d) Spectroscopy with Trapped Ions

Ion traps are promising tools for ultrahigh resolution laser spectroscopy because ions can be ob- served over long periods without perturbations. Therefore, transit time broadening and col- lisional effects can largely be eliminated. Because of these properties ion traps are widely dis- cussed as new frequency standards in the microwave and optical region. For such applications well defined atomic transitions are of interest, which in the microwave range can be found between hyperfine levels of the ionic ground state and in the optical region between long living excited states and the ground state.

Radio-Frequency Ion Trap

A quadrupole radio-frequency ion trap (Paul-trap) consists of a ring electrode and two hyperboli- cally shaped endcap electrodes. When these electrodes are supplied with a dc and ac voltage, under appropriate conditions up to 10 8 ions are trapped in a pseudopotential determined by the applied voltages. In this potential the ions are oscillating on a lower fre- quency, the macromotion, which is additionally modula- ted by the micromotion originating from the ac driving field. The ions are excited by a continuous wave or pulsed laser on a resonance transition or even on a ‘forbidden’ optical transition and their response is observed as fluorescence radiation through one of the endcap electrodes which is formed out of a mesh. Our experiments with trapped ions only should be classified as some first steps on the way to ultrahigh resolution frequency measurements, but they already showed two surprising dis- coveries.

Population Trapping in Excited Yb Ions

When resonantly exciting ytterbium (Yb) ions from the 6s 2 S 1/2 to the 6p 2 P 1/2 state a rapidly de- creasing fluorescence signal can be observed, which goes down to zero level. A further analysis shows that the ions can still be found in the trap but they are transferred to the highly meta- stable 4f 13 6s 2 2 F 7/2 state. Therefore, they are no longer available for a further direct excitation. The population of the 2 F 7/2 state can be verified by selective excitation to higher-lying levels with wavelengths in the vicinity of the resonance line. In this way all ions can be pumped back to the ground state and their presence in the trap checked. A trapping effect in the 2 F 7/2 state is in so far of fundamental importance, as the Yb ion is a hot candidate for the realization of a frequency standard, which in the microwave range is operating on the ground-state hyperfine transition of one of the odd isotopes or in the optical region on one of the well-defined transitions to the 2 D 3/2 or 2 D 5/2 -state. The lifetime of the metastable 2 F 7/2 -state could be measured by first pumping all ions into the metastable state, then blocking the laser and after longer delay probing the re-population of the ground-state and thus the depopulation of the metastable state by a second excitation on the resonance line while monitoring the fluorescence. It was found that the lifetime of the 2 F 7/2 -state by far exceeds the ion-storage time of about 7 h. After a dark period of 4 h less than 2% of the ions, which are still in the trap, have undergone a transition into the ground-state. From this a radiative lifetime of more than 8 days is estimated, which is by far the longest lifetime, which has been observed for an optically excited atomic state. A laser which is stabilized on the 2 S 1/2 --> 2 F 7/2 transition would be the ultimate frequency standard with a Q-value of better than 10 21 . Such an optical atomic clock has unprecedented uses ranging from technological applications like GPS or gravity sensing up to examining pos- sible variations of fundamental physical constants.

Self-Induced Zeeman-Coherences

The macro- and micro-motion of ions in a Paul-trap can limit the ultimate frequency resolution for using these traps as frequency standards. While Doppler broadening of an atomic transition can be avoided by confining the ions within a cloud smaller than the transition wavelength, systematic line shifts caused by the second-order Doppler effect still have to be considered. Storage of single ions, which can efficiently be cooled by optical sideband cooling, would be the most consequent solution, but such experiments suffer from poor signal-to-noise ratios. Therefore, particularly the development of better cooling techniques requires a deeper under- standing of the ion motion and distribution of the ions in the trap. For a sensitive detection of these motions in frequency and amplitude we use a phenomenon which we termed Self-Induced Zeeman Coherences. Ions oscillating in the trap potential and addi- tionally subjected to a small magnetic field, undergo sub-level transitions between adjacent Zeeman states when their motional frequency is identical with the Larmor frequency, i.e., the splitting frequency of these state in the applied magnetic field. These transitions are related to a coherent superposition of adjacent states and originate from the inherent motion of the ions in a slightly inhomogeneous magnetic field. These self-induced transitions are sensitively detected by means of an optical pumping scheme. They allow to quan- tify the distribution of the ions in the trap, their exact oscillation frequencies and amplitudes as well as a moderate cooling of the ions.

Doctoral Theses

H. Lehmitz Kohärenzspektroskopie mit ultrakurzen Lichtimpulsen – Zeit- und frequenzaufgelöste Messungen am Beispiel von Cäsium sowie Voruntersuchungen zu Messungen an gespeicherten Ytterbiumionen School of Electrical Engineering, Helmut-Schmidt-Uiversity, Hamburg 1989 G. A. Newburgh Self Induced Zeeman Coherence and Optical Pulse Train Spectroscopies performed on Paul Trapped Ytterbium Ions School of Electrical Engineering, Helmut-Schmidt-Uiversity, Hamburg 1995 H. Ebensing Untersuchungen zur Ionenbewegung durch selbstinduzierte Kohärenzen an Ca-Ionen in einer Paul-Falle School of Electrical Engineering, Helmut-Schmidt-Uiversity, Hamburg 1998 T. Baier Kohärenzspektroskopie und Untersuchungen zur Dichteverteilung an Kalzium-Ionen in einer Paulfalle School of Electrical Engineering, Helmut-Schmidt-Uiversity, Hamburg 2004

Refereed Publications in Journals and Conference Digests

H. Lehmitz, J. Hattendorf, R. Blatt, H. Harde Observation of Complete Population Trapping in an Excited State of Yb Ions Technical Digest of International Quantum Electronics Conference (Japan Society of Applied Physics, Tokio, 1988), p. 592 (1988) H. Lehmitz, J. Hattendorf, R. Blatt, H. Harde Spectroscopic Studies on Trapped Yb Ions Digest of Technical Papers of the European Conference on Quantum Electronics, (University Hannover, Hannover, 1988), p. MoCB2 (1988) H. Lehmitz, J. Hattendorf, R. Blatt, H. Harde Observation of an Extremely Long Living Metastable State in Yb II Europhysics Conference Abstracts of 20th EGAS-Conference 12 F (European Physical Society, Graz, 1988), p. 140 (1988) H. Lehmitz, J. Hattendorf, R. Blatt, H. Harde Self-Induced Zeeman Coherences in Trapped Ions Europhysics Conference Abstracts of 20th EGAS-Conference 12 F (European Physical Society, Graz, 1988), p. 143 (1988) H. Lehmitz, J. Hattendorf, R. Blatt, H. Harde Population Trapping in Excited Yb-Ions Physical Review Letters 62, 2108 (1989) H. Harde Optical Cooling of Trapped Ions by Means of Self-Induced Zeeman Coherences in International Conference on Quantum Electronics Technical Digest Series 1990, Vol. 8, (Optical Society of America, Washington,DC 1990), p. 278 (1990) H. Harde, H. Lehmitz, J. Hattendorf-Ledwoch, R. Blatt Self-Induced Zeeman-Coherences in a Paul Trap Applied Physics B 53, 131 (1991) H. Ebensing, A. Newburgh, H. Harde Systematic Studies of the Ion Motion in a Paul Trap by Means of Self-Induced Coherences in: ''Quantum Electronics and Laser Science Conference'', 1993 OSA Technical Digest Series, Vol. 3 (Optical Society of America, Washington, DC, 1993), p. 194 (1993) H. Ebensing, T. Baier, G. A. Newburgh, H. Harde Measurement and Interpretation of Motional Frequencies and their Harmonics of Paul Trapped Ions Proceedings of the 1996 European Quantum Electronics Conference, IEEE Catalog No. 96TH8162, ISBN: 0-7803-3171-0, p. 113 (1996) T. Baier, H. Ebensing, H. Harde Measurement and Interpretation of Motional Frequencies and their Harmonics of Paul Trapped Ions Proceedings of the 29th EGAS-Conference, ed. by H.-D. Kronfeldt (Optisches Institut, TU Berlin, Berlin 1997), p. 530 (1997) T. Baier, H. Ebensing, H. Harde Observation of Motion-Induced Coherences with Trapped Ions Proceedings of the 1998 European Quantum Electronics Conference, IEEE Catalog No. 98TH8326, ISBN: O-7803-4233, P. 123 (1998) T. Baier, I. Malchartzek, H. Ebensing, H. Harde Motion-Induced Coherences and Density Distributions in a Paul-Trap Quantum Electronics and Laser Science Conference, OSA Technical Digest (Optical Society of America, Washington DC, 2000), p. 66, QTuA32 (2000) T. Baier, I. Malchartzek, H. Ebensing, H. Harde Motion-Induced Dark Resonances and Density Distribution in a Paul-Trap International Quantum Electronics Conference 2000, IEEE Conference Digest, San Francisco, 7.-12. Mai 2000, Catalog Number 00TH8504, QTuA7, ISBN: 0-7803-6318-3 (2000) T. Baier, I. Malchartzek, H. Ebensing, H. Harde Motion-Induced Dark Resonances and Density Distribution in a Paul-Trap International Quantum Electronics Conference, Nice, 10.-15. September 2000, QTuA7 (2000)

Contributions on National Conferences and Meetings

J. Hattendorf, H. Lehmitz, R. Blatt, H. Harde Nachweis der Mikro- und Makrobewegung von Ionen in einer RF-Ionenfalle über selbstinduzierte Zeeman- Kohärenzen Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Fachausschuss Atomphysik, Bonn, 23. März 1988, Verhandl. DPG (VI) 23, A 41 (1988) H. Lehmitz, J. Hattendorf, R. Blatt, H. Harde Beobachtung des ''Shelving'' an Yb Ionen Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Fachausschuss Atomphysik, Bonn, 24. März 1988, Verhandl. DPG (VI) 23, A 67 (1988) H. Lehmitz, H. Harde Interpretation von selbstinduzierten Zeeman-Kohärenzen an gespeicherten Ionen Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Arbeitsgemeinschaft Quantenoptik, Essen, 6. März 1989, Verhandl. DPG (VI) 24, Q 5.5 (1989) H. Ebensing, A. Newburgh, H. Harde Untersuchungen zu selbstinduzierten Zeeman-Kohärenzen in einer Paul-Falle Frähjahrstagung der Deutschen Physikalischen Gesellschaft, Arbeitsgemeinschaft Quantenoptik, Hannover, 24. März 1992, Verhandl. DPG (VI) 27, Q 12.10, 1415 (1992) H. Ebensing, A. Newburgh, H. Harde Messungen der Bewegungsfrequenzen von gespeicherten Yb-Ionen mittels selbstinduzierter Kohärenzen Poster Lasertag 1992, Hannover, 2. Dezember 1992 H. Ebensing, A. Newburgh, H. Harde Bewegungsfrequenzen von gespeicherten Yb-Ionen mittels selbstinduzierter Kohärenzen Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Arbeitsgemeinschaft Quantenoptik, Berlin, 16. März 1993, Verhandl. DPG (VI) 28, 440 (1993), Q 38.2 H. Ebensing, A. Newburgh, H. Harde Bewegungsfrequenzen und -amplituden von Ionen in einer Paulfalle Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Arbeitsgemeinschaft Quantenoptik, Hamburg, 15. März 1994, Verhandl. DPG (VI) 29, Q 5A.5, 665 (1994) A. G. Newburgh, H. Harde Coherent Population Trapping: Generalization of Two-Field Dark Resonance and Optical Pulse Train Interference Spectroscopy Poster Lasertag 1995, Hannover, 6. Dezember 1995 H. Ebensing, T. Baier, H. Harde Messungen der Ionenbewegung von Ca + in einer Paul-Falle Poster Lasertag 1995, Hannover, 6. Dezember 1995 H. Ebensing, G. A. Newburgh, H. Harde Messung und Interpretation von Harmonischen der Bewegungsfrequenz gespeicherter Ionen in einer Paul-Falle Frühjahrstagung der DPG, Sektion Quantenoptik, Jena, 12. März 1996, Verhandl. DPG (VI) 31, Q 23.3, 241 (1996) G. A. Newburgh, H. Harde Coherent Population Trapping: Generalization of Two-Field Dark Resonance and Optical Pulse Train Interference Spectroscopy Frühjahrstagung der DPG, Sektion Quantenoptik, Jena, 14. März 1996, Verhandl. DPG (VI) 31, Q 34.13, 277 (1996) H. Ebensing, T. Baier, H. Harde Bewegungsspektrum von gespeicherten Ca + -Ionen Poster Lasertag 1996, Hannover, 11. Dezember 1996 T. Baier, H. Ebensing, H. Harde Bewegungsfrequenzen und -amplituden von Ca-Ionen in einer Paul-Falle Frühjahrstagung der DPG, Arbeitsgemeinschaft Quantenoptik, Mainz, 5. März 1997, Verhandl. DPG (VI) 32, A 17.3, 203 (1997) T. Baier, H. Ebensing, H. Harde Bewegungs- und Dunkelresonanzen gespeicherter Ca-Ionen Frühjahrstagung der DPG, Fachverband Atomphysik, Heidelberg, 15. März 1999, Verhandl. DPG (VI) 34, A 1.3, 235 (1999) T. Baier, H. Harde Messung der Bewegungsfrequenzen gespeicherter Ca-Ionen in einer Paul-Falle mittels Zeeman-Kohärenzen und Dunkelresonanzen Poster Norddeutsches Laserkolloquium 1998, Hannover, 9. Dezember 1999

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