Search for the Electron Electric Dipole Moment Using PbO
Fundamental physics with diatomic molecules: from particle physics to quantum computation....! electron electric dipole moment search (CP, new physics) sources of ultracold molecules for wide range of applications: --large-scale quantum computation --time variation of fundamental constants --etc. D. DeMille parity violation: Z Yalecouplings University & nuclear anapole momentsPhysics Department 0 Funding: NSF, Keck Foundation, ARO, DOE (Packard Foundation, Sloan Foundation, Research Corporation, CRDF, NIST) Structure of molecules 0: A diatomic molecule has one atom too many. --Art Schawlow (and most atomic physicists)
....or maybe not? new internal degrees of freedom in molecules useable as a resource? Structure of molecules I: electronic states Energy Electron clouds merge in potential well States of separate d atoms S+P Ve(R ) S+S Vg(R) Internuclear distance R
Structure of molecules II: vibration Energy V(R) Internuclear distance R Structure of molecules III: rotation Moment of intertia I = MR2; Angular momentum J = n; 3Energy Energy of rotation E = J2/2I Angular momentum J/
2+ R 10+ Molecular electric dipoles Wavefunctions of polar molecules No E-field: no dipole! J = 1, mJ = 0 = |p> With E-field: induced dipole z, E + ++ + + |> |s>+|p>
- Small splitting (~10-4 eV) between states of opposite parity (rotation) leads to large polarizability (vs. atoms, ~ few eV) A permanent EDM Violates T and P H Magnetic dipole B - B d P Purcell Ramsey Landau H Electric dipole - d E - d E S T CPT theorem T-violation = CP-violation
Q. How does an electron EDM arise? A. From cloud of accompanying virtual particles Standard Supersymmetry Model t ~ e W e e W d t s ~ b ~ e
W ee Searching for new physics with the electron EDM Yale Yale II Yale II Berkeley (projected) (projected) (2002) (projected) MultiMultiHiggs Higgs Extended Extended Technicolor Technicolor Left-Right Left -Right Symmetric Symmetric Lepton FlavorLepton FlavorChanging Changing Standard Standard
Model Model Alignment Alignment Split SUSY Split SUSY SO(10) GUT SO(10) GUT Seesaw NeutrinoYukawaCouplings Seesaw NeutrinoYukawaCouplings Accidental Accidental Cancellations Cancellations -25 -26 10 Exact Exact Universality Universality
Approx. Approx. Universality Universality Heavy Heavy sFermions sFermions Na ve SUSY Nave SUSY 10 Approx. Approx. CP CP -27 10 -28
~~ -39 10 -40 10 General method to detect an EDM -2dE +2dE B E Energy level picture: S -2dE +2dE
Figure of merit: shift resolution dE 1/ coh S / N 1 E coh N Tint Amplifying the electric field with a polar molecule Electrical Pb polarization of molecule subjects valence int electrons to huge internal field int > 1010 V/cm
O with modest polarizing field Explicit calculations indicate ext ~ 10 valence V/cm + ext electron feels int ~ 2Z3 e/a02 ~ 2.1 - 4.0 1010 V/cm in PbO* Spin alignment & molecular polarization in PbO (no EDM) n - n S + + -
- + -Brf z+ a(1) [3+] J=1J=1 m = -1 + S m=0 - n + m = +1
S B E + + + ||-z n - + - X, J=0+ EDM measurement in PbO* Sn - Sn +
Internal co-magnetometer: most systematics cancel in up/down comparison! Sn + B E + - Sn + - The central dogma of physics (c.f. S. Freedman) Theorist :: Experimentalist :: Fact Farmer ::
Pig :: Truffle PbO vapor cell and oven Sapphire windows bonded to ceramic frame with gold foil glue Gold foil electrodes and feedthroughs quartz oven body 800 C capability wide optical access w/non-inductive heater for fast switching Signal Present Experimental Setup (top view) PM
T Data Processin g E solid quartz light pipes PbO vapor cell B Larmor Precessio n ~ 100 kHz Vacuum chamber quartz oven structure Pulsed Laser
Beam 5-40 mJ @ 100 Hz ~ 1 GHz B Vapor cell technology allows high count rate (but reduced coherence time) Zeeman quantum beats in PbO Excellent fit to Monte Carlo w/PbO motion, known lifetime Shot noise-limited S/N in frequency extraction (Laser-induced spin alignment only here) Current status: a proof of principle [D. Kawall et al., PRL 92, 133007 (2004)] PbO vapor cell technology in place Collisional cross-sections as expected anticipated density OK Signal sizes large, consistent with expectation; improvements under way should reach target count rate: 1011/s. Shot-noise limited frequency measurement using quantum beats in fluorescence g-factors of -doublet states match precisely co-magnetometer will be very effective E-fields of required size applied in cell; no apparent problems First useful EDM data ~early 2006;
de ~ 310-29 ecm within ~2 years...? Applications of ultracold polar molecules Precision measurements/symmetry tests: narrow lines improve sensitivity & molecular structure enhances effects (small energy splittings) Time-reversal violating electric dipole moments (103 vs. atoms) Parity violation: properties of Z0 boson & nuclear anapole moments (1011 !!) New tests of time-variation of fundamental constants? (103 vs. atoms) Coherent/quantum molecular dynamics Novel collisional phenomena (e.g. ultra-long range dimers) ultracold chemical reactions (e.g. tunneling through reaction barriers ) Electrically polarized molecules have tunable interactions that are extremely strong, long-range, and anisotropic--a new regime Models of strongly-correlated systems (quantum Hall effect, etc.) Finite temperature quantum phase transitions New, exotic quantum phases (supersolid, checkerboard, etc.) novel BCS pairing mechanisms (models for exotic superconductivity) Large-scale quantum computation D. DeMille, Phys. Rev. Lett 88, 067901 (2002) Quantum computation with ultracold polar molecules Strong E-field E-field due to each
dipole influences its neighbors +V Standing-wave trap laser beam Weak E-field -V bits = electric dipole moments of polarized diatomic molecules register = regular array of bits in optical lattice trap (weak trap low temp needed!) processor = rf resonance w/spectroscopic addressing (robust, like NMR) interaction = electric dipole-dipole (CNOT gate speed ~ 1-100 kHz) decoherence = scattering from trap laser (T ~ 5 s Nop ~ 104-106 !) readout = laser ionization or cycling fluorescence + imaging (fairly standard) scaling up? (104- 107 bits looks reasonable: one/site via Mott insulator transition) CNOT requires bit-bit interactions With interaction H' =
Without interactions aSaSb |1>a|1>b Desired: |0>a|1>b |1>a|0>b |0>a|0>b a flips if b=1 Undesired: a flips if b=0 Size of interaction term a determines maximum gate speed: -1 ~ ~ a Quantum computation with trapped polar molecules Quantum computer based on ultracold polar molecules in an optical lattice trap can plausibly reach >104 bits and >104 operations in ~5 s decoherence time Based heavily on existing work & likely progress: Main requirement is sample of ultracold (T 10 K) polar molecules with phase space density ~10-3 Anticipated performance is above some very significant technological thresholds:
Nop > 104 robust error correction OK? Crude scaling 300 bits, 104 ops/s teraflop classical computer Cold molecules from cold atoms: photoassociation energ y |e(R)|2 S+P Ve(R) laser |f(R)|2 |g(R)|2 S+S Vg(R) Internuclear distance R EK very weak free-bound (but
excited) transition driven by laser for long times (trapped atoms) electronically excited molecules decay to hot free or to ground-state molecules atoms Production of polar molecules requires assembly from two different atomic species molecules can be formed in single rotational state, at translational temperature of atoms (100 K routine, 1 K possible) BUT molecules are formed in range of high vibrational states MOT trap loss photoassociation spectra RbCs* and Cs2* formation ( = 0) RbCs up to 70% depletion of trap for RbCs
near 100% atom-molecule conversion spectroscopically selective production of individual low-J rotational A.J. Kerman et al., Phys Rev. Lett. 92, 033004 (2004) Verification of polar molecules: behavior in E-field Fitted electric dipole moment for this (=0+) state: = 1.3 Debye Detection of vibrationally excited RbCs Cs,Rb electrode +2 kV 670-745 nm 0.5 mJ time channeltron -2 kV 532 nm
5 mJ 10 ns Vibrationally excited RbCs @T = 100 K PA delay decay time consistent with translational temp. T ~ 100 K as expected from atomic temps. Decay due to ballistic flight of RbCs molecules from ~2 mm diam. detection region Cold molecules from cold atoms: stopping the vibration free-bound (but excited) transition driven by laser energ y |e(R)|
2 S+P Ve(R) laser |f(R)|2 |g(R)|2 S+S Vg(R) Internuclear distance R EK excited molecules can decay to molecular ground state molecules can be formed in single rotational state, at translational temperature of atoms (100 K routine, 1 K possible) BUT molecules are formed in
range of high vibrational states High vibrational states are UNSTABLE to collisions and have NEGLIGIBLE POLARITY need vibrational ground Laser pulses should be able state! to transfer one excited state to vibrational ground state: TRULY ultracold molecules (translation, Production of absolute ground state molecules Epump= 9786.1 cm-1 Edump = 13622.0 cm-1 Raman transfer verified on ~6 separate transitions v=0 Estimated efficiency ~8%, limited by
poor pulsed laser spectral profiles Coming next: distilled sample of polar, absolute ground-state RbCs molecules Lattice Photoassociation CO2 in optical trap Trap allows accumulation of vibrationally excited molecules v = 0, J = 0 polar molecules levitated by electrostatic potential +V STIRAP transfer to X(v=0) w/transformlimited lasers Dipole
CO2 Trap Anticipated: pure, trapped sample of >3104 RbCs(v=0) @n>1011/cm3 T 15 K -V other species (atoms, excited molecules) fall from trap Gravity Status & Outlook: ultracold polar molecules Optical production of ultracold polar molecules now in hand! [J.Sage et al., PRL 94, 203001 (2005)] T ~ 100 K now, but obvious route to lower temperatures Formation rates of up to ~107 mol/s/level in high vibrational states AND efficient transfer to v=0 ground state (~5% observed, 100% possible) Large samples of stable, ultracold polar molecules in reach
molecule trapping (CO2 lattice/FORT), collisions & manipulation (E-fields, rotational transitions, etc.) are next Ultracold polar molecules are set to open new frontiers in many-body physics, precision measurements, & chemical physics DeMille Group Collaborators (L. Hunter [Amherst]), A. Titov, M. Kozlov [PNPI], T. Bergeman [Stony Brook], E. Tiesinga Ph.D. Students S. Sainis, J. Sage, (F. Bay), Y. Jiang, J. Petricka, S. Bickman, D. Rahmlow, N. Gilfoy, D. Glenn, A. Vutha, Undergrads D.Thompson,
Murphree, (J. P. Nicholas, Hamilton M. D. Farkas, J. Waks, J. Brittingham, Y. Gurevich, Y. Huh, A. Garvan, C. Postdocs/Staff: Cheung, S. Cahn, (V. Prasad, C. Yerino, D. D. Kawall, Price)A. J.
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