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Transversely loaded bidimensional-magneto-optical-traps (2D-MOT) have been recently developed as high flux sources for cold strontium atoms to realize a new generation of compact experimental setups. Here, we discuss on the implementation of a cross-polarized bi-color slower for a strontium atomic beam improving the 2D-MOT loading, and increasing the number of atoms in a final MOT by eleven times. Our slowing scheme addresses simultaneously two excited Zeeman substates of the 88Sr 1S0->1P1 transition at 461 nm. We also realized a 3-axis active feedback control of the magnetic field down to the microgauss regime. Such a compensation is performed thanks to a network of eight magnetic field probes arranged in a cuboid configuration around the atomic cold sample, and a pair of coils in Helmholtz configuration along each of three Cartesian directions. Our active feedback is capable of efficiently suppressing most of the magnetically-induced position fluctuations of the 689~nm intercombination-line MOT., 8 pages, 6 figures

The addition of a weak oscillating field modifying strongly dressed spins enhances and enriches the system quantum dynamics. Through low-order harmonic mixing the bichromatic driving generates additional rectified static field acting on the spin system. The secondary field allows for a fine tuning of the atomic response and produces effects not accessible with a single dressing field, such as a spatial triaxial anisotropy of the spin coupling constants and acceleration of the spin dynamics. This tuning-dressed configuration introduces an extra handle for the system full engineering for quantum control applications. Tuning amplitude, harmonic content, spatial orientation and phase relation are control parameters. A theoretical analysis, based on perturbative approach, is experimentally validated by applying a bichromatic radiofrequency field to an optically pumped Cs atomic vapour. We measure the resonance shifts produced by tuning fields up to the third harmonic., Comment: Corrected some typos and expanded the Supplemental Material

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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 (HR), Modified Hyper-Ramsey (MHR), Generalized Hyper-Ramsey (GHR) and hybrid schemes 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, mass spectrometry as well as precision spectroscopy.

International audience; Vapor-cell atomic clocks are widely appreciated for their excellent short-term fractional frequency stability and their compactness. However, they are known to suffer on medium and long time scales from significant frequency instabilities, generally attributed to light-induced frequency-shift effects. In order to tackle this limitation, we investigate the application of the recently proposed autobalanced Ramsey (ABR) interrogation protocol onto a pulsed hot-vapor Cs vapor-cell clock based on coherent population trapping(CPT). We demonstrate that the ABR protocol, developed initially to probe the one-photon resonance of quantum optical clocks, can be successfully applied to a two-photon CPT resonance. The applied method, based on the alternation of two successive Ramsey-CPT sequences with unequal free-evolution times and the subsequent management of two interconnected phase and frequency servo loops, is found to allow a relevant reduction of the clock-frequency sensitivity to laser-power variations. This original ABR-CPTapproach, combined with the implementation of advanced electronics laser-power stabilization systems, yields the demonstration of a CPT-based Cs vapor-cell clock with a short-term fractional frequency stability at the level of 3.1 × 10−13τ−1=2, averaging down to the level of 6 × 10−15 at 2000-s integration time. These encouraging performances demonstrate that the use of the ABR interrogation protocol is a promising option towards the development of high-stability CPT-based frequency standards. Such clocks could beattractive candidates in numerous applications including next-generation satellite-based navigation systems, secure communications, instrumentation, or defense systems.

Tunable electromagnetic sources, such as voltage controlled oscillators (VCO), micro electromechanical systems (MEMS) or diode lasers are often required to be linear during frequency-sweep modulation. In many cases, it might also be sufficient that the degree of the non-linearity can be well controlled. Without further efforts, these conditions are rarely achieved using free running sources. Based on a pre-distortion voltage ramp, we develop in this letter a simple and universal method that minimizes the non-linear frequency response of tunable electromagnetic sources. Using a current-driven Quantum Cascade Laser (QCL) as an example, we demonstrate that the non-linearity can easily be reduced by a factor of ten when using a single distortion parameter $\gamma$. In the investigation of the IR absorption spectrum of ozone at 10\,$\mu$m, an even better reduction of the frequency scale error by two orders of magnitude is obtained by using the pre-distortion method to generate an essentially purely quadratic sweep frequency dependency which can be inverted easily to retrieve precise molecular line positions. After having tested our method on a variety of electromagnetic sources, we anticipate a wide range of applications in a variety of fields., Comment: inspired by the Gamma correction on TVs and videos

When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. This includes precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized auto-balanced Ramsey spectroscopy (GABRS) is proposed. Here, the usual local oscillator frequency control loop is supplemented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different Ramsey period. This second loop feeds back to a secondary clock variable and ultimately compensates for the perturbation of the clock frequency caused by the measurements in the first loop. We show that such a two-loop scheme can lead to perfect compensation of measurement-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors that are typical of other hyper-Ramsey schemes.

Using a free-running distributed-feedback quantum cascade laser (QCL) emitting at 9.54 μm, the pressure shift parameters of four intense rovibrational transitions in the ν 3 fundamental band of ozone induced by oxygen (O 2 ), air and the noble gases helium (He), argon (Ar), and xenon (Xe) are obtained by employing second harmonic detection. The experimental analysis comprises a full uncertainty budget and provides line shift data which are traceable to SI. The high density of transitions in the ν 3 spectral region of ozone make this region particularly difficult to study with more commonly used techniques such as Fourier transform spectroscopy. The comparatively high spectral resolution of the QCL in the MHz range, on the contrary, allows to measure molecular shifts at relatively low pressures (from 2 to 70 hPa), thus reducing the impact of spectral congestion due to pressure broadening of molecular lines. The comparison of our results with published data shows that presently recommended values for the pressure shift are too low in this region. This observation is corroborated by semi-classical calculations using the Robert-Bonamy formalism. A slight negative J dependence, already observed in other ozone vibrational bands, is predicted. Systematic use of our technique could be very useful to support this hypothesis and to make up for the lack of shift parameters for ozone ν 3 transitions in molecular spectral databases. A subsequent stabilization of the QCL onto an optical frequency comb will open up possibilities to perform metrological measurements of Doppler-free molecular lines.

Optical clock interrogation protocols, based on laser-pulse spectroscopy, are suffering from probe-induced frequency-shifts and their variations induced by laser power. Original Hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not apply below fractional frequency changes of 10−18 when decoherence and relaxation by spontaneous emission or collisions are present. We present a universal interrogation protocol based on composite laser-pulses spectroscopy with phase-modulation for both fermionic and bosonic optical clocks, eliminating probe-induced frequency-shifts at all orders even in presence of various dissipative processes. This scheme, using a magic combination of ±π/4 and ±3π/4 phase-modulated generalized Hyper-Ramsey resonances, extremely robust to errors in laser parameters, can be applied to atomic, molecular and nuclear frequency metrology, mass spectrometry and precision spectroscopy.

Optical clock interrogation protocols, based on laser-pulse spectroscopy, are suffering from probe-induced frequency shifts and their variations induced by laser power. Original Hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by laser probe by deriving the exact canonical form of a multi-pulse generalized Hyper-Ramsey (GHR) resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulses spectroscopy with phase-modulation eliminating probe-induced frequency shifts at all orders in presence of various dissipative processes. Unlike frequency shifts extrapolation-based methods, a universal interrogation protocol based on $\pm\pi/4$ and $\pm3\pi/4$ phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultra-robust error signal gradient in presence of substantial uncompensated ac Stark-shifts. Such a scheme can be implemented in two flavours: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular and nuclear frequency metrology, mass spectrometry and to the field of precision spectroscopy. It might be designed using magic-wave induced transitions, two-photon excitation and magnetically-induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement., Comment: In memory of N.F Ramsey and A. Clairon. Accepted for publication in Phys. Rev. A

We present a new interrogation scheme for the next generation of quantum clocks to suppress frequency-shifts induced by laser probing fields themselves based on Generalized Hyper-Ramsey resonances. Sequences of composite laser pulses with specific selection of phases, frequency detunings and durations are combined to generate a very efficient and robust frequency locking signal with almost a perfect elimination of the light-shift from off resonant states and to decouple the unperturbed frequency measurement from the laser's intensity. The frequency lock point generated from synthesized error signals using either $\pi/4$ or $3\pi/4$ laser phase-steps during the intermediate pulse is tightly protected against large laser pulse area variations and errors in potentially applied frequency shift compensations. Quantum clocks based on weakly allowed or completely forbidden optical transitions in atoms, ions, molecules and nuclei will benefit from these hyper-stable laser frequency stabilization schemes to reach relative accuracies below the 10$^{-18}$ level., Comment: accepted for publication in Phys. Rev. A

We develop an universal method to significantly suppress probe-induced shifts in any types of atomic clocks using the Ramsey spectroscopy. Our approach is based on adaptation of the synthetic frequency concept [V. I. Yudin, et al., Phys. Rev. Lett. 107, 030801 (2011)] (previously developed for BBR shift suppression) to the Ramsey spectroscopy with the use of interrogations for different dark time intervals. Universality of the method consists in arbitrariness of the possible Ramsey schemes. However, most extremal results are obtained in combination with so-called hyper-Ramsey spectroscopy [V. I. Yudin, et al., Phys. Rev. A 82, 011804(R) (2010)]. In the latter case, the probe-induced frequency shifts can be suppressed considerably below a fractional level of 10$^{-18}$ practically for any optical atomic clocks, where this shift previously was metrologically significant. The main advantage of our method in comparison with other radical hyper-Ramsey approaches [R. Hobson, et al., Phys. Rev. A 93, 010501(R) (2016); T. Zanon-Willette, et al., Phys. Rev. A 93, 042506 (2016)] consist in much greater efficiency and resistibility in the presence of decoherentization., Comment: 9 pages, 7 figures

An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The phase-shift accumulated at the end of the interrogation scheme offering high-level control of quantum states throughout various laser parameters conditions. The Generalized Hyper-Ramsey Resonance based on independent manipulation of interaction time, field amplitude, phase and frequency detuning is presented to increase the performance of next generation of atomic, molecular and nuclear clocks, to upgrade high resolution frequency measurement in Penning trap mass spectrometry and for a better control of light induced frequency shifts in matter wave interferometers or quantum information processing., accepted for publication in Phys. Rev. A

Quantum engineering of time-separated Raman laser pulses in three-level systems is presented to produce an ultra-narrow optical transition in bosonic alkali-earth clocks free from light shifts and with a significantly reduced sensitivity to laser parameter fluctuations. Based on a quantum artificial complex-wave-function analytical model, and supported by a full density matrix simulation including a possible residual effect of spontaneous emission from the intermediate state, atomic phase-shifts associated to Ramsey and Hyper-Ramsey two-photon spectroscopy in optical clocks are derived. Various common-mode Raman frequency detunings are found where the frequency shifts from off-resonant states are canceled, while strongly reducing their uncertainties at the 10$^{-18}$ level of accuracy., Comment: accepted for publication in PRA

International audience; Radio-frequency quantum engineering of spins is based on the dressing by a nonresonant electromagnetic field. Radio-frequency dressing occurs also for the motion of particles, electrons, or ultracold atoms, within a periodic spatial potential. The dressing, producing a renormalization and also a freeze of the system energy, is described by different approaches: dressed atom, magnetic resonance semiclassical treatment, and continued-fraction solution of the Schrödinger equation. A comparison between these solutions points out that the semiclassical treatment, to be denoted as the S solution, represents the most convenient tool to evaluate the tunneling renormalization of ultracold atoms.

A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a non resonant radio-frequency field. For fermionic species as $^{87}$Sr, $^{171}$Yb, and $^{199}$Hg, particular ratios between the radiofrequency 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 semi-classical radio-frequency dressed spin is numerically computed and compared to an analytical quantum description including higher order magnetic field corrections to the dressed energies., accepted for publication in Phys. Rev. Lett

Exact and asymptotic lineshape expressions are derived from the semi-classical density matrix representation describing a set of closed three-level atomic or molecular states including decoherences, relaxation rates and light-shifts. An accurate analysis of the exact steady-state Dark Resonance profile describing the Autler-Townes doublet, the Electromagnetically Induced Transparency or Coherent Population Trapping resonance and the Fano-Feshbach lineshape, leads to the linewidth expression of the two-photon Raman transition and frequency-shifts associated to the clock transition. From an adiabatic analysis of the dynamical Optical Bloch Equations in the weak field limit, a pumping time required to efficiently trap a large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, Dark Resonance fringes mixing continuous-wave lineshape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency-shifts affecting the central clock fringe computed from asymptotic profiles and related to Raman decoherence process, exhibit non-linear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition., accepted for publication in PRA

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the $^1S_0$-$^3P_0$ clock transition and the differential g-factor between the two clock states for alkaline-earth(-like) atoms, using $^{87}$Sr as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential g-factor in $^{87}$Sr is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below 10$^{-17}$ in lattice clocks., Comment: 13 pages, 12 figures, submitted to PRA

We propose a combination of electromagnetically induced transparency-Raman and pulsed spectroscopy techniques to accurately cancel frequency shifts arising from electromagnetically induced transparency fields in forbidden optical clock transitions of alkaline earth atoms. At appropriate detunings, time-separated laser pulses are designed to trap atoms in coherent superpositions while eliminating off-resonance ac Stark contributions, achieving efficient population transfer up to 60% with inaccuracy

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