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arXiv:0908.2848

Magic Wavelength for Atomic Motion Insensitive Optical Lattice Clocks

Hidetoshi Katori, Koji Hashiguchi, Ekaterina Ilinova, Vitalii D Ovsiannikov

Published Aug 20, 2009• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.0908.2848

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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.
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.
We consider designs of optical lattice clocks in view of the quantum statistics, relevant atomic spins, and atom-lattice interactions. The first two issues lead to two optimal constructions for the clock: a one-dimensional (1D) optical lattice loaded with spin-polarized fermions and a 3D optical lattice loaded with bosons. By taking atomic multipolar interactions with the lattice fields into account, an "atomic motion insensitive" wavelength is proposed to provide a precise definition of the "magic wavelength." We then present a frequency comparison of these two optical lattice clocks: spin-polarized fermionic 87 Sr and bosonic 88 Sr prepared in 1D and 3D optical lattices, respectively. Synchronous interrogations of these two optical lattice clocks by the same probe laser allowed canceling out its frequency noise as a common mode noise to achieve a relative stability of 3 × 10 −17 for an averaging time of τ = 350 s. The scheme, therefore, provides us with a powerful means to investigate intrinsic uncertainty of the clocks regardless of the probe laser stability. We discuss prospects of the synchronous operation of the clocks on the measurement of the geoid height difference and on the search of constancy of fundamental constants.
Magnetic-dipole, electric-quadrupole, and hyperpolarizability effects on clock energy levels are analyzed in detail for Sr atoms in Stark potentials of red-detuned and blue-detuned magic-wavelength optical lattices. A difference between ac Stark shifts in traveling and standing waves is determined numerically. Differences between magic wavelengths for atoms in traveling and standing waves are presented and strategies for minimizing uncertainties of the clock frequency are indicated explicitly. Significant suppression of hyperpolarizability effect is demonstrated analytically for a blue-detuned in comparison with a red-detuned lattice, thus enabling essential deepening of trap potentials, reducing tunneling between lattice wells and collision effects.
The budget of uncertainties of a time-frequency standard on neutral atoms, trapped in an optical lattice with a “magic wavelength” (MWL), includes a number of shift and broadening corrections, coming from interaction of atoms with different fields of environment. The most important corrections are those arising from interaction with the field of lattice wave. The lattice field is essentially stronger than other fields and may introduce severe perturbations on the standard frequency, despite its tuning to the MWL, which was proposed to compensate these perturbations in a standing-wave lattice, ensuring rigorous equality of the working-level shifts, independently of the atomic motion and the laser intensity. The method of determining MWL, based on measuring the shift of the clock frequency in a weak field of a travelling wave accounts for the Stark shift of energy levels, but only linear in the laser intensity, with inclusion of all multipole-interaction terms.
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.
Active clocks could provide better stabilities during initial stages of measurements over passive clocks, in which stabilities become saturated only after long-term measurements. This unique feature of an active clock has led to search for suitable candidates to construct such clocks. The other challenging task of an atomic clock is to reduce its possible systematics. A major part of the optical lattice atomic clocks based on neutral atoms are reduced by trapping atoms at the magic wavelengths of the optical lattice lasers. Keeping this in mind, we find the magic wavelengths between all possible hyperfine levels of the transitions in Rb and Cs atoms that were earlier considered to be suitable for making optical active clocks. To validate the results, we give the static dipole polarizabilities of Rb and Cs atoms using the electric dipole transition amplitudes that are used to evaluate the dynamic dipole polarizabilities and compare them with the available literature values.