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

Generalized Hyper-Ramsey Resonance with separated oscillating fields

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.Comment: accepted for publication in Phys. Rev.

Composite pulses in Hyper-Ramsey spectroscopy for the next generation of atomic clocks

The next generation of atomic frequency standards based on an ensemble of neutral atoms or a single-ion will provide very stringent tests in metrology, applied and fundamental physics requiring a new step in very precise control of external systematic corrections. In the proceedings of the 8th Symposium on Frequency Standards and Metrology, we present a generalization of the recent Hyper-Ramsey spectroscopy with separated oscillating fields using composites pulses in order to suppress field frequency shifts induced by the interrogation laser itself. Sequences of laser pulses including specific selection of phases, frequency detunings and durations are elaborated to generate spectroscopic signals with a strong reduction of the light-shift perturbation by off resonant states. New optical clocks based on weakly allowed or completely forbidden transitions in atoms, ions, molecules and nuclei will benefit from these generalized Ramsey schemes to reach relative accuracies well below the 10$^{-18}$ level.Comment: accepted as proceedings of the 8th Symposium on Frequency Standards and Metrology (Potsdam Germany, 12-16 october 2015

Synthetic Frequency Protocol in the Ramsey Spectroscopy of Clock Transitions

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 figure

Quantum engineering of atomic phase-shifts in optical clocks

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 PR

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

Nuclear Spin Effects in Optical Lattice Clocks

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 PR

Theory of nonlinear sub-Doppler laser spectroscopy taking into account atomic-motion-induced density-dependent effects in a gas

We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean field and single-atom density matrix approximations. This makes it possible to correctly take into account the effects caused by the free motion of atoms in a gas, which lead to a nonlinear dependence of the spectroscopic signal on the atomic density even in the absent of a direct interatomic interaction (e.g., dipole-dipole interaction). Within the framework of this approach, analytical expressions for the light field were obtained for an arbitrary number of resonant waves and arbitrary optical thickness of a gas medium. Sub-Doppler spectroscopy in the transmission signal for two counterpropagating and co-propagating waves has been studied in detail. A previously unknown red shift of a narrow sub-Doppler resonance is predicted in a counterpropagating waves scheme, when the frequency of one wave is fixed and the frequency of the other wave is varied. The magnitude of this shift depends on the atomic density and can be more than an order of magnitude greater than the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz shift). The found effects, caused by the free motion of atoms, require a significant revision of the existing picture of spectroscopic effects depending on the density of atoms in a gas. Apart of fundamental aspect, obtained results are important for precision laser spectroscopy and optical atomic clocks.Comment: 18 pages, 12 figure