Wansbeek et al.. PRA (2010)) Range for Ra+ (5-fold improvent) > 6 TeV/c2 From High Energy Experiments Tevatron MZ’> 0.9 TeV/c2 Expected Range LHC MZ’ ~4.5 TeV/c2

Atomic parity violation (APV) sin2(θW) = (1 – (MW/MZ)2) + rad. corrections + New Physics Standard Model Atomic parity violation is the tiny effect of the weak interaction on the structure of an atomic system. The reason this is interesting is to test the electroweak part of the Standard Model What is plotted here are measurements of the weak mixing angle or Weinberg angle (and actually sine squared of this value) which is a parameter of the SM. It’s value is not predicted, but as a running coupling constant, its behavior as a function of the energy scale at which it is probed is a prediction of the SM. Running all the way from measurements in high energy accelerator experiments down to the atomic energy scale. Low-energy: currently only one measurement in atomic Cs, and the interpretation was complex In addition: there is sensitivity to New Physics -> therefore another APV measurement: Ra+ We want to do better! Kumar, Marciano, Annu. Rev. of Nucl. Part. Sci. 63, 237 (2013) Davoudiasl, Lee, Marciano, Phys. Rev. D 89, 095006 (2014); Phys. Rev. D 92, 055005 (2015)

Some APV Activities Cs The Standard @ Bolder S.C. Bennett, C.E. Wieman, PRL 59, 16 (1999) Fr Atom traps @ Legnaro, Stony Brook TRIUMF G. Stancari et al., E.Phys.J. 150, 389 (2007); G. Gwinner et al., Hyperf. Int. 172, 45 (2006) Yb Biggest APV effects observed @ Berkeley K.Tsigutkin et al., PRA 81, 032114 (2010) Ba+ Idea, @Seattle and @VSI N. Fortson, PRL 70, 2383 (1993); J.A. Sherman et al., Phys.Rev. A 78, 052514 (2008) Ra+ advantageous system @VSI O.O. Versolato et al., Phys. Rev. A 82, 010501(R) (2010) Yb+ @Los Alamos, currently no activity RaF possible molecular system Berger, Hoekstra et al., PRA 82, 052521 (2010)

Experimental Method What Line shape?

D. Budker et al.

Large APV in atomic Yb High S/N D. Budker et al.

Example: Saturated Absorption Spectroscopy of I2 Lock point

Line Shape High S/N Lineshape model: derivative of Lorentzian Iodine Fit Residuals

Line Shape High S/N Better: motivated by experimental procedure Iodine Needed in such experiments Fit Residuals

Requirements for APV Long observations times Undisturbed system Trapping Undisturbed system UHV conditions Determination of Wavefunctions Spectroscopy measurements State lifetime determination Localization to fraction of optical wavelength Laser cooling Lasers, Data Acquisition, long measurement time …

Conceptually very simple experiments A = (N+-N-)/(N++N-) DA = (N++N-)-1/2 = N-1/2 A = 20 x 10-9 2% Measurement N = 6.25 x 1018 events Highest rate, measure Q2: Large Solid Angle Spectrometers F. Maas, Tuesday

Experimental Method Single Ion APV

Weak Interaction in Atoms Interference of EM and Weak interactions E1PNC = Kr Z3 Qw = Kr Z3 (- N + Z (1-4sin2 θW)) Heavy System Measurement Atomic Theory

increase faster than Z3 (Bouchiat & Bouchiat, 1974) Scaling of the APV increase faster than Z3 (Bouchiat & Bouchiat, 1974) Kr relativistic enhancement factor Z3Kr Ra+ effects larger by: 20 (Ba+) 50 (Cs) Ra+ Enhancement Z3 L.W. Wansbeek et al., Phys. Rev. A 78, 050501 (2008) Ba+ Ca+ Sr+ Atomic Number  5-fold improvement over Cs feasible in 1day Relativistic coupled-cluster (CC) calculation of E1APV in Ra+ E1APV = 46.4(1.4) · 10-11 iea0 (−Qw/N) (3% accuracy) Other results: 45.9 · 10-11 iea0 (−Qw/N) (R. Pal et al., Phys. Rev. A 79, 062505 (2009), Dzuba et al., Phys Rev. A 63, 062101 (2001).)

Experimental Method Differential Light shift Energy splittings not to scale N. Fortson, Phys. Rev. Lett. 70, 2383-2386 (1993)

Accuracy of Single Ion Experiment → 10 days for 5 fold improvement over Cs

Atomic Properties Ra ion spectroscopy

Ra+ vs. Ba+ Ra+ Ba+ Largest APV effect Radioactive Readily available 802 nm 62P1/2 1079 nm 614 nm 382 nm 62D5/2 456 nm 650 nm 62D3/2 Iso-electrical 468 nm 494 nm 52D5/2 52D3/2 828 nm 2052 nm 72S1/2 62S1/2 Ra+ has a radioactive problem -> therefore we work mostly with Ba+ Ra+ needs source Largest APV effect Radioactive Readily available Develop experiment

Sources or fragmentation Radium Isotopes 206Pb + 12C ARa + (218-A) n 206Pb beam 12C target TRImP@KVI TRIμP separator Thermal ionizer ΔN <10 To RFQ (Paul trap) Rate after TI 225Ra Electrochemical extraction from 229Th source (ANL) Long lived 229Th source in an oven (TRIP@KVI) Other Isotopes Online production at accelerator facilities TRIP@KVI ( flux ~ 105/s) ISOLDE , CERN ( flux ~ 109/s) We produced radium isotopes using AGOR cyclotron. Etc. LIFETIME OF THE ISOTOPES PRODUCED Sources or fragmentation 26

Ratio measurement Insensitivity of Ratio of measurements of E1APV for isotopes to atomic structure. V. A. Dzuba, V. V. Flambaum, and I. B. Khriplovich, Z. Phys. D, 1, 243 (1985) Best case scenario: For radium a wide range of isotopes is available

Trapped Ra+ Spectroscopy Radiofrequency Quadrupole (RFQ) 7P3/2 7P1/2 708 nm 1079 nm 6D5/2 6D3/2 468 nm 7S1/2 Level Scheme of Ra+

Laser Spectroscopy in Ra+ 6d2D3/2 HFS measurement ̴̴ 3,5 σ Probe of atomic wave functions at the origin Probe of atomic theory & size and shape of the nucleus O. O Versolatao et. al., Phys. Lett. A375 (2011) 3130–3133 G. S. Giri et al. Phys. Rev. A 84, 020503(R) (2011) [10] B.K. Sahoo et al. Phys. Rev. A, 76 (2007) B.K. Sahoo et al. Phys. Rev. A, 79, 052512 (2009)

Atomic wave functions at the origin Probe of S-D E2 matrix element Ra+ measurements Hyperfine Structure: Atomic wave functions at the origin Isotope Shifts: Atomic theory & size and shape of the nucleus We used this system in Fall 2009 to perform measurements and extract hyperfine structures, isotopes shifts and even a lower bound of the lifetime of a meta-stable state in ra+. State lifetime: Probe of S-D E2 matrix element agreement with theory at % level (Safronova, Sahoo Timmermans et al.)

Activity at CERN/ISOLDE

muX@PSI Radium Charge Radium Beamtime to improve sensitivity of muonic x-ray measurements last two weeks

Frank Maas, Tuesday

Ion Traps, Crystal and dynamics Ion Trapping and Laser Cooling Ion Traps, Crystal and dynamics

Single Ion Chemical homologue

Hyperbolic Paul trap VRF 138Ba+ 2P3/2 2P1/2 2D5/2 2D3/2 2S1/2 5 mm 494 nm 650 nm 2S1/2 2D3/2 2D5/2 2P1/2 2P3/2 Ion trap VRF 37 37 37

Detection + PMT 10 µm EMCCD camera The usual detection methods: PMT on one side and EMCCD camera on the other + PMT

650 nm laser frequency (MHz) Detection 138Ba+ 494 nm 650 nm 2S1/2 2D3/2 2D5/2 2P1/2 2P3/2 PMT Lasers 650 nm laser frequency (MHz) Ion trap EMCCD What can we learn from trapped ion images?

Localization in Paul Trap Ion motion Diffraction limited spatial resolution with EMCCD camera Trapping field 10 µm x y Mathieu equation: Effective harmonic potential with micromotion + Stray electric field

DC voltage and ion movement set scale DC voltage easy to measure AC voltage harder to measure larger AC amplitude smaller AC amplitude DC voltage and ion movement set scale Calibrated trap field AC amplitude Determined stray electric field −0.4 V/cm

Creating a Crystal (Effective) trapping field E-field Coulomb repulsion Thomas-Fermi Approximation

Modeling ion crystals Model function for potential energy of the cooled ions in the trap Parameters: trap parameters, number of ions, stray electric field Random starting positions Numerically selfconsistent solution for Stray electric field breaks rotational symmetry

Modeling ion crystals Example results: 6 ions

Six Ions 6 ions Rotating crystal, diffraction ring, averaged over 270s

Information from Images Temperature Trap electric fields Stray electric fields Presence of other ions Ion temperature Trap electric fields Stray electric fields Presence of other ions Indispensible for precision measurements

Lineshape, coherence and two photons Ion Trapping Lineshape, coherence and two photons

Hyperbolic Paul trap VRF Ba+ 5 mm 2P3/2 2P1/2 650 nm 494 nm 2D5/2 NNV subatomic Lunteren 2014-11-05 Hyperbolic Paul trap Ba+ 494 nm 650 nm 2S1/2 2D3/2 2D5/2 2P1/2 2P3/2 Ion trap VRF 5 mm 48 48 48

Ba+ atomic properties 2D5/2 level lifetime Matrix elements 614 nm 456 nm 650 nm 52D5/2 Introduce the Ba+ level scheme Extract these two transition frequencies Transition frequencies Lineshape analysis 494 nm 52D3/2 2052 nm 62S1/2 138Ba+

Line shape modeling |2P1/2⟩ Γ1 Γ2 Δ1 Δ2 γ Ω2 Ω1 |2D3/2⟩ γc |2S1/2⟩ Ba+ |1⟩ |2⟩ |3⟩ |4⟩ |5⟩ |6⟩ |7⟩ |8⟩ Optical Bloch equation 3 level example Δ1 Δ2 γ Ω2 Ω1 |2D3/2⟩ γc |2S1/2⟩ We use the optical Bloch equations It uses the density matrix formalism and the time-dependence of the system is given by this Hamiltonian describing the interaction of the ion with the laser light and a damping matrix describing the decoherence effects. I’m not going to go through all the math, but I just want to describe the ingredients going into this calculations: Then there’s the spontaneous decay from the excited state which leads to relaxation of the populations, and the associated decoherence effect and finally the finite linewidth of the lasers also causes a decoherence effect. Ba+ Ω1, Ω2 Rabi frequencies (laser power) Γ = Γ1 + Γ2 relaxation rate γ = Γ/2 decoherence rate Δ1, Δ2 laser detunings γc laser linewidth

Raman two-photon transitions λ1 = 494 nm λ2 = 650 nm Fluorescence signal 2D5/2 Optical Bloch model example 2D3/2 Ba+ 2S1/2 Detuning blue laser (λ1) [MHz] Fit parameters: transition frequencies

Ba+ laser system Ba+ λ1 = 494 nm λ2 = 650 nm 2S1/2 2D3/2 2D5/2 2P1/2 AOM Frequency comb Laser diagnostics Trap SHG I2 stabilized laser Ti:sapph

Frequency measurements 494 nm laser scanned 650 nm laser scanned + + λ1 50% λ2 50% λ1 80% λ2 20% B E Two 650 nm laser settings probed Interleaved cooling and probing PMT signal PMT signal −50 −25 +25 +50 −50 −25 +25 +50 494 nm laser frequency offset [MHz] 650 nm laser frequency offset [MHz] B E PMT signal PMT signal −50 −25 +25 +50 −50 −25 +25 +50 494 nm laser frequency offset [MHz] 650 nm laser frequency offset [MHz] NNV subatomic Lunteren 2014-11-05

Line shapes and polarization 494 nm linear polarized B 650 nm circularly polarized Zeeman sublevels: 8 level system Magnetic field B Laser polarization pmt signal |1⟩⟨5| |2⟩⟨8| |2P1/2⟩ 650 nm laser frequency offset |4⟩ |3⟩ 494 nm linear polarized B 650 nm circularly polarized Including the Zeeman sublevels, there are now two additional parameters playing a role: the magnetic field causing Zeeman splitting and the polarization of the two laser fields with respect to this. To illustrate that, I have two sets of data here that we collected by keeping the blue laser at a fixed frequency and varying the frequency of the red laser across its corresponding resonance. The two data sets were taken with different polarizations of the lasers. The wide overall shape is the same, this is the one-photon peak of the transition to the excited state. But depending on polarization and magnetic field, also several dark resonance can appear. These are coherent two-photon effects that occur at frequencies where the sum of both a red and a blue photon exactly matches a transition from the ground state to the D level. So does the optical Bloch model work for fitting these lineshapes? |8⟩ |7⟩ |2D3/2⟩ |6⟩ pmt signal |2⟩ |2S1/2⟩ |5⟩ |1⟩⟨8| |2⟩⟨5| |1⟩ 650 nm laser frequency offset

Transition frequencies 494 nm 650 nm Ba+ 2P3/2 2P1/2 2D3/2 2S1/2 494 nm 650 nm 2D5/2 Frequency 650 nm laser − 461 311 000 MHz 494 nm laser detuning varied 650 nm laser intensity varied Frequency 650 nm laser − 461 311 000 MHz We aim to extract transition frequencies, so we need to know Fitted with optical Bloch equation model Extract transition frequencies with 100 kHz accuracy Dijck et al., Phys. Rev. A 91, 060501(R) (2015)

Transition frequencies 494 nm 650 nm Ba+ 2P3/2 2P1/2 2D3/2 2S1/2 494 nm 650 nm 2D5/2 Light shift? Correction in transition frequencies for Ω2 dependent shift consistent with 2° rotation of B-field 650 nm laser intensity varied B-field rotated 2° Frequency 650 nm laser − 461 311 000 MHz 1 2 One-photon peak frequency (MHz) 3 4 5 461 311 878.0 878.5 879.0 879.5 Expected Power 650 nm laser (Ω2 / Ω2,sat) We aim to extract transition frequencies, so we need to know Extract transition frequencies with 100 kHz accuracy Fitted with optical Bloch equation model Dijck et al., Phys. Rev. A 91, 060501(R) (2015)

Metastable State lifetime Ion Trapping Metastable State lifetime

2D5/2 Level Lifetime ‘Electron shelving’ 138Ba+ 2P3/2 2P1/2 2D5/2 Diagnostic: 30 s lifetime sensitive to perturbations of ion Determine D-state lifetime: matrix element 2S1/2

2D5/2 Level Lifetime After collection of many jumps Exponential function Ensemble average is same as average over individual measurements

Several Ions Is the interaction changing the lifetime?

2D5/2 Level Lifetime Zoom in into 200s of data

2D5/2 Level Lifetime Four distributions with only two time constants 1 ion shelved 2 ions shelved all ions shelved Diagnostic: 30 s lifetime sensitive to perturbations of ion Determine D-state lifetime: matrix element A. Mohanty et al., to be submitted

And many Ions Small crystals or clouds Within uncertainties in agreement with single and few ions Small crystals or clouds

Quantum jump spectroscopy 2D5/2 Level Lifetime Shelved interval length [s] Count 5 10 15 20 25 40 60 80 100 Fit exponential 2P3/2 Electron shelving 2P1/2 Ba+ τ ≈ 30 s 2D5/2 2D3/2 2S1/2 Quantum jump spectroscopy Time [s] 100 200 300 400 PMT signal [cps] Unshelved Shelved 2D5/2 Lifetime [s] (at zero pressure) 10 20 30 40 50 60 70 Experiment Theory Plumelle ‘80 Nagourney ‘86 Madej ‘90 Guet ‘91 Gurell ‘07 Safronova ‘10 Auchter ‘14 Sahoo ‘12 This work Dzuba ‘01 Diagnostic: 30 s lifetime sensitive to perturbations of ion Determine D-state lifetime: matrix element A. Mohanty et al., to be submitted

Atomic Parity Violation Prospects for Ra+ Atomic Parity Violation sin2 θW from Atomic Parity Violation large APV (~Z>3) simple atomic structure 𝐸1 𝐴𝑃𝑉 =𝑘∙ 𝑄 𝑊 Ba+ Ra+ developing experimental setup Good understanding of setup atomic properties determination Introducing light fields for APV light shifts Atomic Properties from online produced radium Activity on Ra+ colinear spectroscopy (ISOLDE) Muonic Radium experiments for charge radius E. Dijck A.Mohanty M. Nunez Portela N.Valappol A. Grier O.Boll K. Jungmann L.Willmann

Measurement Cycle

5 ions?

138Ba+ Ion crystal simulations E-field Ion trap is not (very) selective

E-field

Dark ions Chemical reactions!