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Physical Review Letters

Optical Clock with Millihertz Linewidth Based on a Phase-Matching Effect

Deshui Yu, Jingbiao Chen

Published Jan 31, 2007• 33 citations
Publisher

Abstract

We propose a new scheme for the optical frequency standard based on the phase-matching effect of the nonadiabatic interaction of two quasimonochromatic fields with the states 1S0, 1P1, and 3P0 of atoms 88Sr, which are trapped in an optical lattice with magic wavelength. After establishing the phase correlation between two laser fields by the nonadiabatic process, the final linewidth for the difference frequency field, which can be generated by a nonlinear optical crystal, is about 1 mHz.

DOI
10.1103/physrevlett.98.050801

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We propose a new scheme for the optical frequency standard based on the phase-matching effect of the nonadiabatic interaction of two quasimonochromatic fields with the states 1S0, 1P1, and 3P0 of atoms 88Sr, which are trapped in an optical lattice with magic wavelength. After establishing the phase correlation between two laser fields by the nonadiabatic process, the final linewidth for the difference frequency field, which can be generated by a nonlinear optical crystal, is about 1 mHz.
An optical atomic clock scheme is proposed that utilizes two lasers to establish coherent coupling between the 5s2 1S0 ground state of 88Sr and the first excited state, 5s5p 3P0. The coupling is mediated by the broad 5s5p 1P1 state, exploiting the phenomenon of electromagnetically induced transparency. The effective linewidth of the clock transition can be chosen at will by adjusting the laser intensity. By trapping the 88Sr atoms in an optical lattice, long interaction times with the two lasers are ensured; Doppler and recoil effects are eliminated. Based on a careful analysis of systematic errors, a clock accuracy of better than 2 x 10(-17) is expected.
The authors report the observation of the hyperpolarizability frequency shift due to the trapping field in a87Sr optical lattice clock. The authors show that at the magic wavelength of the lattice, where the first order term cancels, this higher order shift will not constitute a limitation to the fractional accuracy of the clock down to the 10-18level. This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm2and by a specific study of the effect of the two two-photon transitions near the magic wavelength. The authors also report an accurate frequency measurement of the clock transition. The frequency is determined to be v1S0-3P0= 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall
A sharp resonance line that appears in three-photon transitions between the 1S0 and 3P0 states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in 10(18).
An ideal superradiant laser on an optical clock transition of noninteracting cold atoms is predicted to exhibit an extreme frequency stability and accuracy far below mHz-linewidth. In any concrete setup sufficiently many atoms have to be confined and pumped within a finite cavity mode volume. Using a magic wavelength lattice minimizes light shifts and allows for almost uniform coupling to the cavity mode. Nevertheless, the atoms are subject to dipole-dipole interaction and collective spontaneous decay which compromises the ultimate frequency stability. In the high density limit the Dicke superradiant linewidth enhancement will broaden the laser line and nearest neighbor couplings will induce shifts and fluctuations of the laser frequency. We estimate the magnitude and scaling of these effects by direct numerical simulations of few atom systems for different geometries and densities. For Strontium in a regularly filled magic wavelength configuration atomic interactions induce small laser frequency shifts only and collective spontaneous emission weakly broadens the laser. These interactions generally enhance the laser sensitivity to cavity length fluctuations but for optimally chosen operating conditions can lead to an improved synchronization of the atomic dipoles.
With the aid of an optical frequency divider based on an optical frequency comb, the frequency of a laser at 431 nm is divided from a cavity-stabilized laser at 578 nm. Using the frequency-stabilized 431 nm laser, we observe a 2.5 kHz linewidth 4f146s2 1S0−4f135d6s2 (J = 2) transition of 171Yb atoms trapped in an optical lattice. By measuring the lattice-induced frequency shift, we determine the magic wavelength of the optical lattice for the 431 nm transition to be 797.97(20) nm. The frequency of the 431 nm transition is measured to be 695 171 054 856.9(1.1) kHz by referencing to the 1S0−3P0 transition at 578 nm of Yb atoms.
With ultracold 87Srconfined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to date of the 1S0-3P0 optical clock transition with a detailed analysis of systematic shifts (19 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 869 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its hertz-level linewidth characterized by an octave-spanning femtosecond frequency comb.