Isotropic Light vs Six-Beam Molasses for Doppler Cooling of Atoms From Background Vapor - Theoretical Comparison

We present a 3D theoretical comparison between the radiation-pressure forces exerted on an atom in an isotropic light cooling scheme and in a six-beam molasses. We demonstrate that, in the case of a background vapor where all the space directions of the atomic motion have to be considered, the mean cooling rate is equal in both configurations. Nevertheless, we also point out what mainly differentiates the two cooling techniques: the force component orthogonal to the atomic motion. If this transverse force is always null in the isotropic light case, it can exceed the radiation-pressure-force longitudinal component in the six-beam molasses configuration for high atomic velocities, hence reducing the velocity capture range.Comment: 10 pages, 8 figure

Probe light-shift elimination in Generalized Hyper-Ramsey quantum clocks

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.

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 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.Comment: accepted for publication in Phys. Rev. Let

Temperature Dependence Cancellation of the Cs Clock Frequency in the Presence of Ne Buffer Gas

The temperature dependence of the Cs clock transition frequency in a vapor cell filled with Ne buffer gas has been measured. The experimental setup is based on the coherent population trapping (CPT) technique and a temporal Ramsey interrogation allowing a high resolution. A quadratic dependence of the frequency shift is shown. The temperature of the shift cancellation is evaluated. The actual Ne pressure in the cell is determined from the frequency shift of the 895nm optical transition. We can then determine the Cs-Ne collisional temperature coefficients of the clock frequency. These results can be useful for vapor cell clocks and especially for future micro-clocks

Coherent population trapping with polarization modulation

Coherent population trapping (CPT) is extensively studied for future vapor cell clocks of high frequency stability. In the constructive polarization modulation CPT scheme, a bichromatic laser field with polarization and phase synchronously modulated is applied on an atomic medium. A high contrast CPT signal is observed in this so-called double-modulation configuration, due to the fact that the atomic population does not leak to the extreme Zeeman states, and that the two CPT dark states, which are produced successively by the alternate polarizations, add constructively. Here we experimentally investigate CPT signal dynamics first in the usual configuration, a single circular polarization. The double-modulation scheme is then addressed in both cases: one pulse Rabi interaction and two pulses Ramsey interaction. The impact and the optimization of the experimental parameters involved in the time sequence are reviewed. We show that a simple sevenlevel model explains the experimental observations. The double-modulation scheme yields a high contrast similar to the one of other high contrast configurations like push-pull optical pumping or crossed linear polarization scheme, with a setup allowing a higher compactness. The constructive polarization modulation is attractive for atomic clock, atomic magnetometer and high precision spectroscopy applications.Comment: 13 pages, 15 figures. To be published in Journ. Appl. Phys.(2016

Dick effect in a pulsed atomic clock using Coherent Population Trapping

The Dick effect can be a limitation of the achievable frequency stability of a passive atomic frequency standard when the ancillary frequency source is only periodically sampled. Here we analyze the Dick effect for a pulsed vapor cell clock using coherent population trapping (CPT). Due to its specific interrogation process without atomic preparation nor detection outside of the Ramsey pulses, it exhibits an original shape of the sensitivity function to phase noise of the oscillator. Numerical calculations using a three-level atom model are successfully compared with measurements; an approximate formula of the sensitivity function is given as an easy-to-use tool. A comparison of our CPT clock sensitivity to phase noise with a clock of the same duty cycle using a two-level system reveals a higher sensitivity in the CPT case. The influence of a free-evolution time variation and of a detection duration lengthening on this sensitivity is studied. Finally this study permitted to choose an adapted quartz oscillator and allowed an improvement of the clock fractional frequency stability at the level of 3.2x10-13 at 1

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 on 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 \cite{totvar}, which is based on extending the data manually in the time domain, our frequency domain variances 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 that allows to compute the Allan variance and its different variants in the frequency domain

Ramsey spectroscopy of high-contrast CPT resonances with push-pull optical pumping in Cs vapor

We report the detection of high-contrast and narrow Coherent Population Trapping (CPT) Ramsey fringes in a Cs vapor cell using a simple-architecture laser system. The latter allows the combination of push-pull optical pumping (PPOP) and a temporal Ramsey-like pulsed interrogation. An originality of the optics package is the use of a single Mach-Zehnder electro-optic modulator (MZ EOM) both for optical sidebands generation and light switch for pulsed interaction. Typical Ramsey fringes with a linewidth of 166 Hz and a contrast of 33 % are detected in a cm-scale buffer-gas filled Cs vapor cell. This technique could be interesting for the development of high-performance and low power consumption compact vapor cell clocks based on CPT.Comment: 9 pages, 8 figure

Ultra-high Resolution Spectroscopy with atomic or molecular Dark Resonances: Exact steady-state lineshapes and asymptotic profiles in the adiabatic pulsed regime

Exact and asymptotic lineshape expressions are derived from the semi-classical density matrix representation describing a set of closed three-level $\Lambda$ 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