D. DeMille, E.Hudson, N.Gilfoy, J.Sage, S.Sainis, S.Cahn, T.Bergeman, * E.Tiesinga † Yale University, * SUNY Stony Brook, † NIST Motivation: why ultracold polar molecules? Photoassociation: Rb + Cs  RbCs* Production & state-selective detection of metastable RbCs (v  1) Production of absolute ground-state RbCs X(v=0) Optical trapping of metastable RbCs (v  1) The (near) future Enhanced sensitivity to variation of  m e /m p in Cs 2 Production of ultracold polar molecules from atoms Funding NSF, Keck Foundation, DOE Packard Foundation DeMille Group

lab picture: people Jeremy Sage Sunil Sainis Jamie Kerman Tom Bergeman (Stony Brook) Eite Tiesinga (NIST) Nate Gilfoy Eric Hudson Theory Experiment (Yale)

Applications of ultracold polar molecules Electrically polarized molecules have tunable interactions that are extremely strong, long-range, and anisotropic--a new regime  New, exotic quantum phases checkerboard, supersolid, BCS, etc.  Models of strongly correlated systems quantum Hall, lattice spin systems, dipolar Wigner crystals, layered/chained systems, etc.  Large-scale quantum computation Coherent/quantum molecular dynamics  Novel collisional phenomena  Ultracold chemical reactions Precision measurements/symmetry tests --narrow lines improve sensitivity AND --molecular structure amplifies effects  Time-reversal violating electric dipole moments (  10 3 vs. atoms)  Parity-violation: anapole moments/Z 0 boson couplings (  !)  Time-variation of fundamental constants (also non-polar) Bohn, Krems, Dalgarno, Hutson, Balakrishnan, Meijer, Ye et al., etc… Hinds et al., Doyle, D.D., Ye, Flambaum, Kozlov, etc… Zoller, Büchler, et al., Lewenstein, Lukin, Demler, Baranov, D.D., etc., etc., etc.…

-V +V Optical lattice w/transverse confinement Strong E-field Weak E-field Electric dipole-dipole interaction Quantum computation w/polar molecules in a lattice bits = electric dipole moments of polarized diatomic molecules register = array of bits in optical lattice (weak trap  low temp  10  K) processor = microwave resonance w/spectroscopic addressing (robust, like NMR) interaction = electric dipole-dipole (strong  fast CNOT gates ~ kHz) decoherence = scattering from trap laser (weak trap  long T ~ 5 s) readout = laser ionization or cycling fluorescence + imaging (fairly standard) scaling up? ( bits reasonable?...one/site via Mott insulator w/ n  cm -3 ) D.D., PRL 88, (2002); Ostrovskaya; Kirby/Cote/Yellin; Kotochigova/Tiesinga;…

Cold molecules from cold atoms I: photoassociation |  e ( R )| 2 |  g (R) | 2 V e (R) V g (R) “Condon radius” R C PA laser Internuclear distance R energy EKEK S+P S+S transition rates governed by free-bound* Franck-Condons polar molecule  heteronuclear heteronuclear excited-state potentials have short range (r -6 only)  PA harder due to van der Waals “speedup” electronically excited molecular states primarily decay into hot free atom pairs  loss of atoms from MOT Seminal early work: Homonuclear expt. Heinzen, Pillet, UConn, etc. (’90s) Theory: Julienne, etc. Heteronuclear expt. Bigelow (‘98) Theory: Wang & Stwalley (’98) spont. emiss.

MOT trap loss photoassociation spectra RbCs and Cs 2 rotational structure (Ω = 0) RbCs rotational + hyperfine structure (Ω = 1,2) dozens of bandheads observed; analysis yields novel information on long-range heteronuclear potentials, non-adiabatic couplings, etc. hfs analysis still needed A.J. Kerman et al., Phys Rev. Lett. 92, (2004) spectroscopically selective production of individual low-J rotational states up to 70% trap depletion for RbCs   (100%) atom-molecule conversion Similar data for KRb (UConn ‘04), NaRb (Rochester ’07) RbCs

Cold molecules from cold atoms II: radiative stabilization |  e ( R )| 2 |  g (R) | 2 V e (R) V g (R) “Condon radius” R C laser Internuclear distance R energy EKEK S+P S+S decay to hot free atom pairs or ground-state molecules (ratio from FCFs: more favorable for heteronuclear!) Dissipation via spontaneous emission  accumulation (metastable,   1 s) BUT electronic ground state population distributed over several high vibrational states molecules at translational temperature of atoms (modulo two photon recoils) rotational state selection in PA + selection rules  few rotational states (1-3)

Detection of metastable RbCs: ionization + mass spec channeltron -2 kV electrode +2 kV Cs,Rb time 10 ns 532 nm 5 mJ nm 0.5 mJ PA laser strong, non- selective excitation ionization pulse Similar detection + temperature measurement in many species: RbCs: Yale, Aero. Corp. KRb: Sao Paolo, UConn NaRb: Rochester LiCs: Freiburg

Ground-state (vibrationally excited) = 100 K Time to ballistically exit detection region t ~ 10 ms  translational temperature T ~ 100  K delay PA

Cold molecules from cold atoms III: stopping the vibration |  i (R) | 2 EKEK |  g ( R )| 2 |  e ( R )| 2 laser Internuclear distance R energy V g (R) S+S V e (R) S+P ~1 rotational state Atomic translational temperature BUT distributed over several high vibrational states Laser transfer from high vibrational level to v=0:  TRULY ultracold molecules (translation, rotation, vibration) High vibrational states UNSTABLE NOT POLAR  want vibrational ground state! NEEDED: initial state location & population pathway w/Franck-Condon overlap for “pump” AND “dump”

Mapping the vibrational distribution of cold RbCs clear ID of (2) 3  + band origin a 3  + A.J. Kerman et al., PRL 92, (2004) clear ID of a 3  + vibrational pattern (weakly bound) ~7% decay into most-populated a 3  + (v = 37) level big, regular patterns in spectrum yield (2) 3  + vibrational splittings (2) 3  + weak, selective excitation ionization +UConn (KRb, 2005) + spin-orbit doubling 2 nd order spin-orbit

v = 0 E pump = cm -1 E dump = cm -1 Transfer verified on ~6 separate transitions Estimated efficiency ~6%, limited by poor pulsed laser spectral profiles Narrow rotational distribution, limited by pulsed laser linewidth (2) 3  + (1) 1  1 J.Sage et al., PRL 94, (2005) Production of vibronic ground state by stimulated pumping

KRb metastable (least bound state) production reported: Hamburg, JILA Heteronuclear molecules from degenerate gases Feshbach resonance No dissipation needed100% transfer to single molecular state Viable pathways for stimulation to X 1  + (v=0) ground state tentatively identified for ALL bialkali species (Stwalley) Stimulated Raman? (Lattice assisted?) JILA, MIT, Florence, Hamburg,… STIRAP: Drummond, Heinzen,... Lattice: Damski et al.; Moore & Sadeghpour; etc. protection from collisions in lattice

Ongoing work: optically trapped polar, absolute ground-state RbCs molecules Lattice CO 2 Trap Photoassociation in optical trap allows accumulation of vibrationally excited molecules Trapped molecular sample will allow study of: atom-molecule collisions molecule-molecule collisions dipolar effects? chemical reactions? 1+1 REMPI & TOF mass spec as before for state-selective detection

Trapped RbCs lifetime vs. precursor atom density  = 270 ms ± 81 ms  atoms ~ cm -3  = 86 ms ± 7 ms  atoms ~ cm -3 Compare to:  atoms ~ 4 s Clear evidence for RbCs collisions!

Coming soon: “distilled” sample of polar, absolute ground-state RbCs molecules Lattice CO 2 Trap Photoassociation in optical trap allows accumulation of vibrationally excited molecules STIRAP transfer to X(v=0) w/transform- limited lasers Dipole CO 2 Trap +V -V Gravity v = 0, J = 0 polar molecules levitated by electrostatic potential other species (atoms, excited molecules) fall from trap Anticipated: pure, trapped sample of >3 /cm 3 T  15 K

Why study time variation of electron-to-proton mass ratio  ? (   m e /m p ) Variation of “constants” motivated by --naïve models of dark energy (an experimental fact!) --ideas about extra dimensions (from string theory) --connections to equivalence principle --tentative observations in cosmological data Grand unified theories suggest (/) ~ 30(/) [variation of   fine structure constant strongly constrained] Optical atomic clocks insensitive to  Laboratory tests now comparable in sensitivity to cosmological limits

Enhanced sensitivity to d  /dt with molecules (   m e /m p ) ~eV

Sensitivity to d  /dt vs. binding energy (   m e /m p ) E R  1.1  “pile-up” near dissociation limit harmonic: linear slope=1/2 anharmonicity slows response response 0 at D e Sensitivity vs. energy Morse potential

d/dt with ultracold Cs 2 ultracold Cs 2  narrow lines (  1 Hz?) X 1  g + a 3  u + high level densities  singlet-triplet overlaps common (?) efficient Cs 2 formation (via photoassociation or Feshbach + stim. Raman) into deeply-bound a 3  u levels possible [favorable FC factors] +

Two-color PA spectroscopy of Cs 2 “Typical” abs. sensitivity  ~ 0.01 Hz for  =   improvement over current limits feasible? 0 g 6s 1/2 +6p 3/2 - a 3  u 6s 1/2 +6s 1/2 + Cs 2 ion detection + Cs 2 X 1  g sensitivity to  + triplet well bottom range studied X1gX1g + Cs 2 formation PA Probe

perturbing singlet level perturbed triplet level GHz binding =4, F=10 =4, F=8,9 S=1, I=7, f=7 GHz binding Theory: E. Tiesenga, T. Bergeman ℓ I S f F Observation of singlet-triplet degeneracy in Cs 2

Demonstrated optical production of ultracold polar v=0 molecules: T ~ 100  K now, but obvious route to lower temperatures Same technique for transfer to ground state applicable to all heteronuclear bialkalis + levels produced by e.g. Feshbach association Formation efficiency of >5% into most-populated v  1 levels of the ground electronic state AND efficient transfer to v=0 ground state (>5% observed, ~100% projected) Demonstrated optical trapping of v  1 levels w/long lifetime  Collisional studies of ultracold, heteronuclear bialkalis  Large samples of stable, trapped, ultracold polar molecules in reach? New system for enhanced sensitivity to variation of   m e /m p identified & under investigation in Cs 2 Status & Outlook: ultracold bialkali molecules from atoms

Heteronuclear  polar? from: M.Aymar & O.Dulieu, J. Chem. Phys. 122, (2005); also: Kotochigova, Julienne, Tiesinga d<10 -2 ~300 GHz binding energy Dipole moment d (Debye) Weakly bound levels  little electron wavefn. hybridization  small dipole moment: d   R 7  (B.E.) range X 1+X 1+ a 3+a 3+ RbCs X(v=0) d = 1.3D Deep X 1  + levels have substantial dipole moment d ~ D (2.54 D = 1 ea 0 ) Dipole moments of heteronuclear bialkalis