Fundamental physics with diatomic molecules: from particle physics to quantum computation....!

1. 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. • parity violation: Z0 couplings & nuclear anapole moments D. DeMille Yale University Physics Department Funding: NSF, Keck Foundation, ARO, DOE (Packard Foundation,Sloan Foundation, Research Corporation, CRDF, NIST)

2. 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…?

3. Structure of molecules I: electronic states States of separated atoms Electron clouds “merge” in potential well S+P Energy Ve(R) S+S Vg(R) Internuclear distance R

4. Structure of molecules II: vibration V(R) Energy Internuclear distance R

5. Structure of molecules III: rotation Angular momentum J/ • • • Moment of intertia I = MR2; Angular momentum J = n; Energy of rotation E = J2/2I 3- Energy 2+ R 1- 0+

6. Molecular electric dipoles polarized molecules act like permanent dipoles With E-field: induced dipole No E-field: no dipole! z, E J = 1, mJ = 0 “=“ |p> - ++ + |>  |s>+|p> + + + - + + ++ + + |>  |s>-|p> J = 0 “=“ |s> + + - + Wavefunctions of polar molecules Small splitting (~10-4 eV) between states of opposite parity (rotation) leads to large polarizability (vs. atoms, ~ few eV)

7. S d P T Purcell Ramsey Landau A permanent EDM Violates T and P CPT theorem T-violation = CP-violation

8. Standard Model Supersymmetry  t W d t s W W b e e   ~ ~ e e e ~ e  A. From cloud of accompanying “virtual” particles Q. How does an electron EDM arise?

9. Searching for new physics with the electron EDM Yale I Yale I Yale II Yale II Berkeley Berkeley (projected) (projected) (projected) (projected) (2002) (2002) Multi - Multi - Higgs Higgs Extended Left - Right Extended Left - Right Technicolor Symmetric Technicolor Symmetric Standard Standard Model Lepton Flavor - Model Alignment Lepton Flavor - Alignment Changing Changing Split SUSY Split SUSY SO(10) GUT SO(10) GUT Seesaw Neutrino Yukawa Couplings Seesaw Neutrino Yukawa Couplings Exact Accidental Approx. Approx. Exact Accidental Approx. Approx. Universality Cancellations CP Universality Universality Cancellations CP Universality ~ Heavy ~ Na ï ve SUSY Heavy Na ï ve SUSY sFermions sFermions - - 39 39 - - 40 40 - - 25 25 - - 26 26 - - 27 27 - - 28 28 - - 29 29 - - 30 30 - - 31 31 - - 32 32 - - 33 33 - - 34 34 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 d d ( ( e e cm cm ) ) × × e e

10.  E E B -2dE +2dE S  w -2dE +2dE General method to detect an EDM Energy level picture: Figure of merit:

11. Amplifying the electric field Ewith a polar molecule Electrical polarization of molecule subjects valence electrons to huge internal field Eint > 1010 V/cm with modest polarizing field Eext ~ 10 V/cm Eext Pb+ Eint O– Explicit calculations indicate valence electron feels Eint ~ 2Z3 e/a02 ~ 2.1 - 4.0  1010 V/cm in PbO* semiempirical: M. Kozlov & D.D., PRL 89, 133001 (2002); ab initio: Petrov, Titov, Isaev, Mosyagin, D.D., PRA 72, 022505 (2005).

12. J=1- J=1+ Brf  z a(1) [3+] E B S S m = -1 m = 0 m = +1 - S || z + X, J=0+ n n - - - - + + + + - - - - n n + + + + Spin alignment & molecular polarization in PbO (no EDM)

13. S S E B E E E S S n n - - + + - - n n + + EDM measurement in PbO* “Internal co-magnetometer”: most systematics cancel in up/down comparison!

14. The central dogma of physics (c.f. S. Freedman) Theorist :: Experimentalist :: Fact   Farmer :: Pig :: Truffle

15. 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

16. Present Experimental Setup (top view) Larmor Precession  ~ 100 kHz B E PMT Vacuum chamber solid quartz light pipes quartz oven structure PbO vapor cell Data Processing Pulsed Laser Beam 5-40 mJ @ 100 Hz  ~ 1 GHz   B Vapor cell technology allows high count rate (but reduced coherence time)

17. 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)

18. [D. Kawall et al., PRL 92, 133007 (2004)] Current status: a proof of principle • 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 ~ 310-29ecm within ~2 years...?

19. 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 computationD. DeMille, Phys. Rev. Lett 88, 067901 (2002)

20. Quantum computation with ultracold polar molecules E-field due to each dipole influences its neighbors Weak E-field Strong E-field +V Standing-wave trap laser beam -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)

21. With interaction H' = aSaSb Without interactions Desired: a flips if b=1 Undesired: a flips if b=0 |1>a|1>b |1>a|1>b |0>a|1>b |0>a|1>b |1>a|0>b |1>a|0>b |0>a|0>b |0>a|0>b CNOT requires bit-bit interactions Size of interaction term “a” determines maximum gate speed: -1 ~  ~ a

22. Quantum computationwith 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

23. Cold molecules from cold atoms: photoassociation • very weak free-bound (but excited) transition driven by laser for long times (trapped atoms) |Ye(R)|2 S+P • electronically excited molecules decay to hot free atoms energy or to ground-state molecules laser Ve(R) |Yf(R)|2 |Yg(R)|2 EK S+S Vg(R) Internuclear distance R • 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

24. RbCs* and Cs2* formation (Ω = 0) MOT trap loss photoassociation spectra RbCs • up to 70% depletion of trap for RbCs  near 100% atom-molecule conversion • spectroscopically selective production of individual low-J rotational states A.J. Kerman et al., Phys Rev. Lett. 92, 033004 (2004)

25. Verification of polar molecules: behavior in E-field Fitted electric dipole moment for this (W=0+) state: m = 1.3 Debye

26. Detection of vibrationally excited RbCs Cs,Rb channeltron -2 kV electrode +2 kV 670-745 nm 0.5 mJ 532 nm 5 mJ 10 ns time

27. Vibrationally excited RbCs @T = 100 K PA delay decay time consistent with translational temp. T ~ 100 mK as expected from atomic temps. Decay due to ballistic flight of RbCs molecules from ~2 mm diam. detection region

28. Cold molecules from cold atoms: stopping the vibration |Ye(R)|2 S+P energy laser Ve(R) |Yf(R)|2 |Yg(R)|2 EK S+S Vg(R) Internuclear distance R • free-bound (but excited) transition driven by laser • 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 state! • Laser pulses should be able to transfer one excited state to vibrational ground state: • TRULY ultracold molecules (translation, rotation, vibration)

29. lab picture: optics

30. Production of absolute ground state molecules Epump= 9786.1 cm-1 Edump = 13622.0 cm-1 • Raman transfer verified on • ~6 separate transitions • Estimated efficiency ~8%, limited by • poor pulsed laser spectral profiles v = 0

31. Coming next: “distilled” sample of polar, absolute ground-state RbCs molecules Lattice CO2 Trap Dipole CO2 Trap Photoassociation in optical trap allows accumulation of vibrationally excited molecules v = 0, J = 0 polar molecules levitated by electrostatic potential -V +V STIRAP transfer to X(v=0) w/transform- limited lasers other species (atoms, excited molecules) fall from trap Gravity Anticipated: pure, trapped sample of >3104 RbCs(v=0) @n>1011/cm3 T  15 K

32. 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

33. Ph.D. Students S. Sainis, J. Sage, (F. Bay), Y. Jiang, J. Petricka, S. Bickman, D. Rahmlow, N. Gilfoy, D. Glenn, A. Vutha, D. Murphree, P. Hamilton DeMille Group Undergrads (J. Thompson, M. Nicholas, D. Farkas, J. Waks, J. Brittingham, Y. Gurevich, Y. Huh, A. Garvan, C. Cheung, C. Yerino, D. Price) Collaborators (L. Hunter [Amherst]), A. Titov, M. Kozlov [PNPI], T. Bergeman [Stony Brook], E. Tiesinga [NIST], R. Paolino [USCGA], J. Doyle [Harvard] Postdocs/Staff: S. Cahn, (V. Prasad, D. Kawall, A. J. Kerman)