A Fermi-degenerate three-dimensional optical lattice clock

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Science  06 Oct 2017:
Vol. 358, Issue 6359, pp. 90-94
DOI: 10.1126/science.aam5538
  • Fig. 1 3D optical lattice configuration and motional state characterization.

    (A) Schematic showing the propagation direction (large arrows) and polarization (double arrows) of the 3D lattice and clock laser beams. The quantization axis is defined by the magnetic field B. The narrow-line clock laser used for precision spectroscopy is phase-stabilized to lattice Embedded Image. The oblique clock laser is used to drive motional sidebands along all three lattice axes. (B) Motional sideband spectroscopy using the oblique clock laser shows no observable red sidebands (SBs), illustrating that atoms are predominantly in the ground band of the lattice. (C) Determination of the magic frequencies for the horizontal Embedded Image and vertical Embedded Image lattices, with mF = ±9/2. The measured frequency shift (filled circles with 1σ error bars) is scaled by the difference in trap depths between the high and low lattice intensities (22). Linear fits to the data are shown by opaque lines, with 1σ statistical uncertainties shown as shaded regions. The difference in the slopes is caused by trapping potential inhomogeneities that do not affect the determination of the magic frequencies (1σ uncertainties indicated by the vertical shaded regions).

  • Fig. 2 Resolved atomic contact interactions.

    (A) Clock spectroscopy data for a two-spin Fermi gas in the mF = ±9/2 stretched states for a 500-mG magnetic field, where a small fraction of the lattice sites contain both spin states. All transitions are saturated. The Embedded Image transition is absent owing to its vanishing dipole matrix element at small magnetic fields. Inset, level diagram at zero magnetic field. (B) Calculated detunings for transitions on singly and doubly occupied sites (22). The solid lines correspond to transitions on singly occupied (orange) and doubly occupied (red and blue) sites with mF = ±9/2. Transitions on doubly occupied sites for arbitrary mF and clock laser polarization lie within the shaded regions. At our operating magnetic field of 500 mG, all resonances for doubly occupied sites are well resolved from the clock transitions.

  • Fig. 3 Narrow-line clock spectroscopy.

    Ramsey spectroscopy data (black filled circles) taken with 1 × 104 atoms at 15 nK for free evolution times of (A) 100 ms, (B) 1 s, (C) 4 s, and (D) 6 s, using 10-ms π/2 pulse times. Red lines show sinusoidal fits. With contact interactions and ac Stark shifts controlled in a 3D lattice, we can measure fringes at an unprecedented 6-s free evolution time with a density of more than 1013 atoms/cm3.

  • Fig. 4 Synchronous clock comparison.

    (A) The Allan deviation of the differential frequency shift between two independent regions of the 3D lattice, each having 3000 atoms (blue filled circles). The blue solid line shows an instability of Embedded Image. The frequency difference is determined through a Bayesian estimation algorithm that determines the eccentricity of the ellipse of the parametric plot of P1 versus P2 (inset, 420 runs). When the number of atoms is reduced to 1000 in each region, the instability increases by Embedded Image (red filled circles and red dashed line). The error bars represent 95% confidence intervals, assuming white frequency noise. (B) A histogram of the measured frequency differences for an averaging time of 2.2 hours and 3000 atoms. The fitted Gaussian gives a fractional frequency difference of 129.6(3.5) × 10–19.

Supplementary Materials

  • A Fermi-degenerate three-dimensional optical lattice clock

    S. L. Campbell, R. B. Hutson, G. E. Marti, A. Goban, N. Darkwah Oppong, R. L. McNally, L. Sonderhouse, J. M. Robinson, W. Zhang, B. J. Bloom, J. Ye

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    • Materials and Methods
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    • Tables S1 and S2
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