Sympathetic cooling of trapped ions has become an indispensable tool for quantum-information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al + with Be + , Mg + , and Ca + ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al + -Ca + crystal for different cooling laser configurations.
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...
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.
Thermal noise in optical cavities imposes a severe limitation in the stability of the most advanced frequency standards at a level of a few 10^(-16) (s/t)^(1/2) for long averaging times t. In this paper we describe two schemes for reducing the effect of thermal noise in a reference cavity. In the first approach, we investigate the potential and limitations of operating the cavity close to instability, where the beam diameter on the mirrors becomes large. Our analysis shows that even a 10 cm short cavity can achieve a thermal noise limited fractional frequency instability in the low 10^(-16) regime. In the second approach, we increase the length of the optical cavity. We show that a 39.5 cm long cavity has the potential for a fractional frequency instability even below 10^(-16), while it seems feasible to achieve a reduced sensitivity of <10^(-10)/g for vibration-induced fractional length changes in all three directions.Comment: 10 pages, 6 figures, 2 table
We demonstrate phase locking of a 729 nm diode laser to a 1542 nm master laser via an erbium-doped-fiber frequency comb, using a transfer-oscillator feedforward scheme which suppresses the effect of comb noise in an unprecedented 1.8 MHz bandwidth. We illustrate its performance by carrying out coherent manipulations of a trapped calcium ion with 99 % fidelity even at few-μs timescales. We thus demonstrate that transfer-oscillator locking can provide sufficient phase stability for high-fidelity quantum logic manipulation even without pre-stabilization of the slave diode laser.
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