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Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty demonstrating incredible control over external perturbations of the clock transition frequency. At the same time there is an increasing demand for atomic and ionic transitions with minimal sensitivity to external fields, with practical operational wavelengths and robust readout protocols. One of the goals is to simplify clock's operation maintaining its relative uncertainty at low 10-18 level. It is especially important for transportable and envisioned space-based optical clocks. We proved earlier that the 1.14um inner-shell magnetic dipole transition in neutral thulium possesses very low blackbody radiation shift compared to other neutrals. Here we demonstrate operation of a bi-colour thulium optical clock with extraordinary low sensitivity to the Zeeman shift due to a simultaneous interrogation of two clock transitions and data processing. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of tensor lattice Stark shift can be also reduced to below 10-18 in fractional frequency units. All these features make thulium optical clock almost free from hard-to-control systematic shifts. Together with convenient cooling and trapping laser wavelengths, it provides great perspectives for thulium lattice clock as a high-performance transportable system., Comment: 25 pages, 9 figures

Due to the low sensitivity of the thulium optical clock to black-body radiation and good accuracy and stability estimations, it appears to be one of the most promising transportable optical clocks. One of the leading systematic effects for Tm clock transition, namely the second-order Zeeman effect, can be canceled by probing two clock transitions between different hyperfine levels of ground and metastable states during the clock operation. We prepare the atoms in $m_F=0$ state of both ground hyperfine levels simultaneously and excite alternately two clock transitions. Here we demonstrate efficient optical pumping into both target states via single-frequency radiation at 418.8 nm. The resulting population of $m_F=0$ states of ground hyperfine levels is 36% and 3.8% of the initial number of atoms with less than 4% and 0.4% on non-zero magnetic sublevels, correspondingly. We performed numerical simulations of the optical pumping process which is able to explain experimental results reasonably well., Comment: 9 pages, 6 figures

With direct polarizability measurements we demonstrated extremely low sensitivity of the inner-shell clock transition at $1.14\,\mu$m in Tm atoms to external dc electric fields and black-body radiation (BBR). We measured differential polarizabilities of clock levels in Tm at wavelengths of 810--860\,nm and at 1064\,nm and inferred the static scalar differential polarizability of the inner-shell clock transition of $-0.047(18)$ atomic units corresponding to only $2\times10^{-18}$ fractional frequency shift from BBR at the room temperature. This is a few orders of magnitude smaller compared to the BBR shift of the clock transitions in the neutral atoms (Sr, Yb, Hg) and competes with the least sensitive ion species (e.g. Al$^+$ or Lu$^+$). For the $1.14\,\mu$m clock transition, we experimentally determined the "magic" wavelength of $813.320(6)$\,nm, recorded the transition spectral linewidth of $10$\,Hz, and measured its absolute frequency of $262\,954\,938\,269\,213(30)$\,Hz., Comment: 9 pages, revised contribution from BBR magnetic field and electric quadrupole shift

Nitrogen-vacancy (NV) center in diamond was found to be a powerful tool for various sensing applications. The main work horse of this center so far has been optically detected electron resonance. Utilization of the nuclear spin has the potential of significantly improving sensitivity in rotation and magnetic field sensors. Ensemble-based sensors consume quite a bit of power, thus requiring an understanding of temperature-related shifts. In this article, we provide a detailed study of the temperature shift of the hyperfine components of the NV center.

Minimization of internal degrees of freedom is an important step in the cooling of atomic species to degeneracy temperature. Here, we report on the loading of 6*10^5 thulium atoms optically polarized at maximum possible magnetic quantum number mf=-4 state into dipole trap operating at 532 nm. The purity of polarizations of the atoms was experimentally verified using a Stern-Gerlach-type experiment. Experimental measured polarization of the state is 3.91(26).

We present the results of a study on relaxation and diffusion processes of rubidium atoms in a rubidium cell with an internal vapor source. The cell is an evacuated glass bulb, which is characterized in that the source of atomic vapors in the form of a metal film Rb is evenly distributed throughout the inner surface of the bulb, and the paraffin film is uniformly distributed over the entire area and over the metal surface. By using laser optical pumping, we performed measurements of the relaxation time and the average number of bounces of optical pumped rubidium atoms in the bulb. We have measured the adsorption time of rubidium atoms by paraffin coating and rubidium atoms diffusion coefficient in paraffin used. A simple model of the pumping and atomic diffusion processes in the cell is discussed as well., Comment: 10 pages, 6 figures

Second-stage laser cooling of thulium atoms at the 530.7 nm transition with a natural linewidth of 350 kHz offers an interesting possibility to study different regimes of a magneto-optical trap (MOT). The intermediate value of the spectral linewidth of the cooling transition allows the observation of three distinct regimes depending on intensity and detuning of the cooling beams. Namely, the "bowl-shaped" regime when light pressure force competes with gravity, the "double structure" regime with interplay between Doppler and polarization-gradient (sub-Doppler) cooling, and the "symmetric" regime when Doppler cooling dominates over sub-Doppler cooling and gravity. The polarization-gradient cooling manifests itself by a two-temperature momentum distribution of atoms resulting in a double-structure of the spatial MOT profile consisting of a cold central fraction surrounded by a hot halo. We studied the "double structure" regime at different saturation parameters and compared observations with calculations based on semiclassical and quantum approaches. The quantum treatment adequately reproduces experimental results if the MOT magnetic field is properly taken into account., Comment: 7 pages, 6 figures

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $\alpha(Z \alpha)^5$ to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using modern experimental data on the electromagnetic form factors of light nuclei., Comment: 8 pages, 1 Figure

We report on the improved measurement of the hyperfine structure of $4f^{12}(^3 H_6)5d_{5/2}6s^2$ $(J=9/2)$ excited state in Tm-169 which is involved in the second-stage laser cooling of Tm. To measure the absolute value of the hyperfine splitting interval we used Doppler-free frequency modulation saturated absorption spectroscopy of Tm atoms in a vapor cell. The sign of the hyperfine constant was determined independently by spectroscopy of laser cooled Tm atoms. The hyperfine constant of the level equals $A_J=-422.112(32)$ MHz that corresponds to the energy difference between two hyperfine sublevels of $-2110.56(16)$~MHz. In relation to the saturated absorption measurement we quantitatively treat contributions of various mechanisms into the line broadening and shift. We consider power broadening in the case when Zeeman sublevels of atomic levels are taken into account. We also discuss the line broadening due to frequency modulation and relative intensities of transitions in saturated-absorption experiments.

We consider a narrow magneto-dipole transition in the $^{169}$Tm atom at the wavelength of $1.14\,\mu$m as a candidate for a 2D optical lattice clock. Calculating dynamic polarizabilities of the two clock levels $[\text{Xe}]4f^{13}6s^2 (J=7/2)$ and $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ in the spectral range from $250\,$nm to $1200\,$nm, we suggest the "magic" wavelength for the optical lattice at $807\,$nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction and other effects which can perturb the transition frequency are calculated. The transition at $1.14\,\mu$m demonstrates low sensitivity to the BBR shift corresponding to $8\times10^{-17}$ in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than $5 \times 10^{-18}$ in fractional units. By direct excitation of the $1.14\,\mu$m transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ of $112\,$ms which corresponds to a natural spectral linewidth narrower than $1.4\,$Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at $532\,$nm.

We present the results of a study of the diffusion of Rb atoms in paraffin - coated resonant vapor cells. We have modeled the Rb diffusion both in the cell and in the coating, assuming that the main loss of Rb atoms is due to the physical absorption of the atoms by the glass substrate. It is demonstrated that the equilibrium atomic density in the cell is a monotonic function of the thickness of the paraffin coating: the density increases with an increase in the thickness of the coating. The diffusion coefficient for rubidium in paraffin thin films has been determined to be equal to 4,7*10^-7 cm^2/s. The results of the experiment might be useful for a better understanding of the details involved in the processes of the interaction of alkali atoms with a paraffin coating.

We present the results of the study of an optical resonant cell filled by a vapor of the Rb atoms and coated with a non-stick polydimethylsiloxane (PDMS) polymer. We show that it is possible to define correctly the diffusion coefficient of the atoms in the coating, using geometric parameters of the cell and the vapor density in the cell volume only. The dependence of the diffusion coefficient on the cell curing time is presented. It is shown that the mysterious cell curing process can be explained in terms of the polymerization of the polymer coating by alkali atoms. Anomalous long dwell time of the Rb atoms on the PDMS coating is discussed as well.

We report on accurate measurements of the scalar and tensor polarizabilities of the 5D fine structure levels 5D3/2 and 5D5/2 in Rb. The measured values show reasonable correspondence to previously published theoretical predictions, but are more accurate. We implemented laser excitation of the 5D level in a laser cooled cloud of optically polarized Rb-87 atoms placed in a constant electric field., Comment: 8 pages, 9 figures

Thulium atoms are trapped in a magneto-optical trap using a strong transition at 410 nm with a small branching ratio. We trap up to $7\times10^{4}$ atoms at a temperature of 0.8(2) mK after deceleration in a 40 cm long Zeeman slower. Optical leaks from the cooling cycle influence the lifetime of atoms in the MOT which varies between 0.3 -1.5 s in our experiments. The lower limit for the leaking rate from the upper cooling level is measured to be 22(6) s$^{-1}$. The repumping laser transferring the atomic population out of the F=3 hyperfine ground-state sublevel gives a 30% increase for the lifetime and the number of atoms in the trap., Comment: 4 pages, 6 figures