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We report on laser spectroscopic measurements on Li$^+$ ions in the experimental storage ring ESR at the GSI Helmholtz Centre for Heavy Ion Research. Driving the $2s\,^3\!{S}_1\;(F=\frac{3}{2}) \,\leftrightarrow\,2p\,^3\!P_2\;(F=\frac{5}{2}) \leftrightarrow 2s\,^3\!{S}_1\;(F=\frac{5}{2})$ $\Lambda$-transition in $^7$Li$^+$ with two superimposed laser beams it was found that the use of circularly polarized light leads to a disappearance of the resonance structure in the fluorescence signal. This can be explained by optical pumping into a dark state of polarized ions. We present a detailed theoretical analysis of this process that supports the interpretation of optical pumping and demonstrates that the polarization induced by the laser light must then be at least partially maintained during the round trip of the ions in the storage ring. Such polarized ion beams in storage rings will provide opportunities for new experiments, especially on parity violation., Comment: 14 pages, 8 figures, new version with small adjustments, closest to final publication in PRAB

We present a digital predistortion (DPD) technique to compensate for in-phase and quadrature (IQ) Mach–Zehnder modulators (MZM) with finite extinction ratio (ER). The proposed method significantly improves the system performance by reducing the impairments introduced by the component imperfections. Our technique is performed in two steps: First, the $\arcsin$ predistorts the nonlinear sinusoidal transfer function of the modulator; second, a constrained optimization method, that utilizes the gradient descent algorithm, predistorts the modulator driving signals, thus mitigating the distortion induced by the finite ER. Since the optimal gradient calculation is rather complex, we introduce a simplified polynomial-based approximation that achieves comparable performance. The DPD gain is assessed via numerical simulations by varying modulation format and ER in an optical back-to-back configuration. The results are presented as required optical signal-to-noise ratio versus the modulator output power ( $\text{P}_{\text{MZM}}$ ) normalized with respect to the MZM input power (continuous wave of the laser, $\text{P}_{\text{CW}}$ ). A considerable improvement is showed when compared to the case without DPD or with the $\arcsin$ module for ERs $\leq$ 20 dB and 32/64QAM.

We demonstrate an all-silicon-photonic coherent link, including a hybrid tunable laser with 45dB SMSR, and

We present preparatory measurements for an improved test of time dilation at the experimental storage ring (ESR) at GSI in Darmstadt. A unique combination of particle accelerator experiments and laser spectroscopy is used to perform this test with the highest precision. 7Li+ ions are accelerated to 34% of the speed of light at the GSI Helmholtzzentrum für Schwerionenforschung and stored in the experimental storage ring. The forward and backward Doppler shifts of an electric dipole transition of these ions are measured with laser spectroscopy techniques. From these Doppler shifts, both the ion velocity β = ν/c and the time dilation factor [Formula: see text] can be derived for testing Special Relativity. Two laser systems have been developed to drive the 3S1→3P2 transition in 7Li+. Moreover, a detector system composed of photomultipliers, both to monitor the exact laser ion beam overlap as well as to optimize fluorescence detection, has been set up and tested. We investigate optical-optical double-resonance spectroscopy on a closed Λ-type three-level system to overcome Doppler broadening. A residual, broadened fluorescence background caused by velocity-changing processes in the ion beam is identified, and a background subtraction scheme implemented. At the present stage the experimental sensitivity, although already comparable with previous measurements on slower ion beams at the TSR storage ring that led to [Formula: see text] –8, suffer from a poor signal-to-noise ratio. Modifications of the ion source as well as the detection system are discussed that promise to improve the sensitivity by one order of magnitude.

Time dilation is one of the most fascinating aspects of special relativity as it abolishes the notion of absolute time. It was first observed experimentally by Ives and Stilwell in 1938 using the Doppler effect. Here we report on a method, based on fast optical atomic clocks with large, but different Lorentz boosts, that tests relativistic time dilation with unprecedented precision. The approach combines ion storage and cooling with optical frequency counting using a frequency comb. 7Li+ ions are prepared at 6.4% and 3.0% of the speed of light in a storage ring, and their time is read with an accuracy of 2×10−10 using laser saturation spectroscopy. The comparison of the Doppler shifts yields a time dilation measurement represented by a Mansouri–Sexl parameter , consistent with special relativity. This constrains the existence of a preferred cosmological reference frame and CPT- and Lorentz-violating ‘new’ physics beyond the standard model.

The Doppler-free laser-spectroscopic frequency measurement of Doppler-shifted optical lines in forward and backward direction of a fast ion beam permits a sensitive test of the relativistic Doppler-formula and, hence, the relativistic time dilation factor γ SR=(1−ν 2/c 2)−1/2. An experiment on metastable 7Li+, stored at a velocity of ν=0.064c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy. Latest tests at two different ion-velocities (ν=0.03c and ν=0.064c) will enhance these measurements. An improved version of this experiment will be carried out at the experimental storage ring (ESR) at the Gesellschaft fur Schwerionenforschung (GSI) in Darmstadt. The ESR permits 7Li+ to be stored at ν=0.33c which promises an improvement of the sensitivity to deviations from γ SRby an order of magnitude. A first test at the ESR has shown the feasibility for this kind of experiment.

The hyperfine structure splittings of the P(10)14-1, R(15)14-1, and R(99)15-1 transitions at 585 nm, P(62)17-1 at 576 nm, and P(80)21-1 at 565 nm in 127 I 2 are measured by heterodyne spectroscopy using two dye lasers. In addition, the absolute frequencies of the hyperfine components P(10)14-1 a 15 and P(80)21-1 a 10 are determined using a self-referenced frequency comb. These frequencies are used in an experiment testing relativistic time dilation by laser spectroscopy on a fast ion beam.

We report on the first laser cooling of a bunched beam of multiply charged C3+ ions performed at the ESR (GSI) at a beam energy of E = 1.47 GeV. Moderate bunching provided a force counteracting the decelerating laser force of one counterpropagating laser beam. This versatile type of laser cooling lead to longitudinally space-charge dominated beams with an unprecedented momentum spread of Δp/p ≈ 10−7. Concerning the beam energy and charge state of the ion, the experiment depicts an important intermediate step from the established field of laser cooling of ion beams at low energies toward the unique laser cooling scheme proposed for relativistic beams of highly charged heavy ions at SIS 300 (FAIR).

The electric dipole intercombination decay rate of the 2s2p 3Po1 level in the Be-like ions N3+ and O4+ has been measured with ions circulating in a heavy-ion storage ring. The observation employed three devices in parallel, two different VUV photon detectors and a residual gas recoil ion detector. The measured transition probabilities of (578 ± 3.3) s−1 for N3+ (level lifetime τ = 1.73 ± 0.01 ms) and of (2315 ± 50) s−1 for O4+ (τ = 0.432 ± 0.009 ms), corroborate the results of recent calculations and improve the precision with which the isoelectronic trend can be established.

The laser-spectroscopic frequency measurement of Doppler-shifted optical lines in the forward and backward directions of a fast ion beam permits a sensitive test of the relativistic Doppler formula and, hence, the relativistic time-dilation factor γSR = 1/[Formula: see text]. An experiment on 7Li+, stored at a velocity of v = 0.065c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy limiting deviations to below 2.2 × 10–7. Ongoing improvements on the experimental setup will further tighten this limit.PACS Nos.: 03.30.+p, 06.30.Ft, and 42.62.Fi

Decay curves of the electric-dipole forbidden decay of the 3s 23p 4 ground configuration 3P1 level in the S-like ions of Ni (Z = 28) and Cu (Z = 29) have been obtained at a heavy-ion storage ring. This completes the earlier measurements on the 1D2 level in Fe (Z = 26) and the 1S0 level in Ar (Z = 18). The lifetime evaluation process is discussed in the context of structural changes and predicted branching fraction changes along the S I isoelectronic sequence. The experimental lifetime values agree with the results of several calculations.

Rates of the electric-dipole forbidden transition in the ground configuration of Cl-like ions of Co, Ni and Cu have been measured optically at a heavy-ion storage ring. Besides testing theory and providing benchmark data for these ions, the data by isoelectronic extrapolation pertain to the Fe X spectrum of high solar interest, for which so far theory and experiment have disagreed.

We have measured dielectronic recombination (DR) resonance strengths and energies for carbon-like Fe XXI forming Fe XX and for boron-like Fe XXII forming Fe XXI via N = 2 → N' = 2 core excitations. All measurements were carried out using the heavy-ion Test Storage Ring at the Max-Planck-Institute for Nuclear Physics in Heidelberg, Germany. We have also calculated these resonance strengths and energies using three independent, state-of-the-art perturbative techniques: a multiconfiguration Breit-Pauli (MCBP) method using the code AUTOSTRUCTURE, a multiconfiguration Dirac-Fock (MCDF) method, and a relativistic configuration interaction method using the Flexible Atomic Code (FAC). Overall, reasonable agreement is found between our experimental results and our theoretical calculations. The most notable discrepancies tend to occur for relative collision energies 3 eV. We have used our measured 2 → 2 results to produce Maxwellian-averaged rate coefficients for Fe XXI and Fe XXII. Our experimentally derived rate coefficients are estimated to be accurate to better than ≈20% both for Fe XXI at kBTe > 0.5 eV and for Fe XXII at kBTe > 0.001 eV. For these results, we provide fits that are accurate to better than 0.5% for Fe XXI at 0.001 eV ≤ kBTe ≤ 10,000 eV and for Fe XXII at 0.02 eV kBTe ≤ 10,000 eV. Our fitted rate coefficients are suitable for ionization balance calculations involving Fe XXI and Fe XXII in photoionized plasmas. Previous published Burgess formula and LS-coupling calculations are in poor agreement with our experimentally derived rate coefficients. None of these published calculations reliably reproduce the magnitude or temperature dependence of our experimental results. Our previously published Fe XXI MCDF results are in good agreement with our experimental results for kBTe 0.07 eV. For both ions in this temperature range our new MCBP, MCDF, and FAC results are in excellent agreement with our experimentally derived rate coefficient.

The frequency measurement of Doppler-shifted optical lines of ions circulating in a storage ring at high speed permits a sensitive test of the relativistic Doppler-formula and, hence, the time dilation factor γSR of special relativity. Previous measurements at the storage ring TSR with 7Li+ at v = 0.065c gave a new, improved limit, but were hampered by the large observed linewidth, exceeding the natural width 15-fold. Recently we have identified the broadening to be caused by velocity-changing processes in the storage ring. Saturation spectroscopy has proven to be largely immune against these effects and has yielded linewidths only a few MHz larger than the natural one. This is the major ingredient for an improved test of γSR, which is now under way.

We present the concluding result from an Ives-Stilwell-type time dilation experiment using 7Li+ ions confined at a velocity of β=v/c=0.338 in the storage ring ESR at Darmstadt. A Λ-type three-level system within the hyperfine structure of the 7Li+3S1 →3P2 line is driven by two laser beams aligned parallel and antiparallel relative to the ion beam. The lasers' Doppler shifted frequencies required for resonance are measured with an accuracy of

We give a brief overview of time dilation tests using high-resolution laser spectroscopy at heavy-ion storage rings. We reflect on the various methods used to eliminate the first-order Doppler effect and on the pitfalls encountered, and comment on possible extensions at future facilities providing relativistic heavy ion beams at $\gamma \gg 1$.

When infrared active molecular ions are stored in a heavy ion storage ring, a fast beam of vibrationally and rotationally relaxed molecules can be obtained. This opens up new opportunities for various experimental studies in molecular ion physics, particularly those involved with spectroscopy and dissociation dynamics of excited states. The analysis of such experiments is facilitated by the fact that the information on the initial states is able to identify and, therefore, eliminate them from the assignment problem. Moreover, when the intensity of the measured transitions is monitored as a function of storage time, the dependence of these processes on the degree of internal relaxation is revealed. We demonstrate these general principles by application to near threshold dissociation spectroscopy of the OH+ molecular ion. The structure of quasibound levels near the dissociation limit of OH+ and its dissociation energy are deduced.

Spectroscopic results obtained on multiply charged few electron ions by using laser stimulated two-step recombination in ion storage rings are presented in an overview. Line splittings in transitions between Rydberg levels were observed for helium like and beryllium like ions. Emphasis is given to results on the beryllium like system N3+ where information about the splitting between high angular momentum levels (l⩾4) was obtained for the Rydberg levels n=13 and 8 with experimental errors of about ±0.02 meV.

The decay rate of the 2s2 2p2 1S0 level in N II has been measured optically (λ = 575 nm) at a heavy-ion storage ring. The result of (1.10 ± 0.27) s-1 agrees with the theoretical predictions. The new data complement an earlier study of the same level decay in O III and F IV. Over this short range of ions, the role of the E2 and M1 decay modes changes dramatically.

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.

Red-detuned laser pumping of an atomic resonance will cool the motion of an ion or atom. The complementary regime of blue-detuned pumping is investigated in this work using a single, trapped Mg+ ion interacting with two laser beams, tuned above and below resonance. Widely thought of as a regime of heating, theory and experiment instead show that stimulated emission of centre-of-mass phonons occurs, providing saturable amplification of the motion. A threshold for transition from thermal to coherent oscillating motion has been observed, thus establishing this system as a mechanical analogue to an optical laser -— a phonon laser. Such a system has been sought in many different physical contexts.

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.

We demonstrate sub-Doppler laser spectroscopy with a beam of ${^{7}\text{L}\text{i}}^{+}$ ions stored at 33.8% of the speed of light in the experimental storage ring at GSI. Using two lasers, the one copropagating and the other counterpropagating, with respect to the ion beam, a fluorescence line is observed via optical-optical double-resonance spectroscopy on a $\ensuremath{\Lambda}$-type level configuration. A linewidth of $\ensuremath{\approx}114\text{ }\text{MHz}$ is found, which is 12 times narrower than the Doppler broadening due to the momentum spread of the ion beam. Interpreted as a test of Lorentz invariance, we find $|{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\alpha}}}_{2}|l1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, a $25\ifmmode\times\else\texttimes\fi{}$ tighter limit on $O\mathbf{(}{(v/c)}^{4}\mathbf{)}$ deviations from time dilation than any other experiment.

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].

The $1S\text{\ensuremath{-}}2S$ two-photon transition in singly ionized helium is a highly interesting candidate for precision tests of bound-state quantum electrodynamics (QED). With the recent advent of extreme ultraviolet frequency combs, highly coherent quasi-continuous-wave light sources at 61 nm have become available, and precision spectroscopy of this transition now comes into reach for the first time. We discuss quantitatively the feasibility of such an experiment by analyzing excitation and ionization rates, propose an experimental scheme, and explore the potential for QED tests.

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.

The coupling between electronic states in a surface-adsorbate system is fundamental to the understanding of many surface interactions. In this Letter, we present the first direct time-resolved observations of the lifetime of core-excited states of an atom adsorbed onto a surface. By comparing laser-assisted photoemission from a substrate with a delayed Auger decay process from an adsorbate, we measure the lifetime of the $4{d}^{\ensuremath{-}1}$ core level of xenon on Pt(111) to be $7.1\ifmmode\pm\else\textpm\fi{}1.1\text{ }\text{ }\mathrm{fs}$. This result opens up time-domain measurements of surface dynamics where energy-resolved measurements may provide incomplete information.

We investigate the laser-assisted photoelectric effect from a solid surface. By illuminating a $\mathrm{Pt}(111)$ sample simultaneously with ultrashort 1.6 and $42\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ pulses, we observe sidebands in the extreme ultraviolet photoemission spectrum, and accurately extract their amplitudes over a wide range of laser intensities. Our results agree with a simple model, in which soft x-ray photoemission is accompanied by the interaction of the photoemitted electron with the laser field. This strong effect can definitively be distinguished from other laser surface interaction phenomena, such as hot electron excitation, above-threshold photoemission, and space-charge acceleration. Thus, laser-assisted photoemission from surfaces promises to extend pulse duration measurements to higher photon energies, as well as opening up measurements of femtosecond-to-attosecond electron dynamics in solid and surface-adsorbate systems.

We observe the laser-assisted photoelectric effect on a surface for the first time. Simultaneously illuminating Pt(111) with the fundamental and 27th harmonic of a Ti:sapphire femtosecond laser results in energy modulation of the photoelectron spectrum.

We report the first observation of the laser-assisted photoelectric effect from a solid surface. By illuminating a Pt(111) sample simultaneously with ultrashort 1.6 eV and 42 eV pulses, we observe sidebands in the extreme ultraviolet photoemission spectrum. The magnitude of these sidebands as a function of time delay between the laser and extreme ultraviolet pulses represents a cross-correlation measurement of the extreme ultraviolet pulse. This effect promises to be useful to extend extreme ultraviolet pulse duration measurements to higher photon energies, as well as opening up femtosecond-to-attosecond time-scale electron dynamics in solid and surface-adsorbate systems.

We report on the experimental demonstration of laser cooling of a C3+ion beam performed at the ESR (GSI) at an energy of E = 1.47 GeV. The decelerating laser force of one Doppler-tuned UV laser beam was counteracted by moderately bunching the beam. This versatile scheme lead to longitudinally ‘space-charge dominated’ beams with an unprecedented momentum spread of Δp/p ≈ 10–7. Concerning beam energy and charge state of the ion, the experiment depicts an important step from the field of laser cooling of ion beams at low energies toward the laser cooling scheme proposed for relativistic beams of highly charged heavy ions at the future GSI facility FAIR.

We report on first laser cooling studies of bunched beams of triply charged carbon ions stored at an energy of 1.46 GeV at the ESR (GSI). Despite for the high beam energy and charge state laser cooling provided a reduction of the momentum spread of one order of magnitude in space‐charge dominated bunches as compared to electron cooling. For ion currents exceeding 10 μA intra‐beam‐scattering losses could not be compensated by the narrow band laser system presently in use. Yet, no unexpected problems occurred encouraging the envisaged extension of the laser cooling to highly relativistic beams. At ESR, especially the combination with modest electron cooling provided three‐dimensionally cold beams in the plasma parameter range of unity, where ordering effects can be expected and a still unexplained signal reduction of the Schottky signal is observed.

A precise, laser-spectroscopic test of time dilation in special relativity has been performed with fast ions stored in the heavy-ion storage ring TSR in Heidelberg. At a velocity of 6.4% of the speed of light, the Doppler-shifted frequencies of a transition in 7Li+ have been measured in forward and backward direction. First results confirm relativity and set an improved limit of 2.2 x for deviations from the Lorentz factor 7 s ~ = 1/J1 v2/c2. Ongoing improvements will tighten the limit further. Preliminary investigations indicate that Doppler-type experiments can have unique sensitivity for testing Lorentz/CPT-violating extensions of the Standard Model.

An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in 7 Li + ions at v = 0.064c have been measured in the forward and backward direction to an accuracy of Δν/ν = 1 × 10 - 9 using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of 2.2 × 10 - 7 for deviations from the time dilation factor γ S R = (1 - ν 2 /c 2 ) - 1 / 2 .

Dielectronic recombination(DR) of lithium-like Ti19+(1s2 2s) ions via 2s->2p core excitations has been measured at the Heidelberg heavy ion storage ring TSR. We find that not only external electric fields (0 2p_{1/2} and 2s -> 2p_{3/2} excitations of the Li-like core, extracting initial slopes and saturation fields of the enhancement. We find that for Ey > 80 V/cm the field induced enhancement is about 1.8 times stronger for the 2p_{3/2} series than for the 2p_{1/2} series., 10 pages, 3 figures, to be published in Journal of Physics B, see also http://www.strz.uni-giessen.de/~k3

Eine der weitreichendsten Konsequenzen der Speziellen Relativitatstheorie ist das Phanomen der Zeitdilatation. Diese wurde nun am Max-Planck-Institut fur Kernphysik mit der bisher hochsten Genauigkeit gemessen [1].

We report the status of an experimental test of time dilation in Special Relativity. This is accomplished by simultaneously measuring the forward and backward Doppler shifts of an electronic transition of fast moving ions, using high-precision laser spectroscopy. From these two Doppler shifts both the ion velocity ? = v/c and the time dilation factor can be derived. From measurements based on saturation spectroscopy on lithium ions stored at ? = 0.03 and ? = 0.06 in the TSR heavy-ion storage ring, we achieved an upper limit for a [?2] deviation from Special Relativity of . In recent measurements on a ? = 0.34 Li+ beam in the ESR storage ring we used optical-optical double-resonance spectroscopy which, in combination with the TSR result, gives improved sensitivity on the [?4] term of . We discuss current limitations and possible improvements that promise an enhancement of the sensitivity by at least one order of magnitude in the future.

We discuss the axial dynamics of laser-cooled relativistic C3+ ion beams at moderate bunching voltages. Schottky noise spectra measured at a beam energy of 122 MeV/u are compared to simulations of the axial beam dynamics. Ions confined in the bucket are addressed by the narrow-band force of a laser beam counter-propagating to the ion beam, while the laser frequency is detuned relatively to the cooling transition frequency in the rest frame of the bucket. At large detuning comparable to the momentum acceptance of the bucket, the axial dynamics can be well explained by the secular motion of individual non-interacting ions. At small detuning, corresponding to a small axial momentum spread Δpaxial/paxial < 10−6 of the ions, the measured Schottky noise spectra can no longer be explained using an approach which neglects the ion-ion interaction. Instead, the model fails when the ion bunch enters the space-charge dominatedregime, at which the mutual Coulomb-energy of the ions becomes comparable to the kinetic energy of the ions.