Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform efficient quantum logic detection techniques. This amplifies the recoil signal from a few absorbed photons to thousands of fluorescence photons. We resolve the line centre of a dipole-allowed transition in 40 Ca þ to 1/300 of its observed linewidth, rendering this measurement one of the most accurate of a broad transition. The simplicity and versatility of this approach enables spectroscopy of many previously inaccessible species. P recision optical spectroscopy of broad transitions provides information on the structure of molecules 1 , it allows tests of quantum electrodynamics 2 , and, through comparison with astrophysical data, probes for a possible variation of fundamental constants over cosmological scales 3,4 . Nuclear properties are revealed through isotope shift measurements 5-9 , or absolute frequency measurements 10,11 . Trapped ions are particularly well suited for such high precision experiments. The ions are stored in an almost field-free environment and can be laser-cooled to eliminate Doppler shifts. These features have enabled record accuracies in optical clocks [12][13][14][15] . For long-lived excited states such as in atoms with clock transitions, the electron-shelving technique amplifies the signal from a single absorbed photon by scattering many photons on a closed transition through selective optical coupling of one of the two spectroscopy states to a third electronic level 16 . The invention of quantum logic spectroscopy (QLS) 12,17 removed the need to detect the signal on the spectroscopically investigated ion (spectroscopy ion) by transferring the internal state information through a series of laser pulses to the co-trapped, so-called logic ion where the signal is observed via the electron-shelving technique. However, this original implementation of QLS requires long-lived spectroscopy states to implement the transfer sequence. For transitions with a short-lived excited state, spectroscopy of trapped ions is typically implemented through detection of scattered photons in laserinduced fluorescence 7,18-22 or detection of absorbed photons in laser absorption spectroscopy 23 . Neither of the two techniques reaches the fundamental quantum projection noise limit as in the electron-shelving technique 24 due to low light collection efficiency in laser-induced fluorescence and small atom-light coupling in laser absorption spectroscopy. In a variation of absorption spectroscopy, the detuning-dependent effect of...
In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the AC Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for 5 ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10 -18 range for optical clocks based on the Sr + and Yb + E2 transitions, and even lower for Yb + E3, In + and Al + . Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed.
For atomic frequency standards in which fluctuations of the local oscillator (LO) frequency are the dominant noise source, we examine the role of the servo algorithm that predicts and corrects these frequency fluctuations. We derive the optimal linear prediction algorithm, showing how to measure the relevant spectral properties of the noise and optimise servo parameters while the standard is running, using only the atomic error signal. We find that, for realistic LO noise spectra, a conventional integrating servo with a properly chosen gain performs nearly as well as the optimal linear predictor. Using simple analytical models and numerical simulations, we establish optimum probe times as a function of clock atom number and of the dominant noise type in the local oscillator. We calculate the resulting LO-dependent scaling of achievable clock stability with atom number for product states as well as for maximally-correlated states.The instability of frequency standards limits the total uncertainty achievable in a measurement of finite duration [1,2]. This limit can be practically relevant even when performing measurements of static frequency ratios, since many-month-long measurement campaigns place stringent demands on the reliability of all components in an experiment. Instability becomes a fundamental concern when attempting to measure time-varying frequency ratios. For instance, in the emerging field of chronometric leveling [3][4][5], direct observation of tidal fluctuations expected in the gravitational red shift [6] requires frequency ratio measurements with a fractional uncertainty at the level of 10 −18 to be completed in a matter of hours. Physics beyond the Standard Model might be detectable in clock frequency ratio measurements as postulated transient shifts associated with dark-matter domain walls [7] or ultralight scalar darkmatter candidates [8,9]. Searches for such signals require the highest possible measurement resolution at timescales where the statistical uncertainty due to instability plays a far greater role than long-term systematic uncertainty.Of the noise processes contributing to the instability of atomic frequency standards, the most fundamental one is quantum projection noise [10], which arises from the discreteness in the measurement results obtainable from a finite number of atoms. For an ensemble of N uncorrelated two-level atoms, this noise imposes a minimum statistical uncertaintyon any measurement of the phase accumulated in an atomic superposition state. For a standard operating at a frequency ω and in the ideal case of Ramsey interrogation without technical noise, this leads to a long-term fractional * Ian.Leroux@nrc-cnrc.gc.ca; Current Address: National Research Council Canada, Ottawa, Ontario, Canada K1A 0R6 instability [11]where T is the duration of a single Ramsey interrogation and T c is the length of the frequency standard's operating cycle, such that τ/T c measurements can be performed in an averaging time τ. This quantum projection noise limit (QPN) 1 for clocks using unco...
We introduce and demonstrate double-bright electromagnetically induced transparency (D-EIT) cooling as a novel approach to EIT cooling. By involving an additional ground state, two bright states can be shifted individually into resonance for cooling of motional modes of frequencies that may be separated by more than the width of a single EIT cooling resonance. This allows threedimensional ground state cooling of a 40 Ca + ion trapped in a linear Paul trap with a single cooling pulse. Measured cooling rates and steady-state mean motional quantum numbers for this D-EIT cooling are compared with those of standard EIT cooling as well as concatenated standard EIT cooling pulses for multi-mode cooling. Experimental results are compared to full density matrix calculations. We observe a failure of the theoretical description within the Lamb-Dicke regime that can be overcome by a time-dependent rate theory. Limitations of the different cooling techniques and possible extensions to multi-ion crystals are discussed.
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