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Europhysics Letters (EPL)

The “Trapped State” of a Trapped Ion—Line Shifts and Shape

Ingo Siemers, Michael Schubert, R. Blatt, Werner Neuhauser, P. E. Toschek

Published Feb 14, 1992• 68 citations
Publisher

Abstract

The fluorescence of a single r.f.-trapped and cooled Ba + ion, induced by the light of two lasers, shows a null at the S 1/2 - D 3/2 resonance of the frequency difference. We have measured the Zeeman effect and power broadening of this "dark line", and also the shift of the associated "bright" line, which is related to the Raman light shift. A 75 kHz wide dark line was observed. Such a resonance might be used to control a 147 THz standard frequency free of systematic shifts in excess of 10 -15 .

DOI
10.1209/0295-5075/18/2/009

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The fluorescence of a single r.f.-trapped and cooled Ba + ion, induced by the light of two lasers, shows a null at the S 1/2 - D 3/2 resonance of the frequency difference. We have measured the Zeeman effect and power broadening of this "dark line", and also the shift of the associated "bright" line, which is related to the Raman light shift. A 75 kHz wide dark line was observed. Such a resonance might be used to control a 147 THz standard frequency free of systematic shifts in excess of 10 -15 .
The simultaneous excitation of adjacent atomic transitions by two light waves equally detuned from their resonances gives rise to destructive interference of the transitions and causes a narrow dark line, or coherent dip, to appear in both light scattering and absorption. With one of the light fields detuned from resonance, the line is asymmetric and is accompanied by a shifted bright line; the two are represented by a Fano line profile. The spectral separation ∊ of the bright and dark lines is closely related—although not identical—to the net shift that is found in the two-photon-resonant denominator of the susceptibility, to the shift of the normal modes of the atom’s two internal excitations, and to the net difference of the energy separations of dressed and bare atomic levels. We report measurement of the resonance shift ∊ of the 2S1/2–2D3/2 transition of a single cooled and trapped Ba+ ion, and we analyze its relationship to those identified light shifts.
Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. We have tested a novel method to probe the motional state of a confined three-level ion. Actually, dark resonances observed with two counterpropagating laser beams are very sensitive to the trapped ion's velocity. Their contrast increases with reduced micromotion and allows in this way to control the oscillation amplitude of the stored ion. The influence of different parameters such as laser linewidth and power has been investigated experimentally and numerically.
We study cooling of the collective vibrational motion of two 138Ba+{}^{138}{\mathrm{Ba}}^{+}138Ba+ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances ${S}_{1/2}\ensuremath{-}{P}_{1/2}$ (493 nm) and ${P}_{1/2}\ensuremath{-}{D}_{3/2}$ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split ${S}_{1/2}\ensuremath{-}{D}_{3/2}$ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.
We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S(1/2) ground state or the 5D(3/2) metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.
Single ions trapped and laser cooled provide ideal objects for high resolution spectroscopy and frequency standards. For the latter purpose we are investigating the 5s2 1S0 → 5s5p 3P0 transition of In+. With a natural linewidth of only 1.1 Hz this resonance offers very high resolution and is highly immune to frequency shifts due to external electromagnetic fields, because it connects two levels with vanishing electronic magnetic momenta [1]. The wavelength of this clock transition is 236.5 nm and is technically very convenient, since it coincides with the fourth harmonic of the 946 nm Nd:YAG laser line. So this intrinsically frequency stable solid-state laser can be used to excite the transition [2]. For laser cooling and fluorescence detection of the indium ion the 5s2 1So -> 5s5p 3P1 transition at 230.6 nm can be employed. The use of the relatively narrow intercombination line for laser cooling allows us to study optical sideband cooling in the strong binding regime, where the oscillation frequencies of the ion in the trap (around 1 MHz) are larger than the optical linewidth of 360 kHz. In this parameter range laser cooling is possible to the quantum ground state of the vibrational motion in the trap corresponding to a temperature of roughly 100 μK. The same low temperature was obtained with sideband cooling of a small Coulomb crystal consisting of two ions, creating an interesting new quantum few-particle system.
Micromotion induced by the radio-frequency field contributes greatly to the systematic frequency shifts of optical frequency standards. Although different strategies for mitigating this effect have been proposed, trapping ions optically has the potential to provide a generic solution to the elimination of micromotion. This could be achieved by trapping a single ion in the dipole trap composed of a highpower laser field. Here, we present the setup of the dipole trap composed of a 532 nm laser at a power of 10 W aiming to optically trap a single 40Ca+ and we observe an AC-Stark shift of the fluorescence spectrum line of ∼22 MHz caused by the 532 nm dipole beam. The beam waist of the dipole laser is several microns, which would provide a dipole potential strong enough for all-optical trapping of a single 40Ca+ ion.