Kenneth Brown, Georgia Institute of Technology

Cold Molecular Ions 15  m Ca + X + ?

Ion Trap Ions are trapped in an oscillating quadrupole field Ion stability is based on charge to mass ratio Radial pseudopotential is weaker for larger masses RF ground DC RF ground DC Stability condition  V rf / (r 0 2  rf 2 )] <1

Ions for Doppler Cooling 397 nm 866 nm S 1/2 D 3/2 P 1/2 Ca + 40 Ca + X 2  v’=0 X 2  v=0 BH + Challenges of Laser-Cooling Molecular Ions J. H. V. Nguyen, C. R. Viteri, E. G. Hohenstein, C. D. Sherrill, K. R. Brown, and B. Odom New J. Phys. 13, (2011) X 2  v’=1 370 nm 935 nm S 1/2 D 3/2 P 1/2 Yb Yb + [3/2] 1/2

Doppler Laser Cooling 5 After n absorption-emission cycles, the average atom momentum is reduced by n ħ k. Absorbed photons must be resonant with the Doppler-shifted transition. Cooling rate and temperature limit are proportional to the linewidth.

Doppler Recooling R.J. Epstein et al., Phys. Rev. A (2007) 397 nm 866 nm S 1/2 D 3/2 P 1/2 Simple experimental setup. Difficult for low heating rates. transition linewidth > trap frequency.

Sideband Cooling g e 729 nm 854 nm n n -1 S 1/2 m = -1/2 n -1 n P 3/2 m = -3/2 D 5/2 m = -5/2

Sideband Measurement 397 nm 866 nm S 1/2 D 3/2 P 1/2 D 5/2 P 3/2 854 nm 729 nm J. Labaziewicz et al. Phys. Rev. Lett. 100, (2008) Temperature measurement conceptually simpler. RSB=k BSB=k Transition linewidth < trap frequency.

Atomic & Molecular Ions (115 mK) A. Ostendorff, et al., Phys. Rev. Lett., 97, (2006) K. Mølhave and M. Drewsen, Phys. Rev. A. 62, (2000) Laser cooled Mg + cools MgH + Laser cooled Ba + cools AlexaFlour + Laser-cooled MS: T. Baba and I. Waki, Jpn. J. Appl. Phys., 35, L (1996)

Molecular Ion Spectroscopy J. C. J. Koelemeij, et al. Phys. Rev. Lett (2007) Fluorescence detected REMPD

Molecular Ion Spectroscopy Action Spectroscopy X. Tong, A. Winney, and S. Willitsch Phys. Rev. Lett (2010) N Ar  Ar + + N 2 This reaction is energetically forbidden when N 2 + is in the ground state.

One Ion Limit Ca + CO Trap atomic and molecular ions2. Laser cool ion crystal 3. Heat ion crystal by exciting the molecular ion. 4. Measure temperature change by laser-induced atomic fluorescence

Quantum Logic Spectroscopy A B g e 0 1 A B g e 0 1 A B g e 0 1 Control Spect. Motion Sideband cool to vibrational ground state of the crystal. Excite the spectroscopy ion at the A-B transition plus one motional quanta. If the motion is excited, the g-e transition minus one motional quanta can be observed. Initialize Probe Detect P. O. Schmidt et al., Science 309, 749 (2005)

Be + -Al + Clock Figures from P. O. Schmidt et al., Science 309, 749 (2005) Clock measurement described in T. Rosenband et al., Science 319, 1808 (2008) Tests of Relativity C. W. Chou et al., Scienc, 329, 1630 (2010) A B g e Control Spectroscopy A-B transition in Al + measured by monitoring the population in g by Be + fluorescence.

QLS and SHS

C.R. Clark, J.E. Goeders, Y. Dodia, C.R. Viteri, and KRB, PRA, 81, (2010) Sympathetic Heating Spectroscopy 397 nm 866 nm S 1/2 D 3/2 P 1/  Isotope Abundance  40 Ca 96.9%  44 Ca 2.09% D. Lucas et al., PRA 69, (2004)  Isotope Shift  44 Ca 1 S P 1 : 774 MHz  44 Ca + S 1/2 -P 1/2 : 842 MHz  44 Ca + D 3/2 -P 1/2 : MHz

Cooling vs Heating Cooling Heating LIF SHS (t heat =250 ms) # of Photons 40 s 397 =7 40 s 866 =1000 t meas =3 ms 44 s 397 =0.03 t meas =750 ms 40 Ca + 44 Ca + cool heat recool

SHS Limits For t heat = 1s, there is measurable trap heating. t heat = 1s t recool = 0.39 s t int = 0.5 s Compare to t meas =1.89 s. Calculated fluorescence lost in the detector noise. <1000 photons into 4 

J. E. Goeders, C. R. Clark, G. Vittorini, K.E. Wright, C. Ricardo Viteri, and KRB Resolved Sideband Mass Spectrometry 397 nm 866 nm S 1/2 D 3/2 P 1/2 D 5/2 P 3/2 854 nm 729 nm

729 nm laser Central frequency drifts less than 10 kHz over 7 hrs ATFilms ULE Spacer 100,000 finesse 500 MHz FSR

Zeeman Spectroscopy 729 nm 397 nm 866 nm

Zeeman Spectroscopy

Normal Modes of Two Ions Axial modes Axial frequency of M 1 M1/M2M1/M2 M. Drewsen et al. PRL (2004).

Two Calcium Ions COM BM S 1/2 -D 5/2 Frequency Offset [MHz] Intensity (Arb. Units)

Other Ions Load CaH + or CaO + by leaking in torr H 2 or O 2 Load other isotopes by resonant enhanced two photon ionization

Center of Mass Mode 40 Ca Ca + 40 Ca CaO + 40 Ca Ca + 40 Ca Ca + 40 Ca Ca + 40 Ca Ca + 40 Ca CaH + Frequency Offset (MHz) Population in D 5/

J. H. V. Nguyen, C. R. Viteri, E. G. Hohenstein, C. D. Sherrill, K. R. Brown, and B. Odom New J. Phys. 13, (2011) Application to laser-cooling BH + Laser Cooling of SrF DeMille and coworkers Phys. Rev. Lett. 103, (2009) Nature 467, 820 (2010)

K=0K=1K=2K=3   2 2 v’=0 v’=1 v’=n v=0 v=1

K=0K=1K=2 v’=0 v’=1 v’=n v=0  2 X  2 B  2 A  2 X dissociative Complications Parity Violation Vibrational Decay Photodissociation Predissociation

BH + Vibrational relaxation transforms spread in vibrational states into a spread in rotational states 379nm 417 nm

Precision Spectroscopy v’=0 v’=1  2 X  2 A v=0 Cooling lasers: v=0 ← v’=0, Δ J=0,-1 C1-C2 (one laser plus EOM) C3-C4 (two lasers) Repump lasers: v=0 ← v’=1 Δ J=0,-1 R1-R2 (one laser plus EOM) R1-R4 (one pulsed laser) v=0 ← v’=0, Δ J=-1 PR1-PR2 (one pulsed laser)

Photons Scattered

Conclusions and Outlook  Single ion techniques can be used to accurately measure lines for both allowed and forbidden transitions  BH + is a promising candidate for direct laser cooling  Vibrational overtones of CaH + are good QLS candidates (wavelengths from M. Kajita)  nm  nm  nm

Cold Molecular Ions Surface Electrode Traps QEC and Resources Q1Q1 Q1Q1 T|+  A A Postdoc position available