No Arabic abstract
Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground-states in alkali atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called heading errors of alkali-vapor atomic magnetometers operating in the geophysical field range (B approx. 0.2-0.7 G). Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization and frequency, a technique that can be readily applied in practical situations.
We analyze both the s- and p-wave collision induced frequency shifts and propose a over-$pi$ pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a function of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over-$pi$ pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of $10^{-18}$ in both Sr and Yb optical lattice clocks by canceling the collisional frequency shift.
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold $^{88}$Sr$_2$ molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite $f$-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art textit{ab initio} model.
Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the 6S_{1/2} and 5D_{3/2} states to 0.1% precision. We find R = Delta_S / Delta_D = -11.494(13) at 514.531 nm where Delta_{S,D} are the light shifts of the m = +/- 1/2 splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.
We present an optical approach to compensating for spatially varying ac-Stark shifts that appear on atomic ensembles subject to strong optical control or trapping fields. The introduction of an additional weak light field produces an intentional perturbation between atomic states that is tuned to suppress the influence of the strong field. The compensation field suppresses sensitivity in one of the transition frequencies of the trapped atoms to both the atomic distribution and motion. We demonstrate this technique in a cold rubidium ensemble and show a reduction in inhomogeneous broadening in the trap. This two-colour approach emulates the magic trapping approach that is used in modern atomic lattice clocks but provides greater flexibility in choice of atomic species, probe transition, and trap wavelength.
Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancellation at the ten parts per billion level. Theory and empirical measurements can be used at varying levels of precision to determine the magic wavelength where shift cancellation occurs. However, lasers exhibit background spectra from amplified spontaneous emission or other lasing modes which can easily contaminate measurement of the magic wavelength and its reproducibility in other experiments or conditions. Indeed, residual light shifts from laser background have plagued optical lattice clock measurements for years. In this work, we develop a simple theoretical model allowing prediction of light shifts from measured background spectra. We demonstrate good agreement between this model and measurements of the background light shift from an amplified diode laser in an Yb optical lattice clock. Additionally, we model and experimentally characterize the filtering effect of a volume Bragg grating bandpass filter, demonstrating that application of the filter can reduce background light shifts from amplified spontaneous emission well below the $10^{-18}$ fractional clock frequency level. This demonstration is corroborated by direct clock comparisons between a filtered amplified diode laser and a filtered titanium:sapphire laser.