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...

With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10 −17 and below, new applications such as chronometric levelling with few-cm height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminium ion, which is interrogated via quantum logic spectroscopy. We employ singlycharged calcium as the logic ion for sympathetic cooling, state preparation and readout.Here we present a simple and compact physics and laser package for manipulation of 40 Ca + . Important features are a segmented multi-layer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40 Ca + repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27 Al + , derived from measurements with a single calcium ion. The micromotion-induced secondorder Doppler shift for 27 Al + has been determined to be δνEMM ν = −0.4 +0.4 −0.3 × 10 −18 and the black-body radiation shift is δν BBR /ν = (−4.0±0.4)×10 −18 . Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ω rad,Ca+ ≈ 2π × 2.5 MHz (ω ax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.

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.

We present a highly stable bow-tie power enhancement cavity for critical second harmonic generation (SHG) into the UV using a Brewster-cut β-BaBO (BBO) nonlinear crystal. The cavity geometry is suitable for all UV wavelengths reachable with BBO and can be modified to accommodate anti-reflection coated crystals, extending its applicability to the entire wavelength range accessible with non-linear frequency conversion. The cavity is length-stabilized using a fast general purpose digital PI controller based on the open source STEMlab 125-14 (formerly Red Pitaya) system acting on a mirror mounted on a fast piezo actuator. We observe 130 h uninterrupted operation without decay in output power at 313 nm. The robustness of the system has been confirmed by exposing it to accelerations of up to 1 g with less than 10% in-lock output power variations. Furthermore, the cavity can withstand 30 min of acceleration exposure at a level of 3 g without substantial change in the SHG output power, demonstrating that the design is suitable for transportable setups.

We present the design, construction, and characterization of a multichannel, low-drift, low-noise dc voltage source specially designed for biasing the electrodes of segmented linear Paul traps. The system produces 20 output voltage pairs having a common-mode range of 0 to +120 V with 3.7 mV/LSB (least significant bit) resolution and differential ranges of ±5 V with 150 μV/LSB or ±16 V with 610 μV/LSB resolution. All common-mode and differential voltages are independently controllable, and all pairs share the same ground reference. The measured drift of the voltages after warm-up is lower than 1 LSB peak-to-peak on the time scale of 2 h. The noise of an output voltage measured with respect to ground is <10 μVRMS within 10 Hz–100 kHz, with spectral density lower than 3 nV Hz−1/2 above 50 kHz. The performance of the system is limited by the external commercial multichannel DAC unit NI 9264, and in principle, it is possible to achieve higher stability and lower noise with the same voltage ranges. The system has a compact, modular, and scalable architecture, having all parts except for the DAC chassis housed within a single 19″ 3HE rack.