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We report on observations of thermal motion of a single, Doppler-cooled ion along the axis of a linear radio-frequency quadrupole trap. We show that for a harmonic potential the thermal occupation of energy levels leads to Gaussian distribution of the ion's axial position. The dependence of the spatial thermal spread on the trap potential is used for precise calibration of our imaging system's point spread function and sub-milliKelvin thermometry. We employ this technique to investigate the laser detuning dependence of the Doppler temperature., Comment: 5 pages, 4 figures

We report on injection locking of optically excited mechanical oscillations of a single, trapped ion. The injection locking dynamics are studied by analyzing the oscillator spectrum with a spatially selective Fourier transform technique and the oscillator phase with stroboscopic imaging. In both cases we find excellent agreement with theory inside and outside the locking range. We attain injection locking with forces as low as 5(1)×10^(-24) N so this system appears promising for the detection of ultraweak oscillating forces.

We apply a recently demonstrated method for precision spectroscopy on strong transitions in trapped ions to measure both fine-structure components of the $3s\text{\ensuremath{-}}3p$ transition in ${^{24}\text{M}\text{g}}^{+}$ and ${^{26}\text{M}\text{g}}^{+}$. We deduce absolute frequency reference data for transition frequencies, isotope shifts, and fine-structure splittings that in particular are useful for comparison with quasar absorption spectra, which test possible space-time variations of the fine-structure constant. The measurement accuracy improves previous literature values, when existing, by more than two orders of magnitude.

Absolute frequency measurements on single trapped ions reached tremendous accuracies by probing narrow transitions in tightly confined ions (resolved sideband regime) [1,2]. A variety of interesting transitions may hardly be studied in this regime, because their transition linewidths well exceed common (secular) trap frequencies. Accurate spectroscopy in the so-called weak binding limit is challenging, since an interrogating laser induces detuning dependent heating and cooling which distorts the line profile. We present both theory and experimental demonstration of a spectroscopic method (Fig. 1) which essentially removes these limitations and allows us to observe a well understood line shape with high signal-to-noise ratio (Fig. 2) [3].

Cooling of atoms and ions [1,2] using a red-detuned laser has had a profound impact on science and technology [3–5]. In this work simultaneous laser cooling and blue-detuned laser pumping of a Mg+ ion in a Paul trap is studied. Blue-detuned pumping is conventionally referred to as the heating regime, and in early work, remarkably complex behaviors (bistability and limit cycles) have been associated with this regime [6,7]. These behaviors have so far not been fully explained. Here, it is shown that blue-detuned pumping, as opposed to heating, causes stimulated emission of center-of-mass phonons, leading to coherent oscillatory motion of the ion in analogy with a laser. Mechanical amplification is calculated as well as the threshold pumping condition for oscillation. A single ion in a linear radio-frequency trap is studied to verify these predictions (figure 1 left panel). Blue-detuned pumping of the magnesium D2 transition at 279.6 nm provides amplification along the long axis of the ion trap so as to excite only axial oscillations. A slightly off-axis, red-detuned beam cools the center-of-mass motion to approximately 1 mK. The experimental arrangement is identical to that detailed in ref. [8].

We demonstrate a method for precision spectroscopy on trapped ions in the limit of unresolved motional sidebands. By sympathetic cooling of a chain of crystallized ions, we suppress adverse temperature variations induced by the spectroscopy laser that usually lead to a distorted line profile and obtain a Voigt profile with negligible distortions. We applied the method to measure the absolute frequency of the astrophysically relevant $D2$ transition in single $^{24}\mathrm{Mg}^{+}$ ions and find $1\text{ }072\text{ }082\text{ }934.33(16)\text{ }\text{ }\mathrm{MHz}$, a nearly 400-fold improvement over previous results. Further, we find the excited state lifetime to be 3.84(10) ns.

A trapped Mg+ion is laser cooled within a Paul trap, and is simultaneously excited using a continuous blue-detuned pump wave. The ion subsequently exhibits coherent oscillatory motion with a well-defined threshold.

A cooled, trapped Mg^+ ion is excited using a continuous, blue-detuned pump. Coherent oscillatory motion is observed. It is shown to result from stimulated emission of center-of-mass phonons, constituting the mechanical analog of a laser.