Exploring the Use of Ramsey-CPT Spectroscopy for a Microcell-Based Atomic Clock.

We investigate the application of Ramsey spectroscopy for the development of a microcell atomic clock based on coherent population trapping (CPT). The dependence of the central Ramsey-CPT fringe properties on key experimental parameters is first studied for optimization of the clock's short-term frequency stability. The sensitivity of the clock frequency to light-shift effects is then studied. In comparison with the continuous-wave (CW) regime case, the sensitivity of the clock frequency to laser power variations is reduced by a factor up to 14 and 40.3 for dark times of 150 and [Formula: see text], respectively, at the expense of intensity 3.75 times higher for short-term stability optimization. The dependence of the clock frequency on the microwave power is also reduced in the Ramsey case. We demonstrate that the Ramsey-CPT interrogation improves the clock Allan deviation for averaging times higher than 100 s. With a dark time of [Formula: see text], a clock fractional frequency stability of 3.8 ×10-12 at 104 s is obtained, in comparison with the level of 8×10-11 obtained in the standard CW case, in similar environmental conditions. These results demonstrate that Ramsey-based interrogation protocols might be an attractive approach for the development of chip-scale atomic clocks (CSACs) with enhanced mid- and long-term stability.

Enhanced observation time of magneto-optical traps using micro-machined non-evaporable getter pumps.

We show that micro-machined non-evaporable getter pumps (NEGs) can extend the time over which laser cooled atoms can be produced in a magneto-optical trap (MOT), in the absence of other vacuum pumping mechanisms. In a first study, we incorporate a silicon-glass microfabricated ultra-high vacuum (UHV) cell with silicon etched NEG cavities and alumino-silicate glass (ASG) windows and demonstrate the observation of a repeatedly-loading MOT over a 10 min period with a single laser-activated NEG. In a second study, the capacity of passive pumping with laser activated NEG materials is further investigated in a borosilicate glass-blown cuvette cell containing five NEG tablets. In this cell, the MOT remained visible for over 4 days without any external active pumping system. This MOT observation time exceeds the one obtained in the no-NEG scenario by almost five orders of magnitude. The cell scalability and potential vacuum longevity made possible with NEG materials may enable in the future the development of miniaturized cold-atom instruments.

Composite laser-pulses spectroscopy for high-accuracy optical clocks: a review of recent progress and perspectives.

Probing an atomic resonance without disturbing it is an ubiquitous issue in physics. This problem is critical in high-accuracy spectroscopy or for the next generation of atomic optical clocks. Ultra-high resolution frequency metrology requires sophisticated interrogation schemes and robust protocols handling pulse length errors and residual frequency detuning offsets. This review reports recent progress and perspective in such schemes, using sequences of composite laser-pulses tailored in pulse duration, frequency and phase, inspired by NMR techniques and quantum information processing. After a short presentation of Rabi technique and NMR-like composite pulses allowing efficient compensation of electromagnetic field perturbations to achieve robust population transfers, composite laser-pulses are investigated within Ramsey's method of separated oscillating fields in order to generate non-linear compensation of probe-induced frequency shifts. Laser-pulses protocols such as hyper-Ramsey, modified hyper-Ramsey, generalized hyper-Ramsey and hybrid schemes as auto-balanced Ramsey spectroscopy are reviewed. These techniques provide excellent protection against both probe induced light-shift perturbations and laser intensity variations. More sophisticated schemes generating synthetic frequency-shifts are presented. They allow to reduce or completely eliminate imperfect correction of probe-induced frequency-shifts even in presence of decoherence due to the laser line-width. Finally, two universal protocols are presented which provide complete elimination of probe-induced frequency shifts in the general case where both decoherence and relaxation dissipation effects are present by using exact analytic expressions for phase-shifts and the clock frequency detuning. These techniques might be applied to atomic, molecular and nuclear frequency metrology, Ramsey-type mass spectrometry as well as precision spectroscopy.

Doppler-free spectroscopy on the Cs D1 line with a dual-frequency laser.

We report on Doppler-free laser spectroscopy in a Cs vapor cell using a dual-frequency laser system tuned on the Cs D1 line. Using counter-propagating beams with crossed linear polarizations, an original sign reversal of the usual saturated absorption dip and large increase in Doppler-free atomic absorption is observed. This phenomenon is explained by coherent population trapping (CPT) effects. The impact of laser intensity and light polarization on absorption profiles is reported in both single-frequency and dual-frequency regimes. In the latter, frequency stabilization of two diode lasers was performed, yielding a beat note fractional frequency stability at the level of 3×10-12 at 1 s averaging time. These performances are about an order of magnitude better than those obtained using a conventional single-frequency saturated absorption scheme.

Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications.

This paper reports on an original architecture of microfabricated alkali vapor cell designed for miniature atomic clocks. The cell combines diffraction gratings with anisotropically etched single-crystalline silicon sidewalls to route a normally-incident beam in a cavity oriented along the substrate plane. Gratings have been specifically designed to diffract circularly polarized light in the first order, the latter having an angle of diffraction matching the (111) sidewalls orientation. Then, the length of the cavity where light interacts with alkali atoms can be extended. We demonstrate that a longer cell allows to reduce the beam diameter, while preserving the clock performances. As the cavity depth and the beam diameter are reduced, collimation can be performed in a tighter space. This solution relaxes the constraints on the device packaging and is suitable for wafer-level assembly. Several cells have been fabricated and characterized in a clock setup using coherent population trapping spectroscopy. The measured signals exhibit null power linewidths down to 2.23 kHz and high transmission contrasts up to 17%. A high contrast-to-linewidth ratio is found at a linewidth of 4.17 kHz and a contrast of 5.2% in a 7-mm-long cell despite a beam diameter reduced to 600 µm.

Magic radio-frequency dressing of nuclear spins in high-accuracy optical clocks.

A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a nonresonant radio-frequency field. For fermionic species as (87)Sr, (171)Yb, and (199)Hg, particular ratios between the radio-frequency driving amplitude and frequency lead to "magic" magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first-order magnetic variations are produced within a relative uncertainty below the 10(-18) level. An Autler-Townes continued fraction describing a semiclassical radio-frequency dressed spin is numerically computed and compared to an analytical quantum description including higher-order magnetic field corrections to the dressed energies.

Stability variances: a filter approach.

We analyze the Allan variance estimator as the combination of discrete-time linear filters. We apply this analysis to the different variants of the Allan variance: the overlapping Allan variance, the modified Allan variance, the Hadamard variance and the overlapping Hadamard variance. Based upon this analysis, we present a new method to compute a new estimator of the Allan variance and its variants in the frequency domain. We show that the proposed frequency domain equations are equivalent to extending the data by periodization in the time domain. Like the total variance, which is based on extending the data manually in the time domain, our frequency domain variance estimators have better statistics than the estimators of the classical variances in the time domain. We demonstrate that the previous well-know equation that relates the Allan variance to the power spectrum density (PSD) of continuous-time signals is not valid for real world discrete-time measurements and we propose a new equation that relates the Allan variance to the PSD of the discrete-time signals and allows computation of the Allan variance and its different variants in the frequency domain.

Investigations on continuous and pulsed interrogation for a CPT atomic clock.

We investigated the influence of some critical parameters and operating conditions such as cell temperature, laser intensity, and interrogation technique affecting the performances of a gas cell Cs frequency standard based on coherent population trapping (CPT). Thanks to an original experimental setup, the atoms can be trapped in the dark state and interrogated using continuous wave (CW) or pulsed coherent optical radiations. Using a double-lambda scheme, a signal contrast as high as 52% has been measured in the continuous regime for an optimum cell temperature of 35 degrees C. Compared with the conventional continuous CPT interrogation, the pulsed interrogation technique reduces the light shift by a factor of 300 and allowed it to reach high-frequency stability for higher laser intensities. The frequency stability has been measured to be 9 x 10(-13) for a 1 s integration time. Main noise contributions limiting the short-term and medium-term frequency stability are reviewed and estimated.

Oscillation of the center of the Rabi pedestal in an optically pumped Cs beam standard.

This paper is devoted to the study of the symmetry of the Rabi pedestal of the clock transition in an optically pumped Cs beam frequency standard. The frequency of the microwave oscillator is locked on the center of the Rabi pedestal using a square wave frequency modulation. We observe a modulation of the center frequency as a function of the modulation depth. Experimental investigations on this unexpected effect are reported.