Narrow oppositeparity level crossings in a diatomic free

Narrow opposite-parity level crossings in a diatomic free radical Dave De. Mille, E. Altuntas, J. Ammon, S. B. Cahn, R. Paolino* Physics Department, Yale University *Physics Department, US Coast Guard Academy • Motivation: nuclear spin-dependent parity violation • PV measurement strategy: Zeeman-tuned rotational degeneracies • Measurements: Stark-induced transitions near a rotational level crossing • Outlook De. Mille Funding: NSF Group

Mechanisms for atomic/molecular parity violation Electroweak coupling to nuclear spin: “NSD-PV” e e Ve+Ae Z 0 N e g + VN+AN NSD-PV from direct Z 0 exchange: + numerically suppressed I N nuclear spin I Z 0, W ± PV weak interactions inside nucleus induce nuclear “anapole moment” that couples to electron magnetically Weak-interaction Hamiltonian HW mixes hyperfine states with opposite parity

Enhanced parity mixing via systematic level degeneracies in diatomic free radicals Example: 2 S with single nuclear spin I=1/2 (e. g. 138 Ba. F) Typically several crossings for B = 0. 3 - 1 T JP Rotation + e- spin 1/2 3/2 - + nuclear spin (I=1/2) - 1 - 1/2 - 01+ 1/2+ 0+ 2 1 - Effective energy separation D ~ 1 k. Hz ~ 10 -11 e. V near crossing 1011 enhancement vs. atoms! B

The ZOMBIES NSD-PV experiment at Yale Z eeman-tuned O ptically prepared and detected Molecular B eams for the Investigation of E lectroweak effects using S tark interference

Molecule PV experimental schematic Superconducting solenoid B (1) E 0 (2) (1) (2) (3) (4) (3) E 0 Laser |-> Laser |+>

Stark interference method: apply oscillating E-field to mix nearly-degenerate levels Zeeman-shifted Energy E Center of Magnet: Homogeneity d. B/B < 10 -7 EE E+ Position z Time t = z/v

Strategy to detect PV in near-degenerate levels |-> |+> D. D. , S. B. Cahn, D. Murphree, D. A. Rahmlow, and M. G. Kozlov Phys. Rev. Lett. 100, 023003 (2008) Large Stark Term Even in E 0 Small Weak Term

Signal, Asymmetry, Sensitivity

Experimental study of Stark-induced transitions at level crossings in 138 Ba. F |ms, m. I, m. N>

Opposite-parity level crossing spectroscopy Apply unipolar E-field pulse E- E-field from step potential on cylindrical boundary -V E+ +V

Simple Stark-induced transition at a level crossing |-> |+>

Typical level-crossing data: lineshape & position B-field at crossing from position of peak Interaction time t from width of peak Matches calculated FWHM d. D ~ 6 k. Hz D (k. Hz)

Rabi flopping: period vs. E 0 determines d Peak normalized signal [suppressed Dipole matrix element d = 3574(7) Hz/(V/cm) by spin flip] Peak applied electric field E 0 [V/cm]

Complex lineshapes from off-resonant Stark shifts Apply single E-field pulse Spatially-varying detuning due to offresonant Stark shifts E- E+ Center of Magnet

Data: lineshapes from off-resonant Stark shifts Data and fit including spatially-varying Stark shift Fit at several different E 0 values determines crossing position vs. B, and Stark shift strength

Calculated level crossings in 138 Ba. F |ms, m. I, m. N> 16

Extracted data from 138 Ba. F crossings: crossing positions & dipole matrix elements Type Initial Calc. X Obs. X (Gauss) PR EL (Gauss) Calc. d Obs. d Unc. obs. (Hz/V/cm) IM INA RY Generally excellent agreement with all predictions from standard spin/rotation/hyperfine + Zeeman Hamiltonian treatment; some details still to be completed in fit

Initial, very preliminary NSD-PV data in 138 Ba. F Shaped E-field Normalized Signal S 0, 4 0, 3 0, 2 0, 1 Take NSD-PV data HERE Positive E 0 a Negative E 0 0 -10 -5 0 Detuning D (k. Hz) 5 10

Conclusions & Outlook: Parity Violation with Diatomic Free Radicals • Opposite-parity level-crossing spectroscopy: linewidth (as small as 4 k. Hz), lineshapes, positions, matrix elements, etc. all in agreement with theory • Molecular systems very promising for study of NSD-PV: excellent S/N & systematics, leverage from developed techniques • Multiple nuclei available for anapole moment determination (we will use 137 Ba in 137 Ba. F first; 19 F in 138 Ba. F now for testing) • Measurements of fundamental Z 0 couplings possible in long term? • Likely extensions with new molecular data, improved molecular beams, laser cooling, etc: an “anapole factory”…? • n. b. same level crossings suggested for simulation of conical intersections in trapped ultracold molecules [Hutson, Krems, etc. ]

Emine Altuntas Jeff Ammon John Barry Colin Bruzewicz Sid Cahn, Ph. D Eustace Edwards Danny Mc. Carron, Ph. D Eric Norrgard Brendon O’Leary Toshihiko Shimasaki Matt Steinecker Adam West, Ph. D De. Mille Group Prof. Rich Paolino US Coast Guard Academy