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arXiv:0906.1419 · Physical Review A

Rabi spectroscopy and excitation inhomogeneity in a one-dimensional optical lattice clock

Sebastian Blatt, Jan W. Thomsen, Gretchen K. Campbell, Andrew D. Ludlow, Matthew D. Swallows, Michael J. Martin, Martin M. Boyd, J. Ye

Published Nov 6, 2009• 165 citations
arXivHTMLPDF

Abstract

We investigate the influence of atomic motion on precision Rabi spectroscopy of ultracold fermionic atoms confined in a deep one-dimensional optical lattice. We analyze the spectral components of longitudinal sideband spectra and present a model to extract information about the transverse motion and sample temperature from their structure. Rabi spectroscopy of the clock transition itself is also influenced by atomic motion in the weakly confined transverse directions of the optical lattice. By deriving Rabi flopping and Rabi line shapes of the carrier transition, we obtain a model to quantify trap-state-dependent excitation inhomogeneities. The inhomogeneously excited ultracold fermions become distinguishable, which allows $s$-wave collisions. We derive a detailed model of this process and explain observed density shift data in terms of a dynamic mean-field shift of the clock transition.

DOI
10.1103/physreva.80.052703

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We investigate the influence of atomic motion on precision Rabi spectroscopy of ultracold fermionic atoms confined in a deep one-dimensional optical lattice. We analyze the spectral components of longitudinal sideband spectra and present a model to extract information about the transverse motion and sample temperature from their structure. Rabi spectroscopy of the clock transition itself is also influenced by atomic motion in the weakly confined transverse directions of the optical lattice. By deriving Rabi flopping and Rabi line shapes of the carrier transition, we obtain a model to quantify trap-state-dependent excitation inhomogeneities. The inhomogeneously excited ultracold fermions become distinguishable, which allows sss-wave collisions. We derive a detailed model of this process and explain observed density shift data in terms of a dynamic mean-field shift of the clock transition.
At ultracold temperatures, the Pauli exclusion principle suppresses collisions between identical fermions. This has motivated the development of atomic clocks with fermionic isotopes. However, by probing an optical clock transition with thousands of lattice-confined, ultracold fermionic strontium atoms, we observed density-dependent collisional frequency shifts. These collision effects were measured systematically and are supported by a theoretical description attributing them to inhomogeneities in the probe excitation process that render the atoms distinguishable. This work also yields insights for zeroing the clock density shift.
Abstract The clock transition at a wavelength of 1.14 μm in thulium atoms in an optical lattice in the Lamb – Dick regime is studied. The capture of thulium atoms makes it possible to suppress completely both the transition broadening due to the first-order Doppler effect and the shift of the transition frequency caused by the recoil effect. The excitation spectra of sideband oscillation frequencies and Rabi oscillations of population between the clock transition levels upon resonance excitation are investigated.
Optical lattice clocks achieve fractional frequency uncertainties of 10⁻¹⁸, yet stability is constrained by the dead time between cooling, preparation, interrogation, and detection. This sampling aliases local-oscillator noise into the clock signal (the Dick effect) and prevents continuous accumulation of oscillator phase information. We demonstrate spatially defined Rabi spectroscopy of ultracold ⁸⁸Sr atoms continuously transported in a moving optical lattice. A longitudinal excitation geometry preserves Lamb-Dicke confinement and suppresses Doppler broadening. Clock excitation is enabled only within a localised region by a transverse magnetic mixing field, defining the atom-laser interaction in space rather than in time and decoupling interrogation from preparation and detection. Transporting atoms at 16 mm s⁻¹ through a 12-mm interaction region yields a 1.2-Hz-wide spectrum close to the transit-time Fourier limit while maintaining uninterrupted atom delivery. This approach provides a practical route toward dead-time-free optical clock interrogation of continuously delivered atomic ensembles.
We study the influence of ultracold collisions induced by the inhomogeneous excitation on the clock-transition frequency in one- and two-dimensional shallow blue-detuned (BD) 87{}^{87}87Sr optical lattice clocks with a magic wavelength of ${\ensuremath{\lambda}}_{b}=389.889$ nm. The minimal lattice potential required to tightly confine atoms in each single lattice site is much larger than that required for a red-detuned (RD) lattice operating at ${\ensuremath{\lambda}}_{r}=813.4$ nm because of the relatively smaller magic wavelength. For a deep optical lattice, the two-body interactions of atoms in a single lattice site mainly contribute to the clock-transition frequency shift, while the intersite collisions primarily affect the collisional shift in a shallow optical lattice. For an effective misalignment angle $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}10$ mrad of the probe beam with respect to the lattice axis, the fractional collisional shifts in both one- and two-dimensional BD lattices are at the ${10}^{\ensuremath{-}16}$ level.
A recent realization of three-dimensional optical lattice clocks circumvents short-range collisional clock shifts which have been the bottle neck towards higher precision; the long-range electronic dipole-dipole interaction between the atoms becomes the primary source of clock shift due to interatomic interactions. We study the Rabi spectroscopy of three-dimensional optical lattice clocks with unity filling. From the Lindblad equation governing the time evolution of the density matrix of the atoms, we derive the Bloch equations in the presence of the external Rabi driving laser field, and solve the equations approximately to the first order of the coupling strength of the dipole-dipole interaction between the atoms. We find that the clock shift equals the product of the coupling strength, a factor determined by the parameters of the Rabi pulse, and another factor depending on the configuration of the three-dimensional optical lattice. Our result on the clock shift within the Rabi spectroscopy can be checked by measurements in a future experiment.
We have investigated the frequency shifts caused by inhomogeneous excitation in a 171Yb optical lattice clock. The dependences of the inhomogeneity on the temperature of the cold ytterbium atoms and the misaligning angle between the lattice laser and the clock laser are analyzed by numerical calculations. The dependence of the fractional collisional frequency shift on the ground state fraction under different cold atom temperatures, atom numbers, lattice trap depths and unequal transverse and longitudinal temperatures are also shown. The results show that the uncertainty of the ytterbium clocks, contributed by the inhomogeneous excitation, can be reduced to be 10−19 or even lower with certain conditions.