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arXiv:1008.5005 · Physical Review A

Lattice-induced nonadiabatic frequency shifts in optical lattice clocks

K. Beloy

Published Sep 29, 2010• 4 citations
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Abstract

We consider the frequency shift in optical lattice clocks which arises from the coupling of the electronic motion to the atomic motion within the lattice. For the simplest of three-dimensional lattice geometries this coupling is shown to affect only clocks based on blue-detuned lattices. We have estimated the size of this shift for the prospective strontium lattice clock operating at the 390-nm blue-detuned magic wavelength. The resulting fractional frequency shift is found to be on the order of ${10}^{\ensuremath{-}18}$ and is largely overshadowed by the electric quadrupole shift. For lattice clocks based on more complex geometries or other atomic systems, this shift could potentially be a limiting factor in clock accuracy.

DOI
10.1103/physreva.82.031402

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We consider the frequency shift in optical lattice clocks which arises from the coupling of the electronic motion to the atomic motion within the lattice. For the simplest of three-dimensional lattice geometries this coupling is shown to affect only clocks based on blue-detuned lattices. We have estimated the size of this shift for the prospective strontium lattice clock operating at the 390-nm blue-detuned magic wavelength. The resulting fractional frequency shift is found to be on the order of 10\ensuremath−18{10}^{\ensuremath{-}18}10\ensuremath−18 and is largely overshadowed by the electric quadrupole shift. For lattice clocks based on more complex geometries or other atomic systems, this shift could potentially be a limiting factor in clock accuracy.
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.
We report a hitherto undiscovered frequency shift for forbidden J = 0-->J = 0 clock transitions excited in atoms confined to an optical lattice. These shifts result from magnetic-dipole and electric-quadrupole transitions, which have a spatial dependence in an optical lattice that differs from that of the stronger electric-dipole transitions. In combination with the residual translational motion of atoms in an optical lattice, this spatial mismatch leads to a frequency shift via differential energy level spacing in the lattice wells for ground state and excited state atoms. We estimate that this effect could lead to fractional frequency shifts as large as 10(-16), which might prevent lattice-based optical clocks from reaching their predicted performance levels. Moreover, these effects could shift the magic wavelength in lattice clocks in three dimensions by as much as 100 MHz, depending on the lattice configuration.
We investigated the properties of optical lattice clocks operated with a repulsive light-shift potential. The magic wavelength, where light-shift perturbation for the clock transition cancels, was experimentally determined to be 389.889(9) nm for 87Sr. The hyperpolarizability effects on the clock transition were investigated theoretically. With minimal trapping field perturbation provided by the blue-detuned lattice, the fractional uncertainty due to the hyperpolarizability effects was found to be 2x10;{-19} in the relevant clock transition.
In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may introduce atomic-motion dependent clock uncertainties in optical lattice clocks. We show that the magic wavelength can be defined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves by allowing a spatially constant light shift arising from the latter two interactions. Experimental prospects of such lattices used with a blue magic wavelength are discussed.
Abstract Results of theoretical evaluations of uncertainties arising from the atom-lattice interaction effects on the clock frequency are presented for Sr atoms. Possibilities for simultaneous tuning of optical lattice frequency and intensity parameters are discussed aiming at minimizing uncertainties induced by interaction of Sr atoms with the field of magic-wavelength optical lattice. The fractional contributions to the clock-frequency shift from the spontaneous emission of the lattice-beam amplifier after having passed the optical fiber are determined at the level below 10 −18 .
In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may alter the definition of the magic wavelength to minimize the uncertainty of optical lattice clocks. We show that the magic wavelength can be determined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves. Experimental prospects of such lattices used with a blue magic wavelength are discussed.