Exploring Gravity With Optical Clocks

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Lattice optical clocks

Lattice optical clocks

The fundamental feature of neutral atom optical clocks is that a comparatively large number (~104) of QFRs are used simultaneously, resulting in a high signal-to-noise ratio. This leads, in turn, to a short-term stability which is potentially much higher (by a factor 102) than that obtainable with optical atomic clocks based on a single ion. Lattice optical clocks with neutral atoms confine the atoms (for a short time) in a so-called "magic-wavelength optical lattice" [Katori 2003], where the wavelength is chosen such that the energy shifts of the lower and upper states of the clock transition are exactly equal and thus the trapping potential exerts no shift on the clock transition. The wavelength values are 813 nm for Strontium (Sr) atoms and 759 nm for Ytterbium (Yb) atoms. The clock transition is a singlet-to-triplet transition (1S0 → 3P0) that is nearly forbidden and therefore exhibits an extremely narrow (theoretical) linewidth << 1 Hz. In practice, due to a finite interrogation time, it is of the order of a 1 - 10 Hz.

The Figure below shows a: schematic of a lattice clock apparatus with its main elements.

An atomic beam is produced by an oven and travels towards the right through a space-varying magnetic field (Zeeman slower). In it, the atoms are slowed down by a laser beam (blue arrow) that eventually stops the atoms inside the experimental chamber (square). The red double arrows indicate the laser beams used for 2nd stage cooling and atom trapping in the magneto-optical trap (MOT). Shwon in orange-red is the lattice laser standing wave, in yellow, the clock laser wave. Inset at bottom: the potential energy felt by the atoms due to the lattice laser. Since the lattice wavelength is longer than the atomic transition wavelength, the potential minima correspond to the high-intensity regions of the standing wave. The atoms are so cold that they are trapped in the potential minima.

The preparation of a sample of ultracold neutral atoms follows the same basic principle for all species currently considered as optical clock candidates (Figs. 2, 3). Efficient precooling to temperatures in the mK range is done on a spectrally broad 1S0 → 1P1 (some tens of MHz) cycling transition (refer to Fig. 4 for the atomic level scheme), followed by a "second stage" (postcooling stage), typically on the 1S03P1 intercombination transition, which brings the temperature down into the μK range. The atoms are then transferred into an optical lattice, formed by at least two counterpropagating laser beams of (same) suitable "magic" wavelength. Theoretical investigations have shown that it should be possible to control higher order perturbations caused by these lattice laser waves at levels allowing an inaccuracy below one part in 1017 [Porsev 2008].

Figure 3 Basic steps of operation of a lattice optical clock (after C. Oates, NIST, U. Sterr, PTB).
Top row:(a) precooling and trapping: atoms produced by an oven are slowed down, then cooled and simultaneously trapped in a magneto-optical trap produced by two coils and six counter-propagating 1st stage cooling laser beams (blue).
(b) postcooling and trapping: Once the atoms are cold enough, the 2nd stage cooling laser beams nearly resonant with the 1S03P1 transition are turned on, forming a 2nd stage MOT. The atoms are cooled further, because the transition to the 3P1 level is spectrally narrow. The counterpropagating optical lattice laser beams (red) are also turned on.
(c) intercombination transition interrogation: when the atoms are again cooled sufficiently, the 2nd stage cooling beams are turned off, leaving a fraction of the atoms trapped in the optical lattice. The clock laser beam is turned on for a short time (not shown), exciting a fraction of the atoms from the 1S0 to the 3P0 state. Subsequently, a pulse of 1st stage cooling light (blue) is applied. The ensuing fluorescence of the decay from the 1P0 state is measured; its strength is an indication of the number of atoms that was not excited by the clock laser, and represents the spectroscopic (clock absorption) signal also shown in Fig. 1. After interrogation, the atoms are lost and the cycle is repeated, with the clock laser frequency changed by a small amount. In this way, the resonance line is obtained, that also gives an error signal for correction of the laser frequency.

Bottom inset: geometry of the lattice laser beams (red), produced by retroreflection, and the superposed probe beam (yellow). A magnetic field is applied to compensate the earth field or, in case of a bosonic atomic species, to make the clock transition an allowed one.

Two types of atoms can serve as a QFR. Fermionic isotopes, in which the 1S03P0 transition possesses a finite linewidth of typically a few mHz due to hyperfine mixing in the excited state are one choice. However, it is also possible to use the bosonic isotopes where the strongly forbidden transition becomes weakly allowed by admixing some 3P1 or 1P1 character to the 3P0 state, by applying a magnetic field to the atomic sample. The availability of both bosons and fermions opens interesting possibilities and in-depth studies of the respective advantages and disadvantages of the various species, such as density-induced frequency shifts or line broadening, and will be pursued in this project.

Figure 4 shows the relevant energy diagrams of the two atomic species used in the SOC2 project.

Figure 4 Level schemes for Sr (top) and Yb (bottom) showing some of the relevant transitions. Color (grey) double arrows: transitions excited by lasers. Black single arrows: spontaneous emission loss channels. G denotes the spontaneous emission rates. The magic wavelengths for the optical lattice are not shown in this diagram.

References

[Katori 2003] H. Katori, M. Takamoto, V. G. Pal'chikov, V. D. Ovsiannikov,
"Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap",
Phys. Rev. Lett. 91, 173005 (2003); doi: 10.1103/PhysRevLett.91.173005

[Porsev 2008] S. G. Porsev, A. D. Ludlow, M. M. Boyd and J. Ye,
"Determination of Sr properties for a high-accuracy optical clock",
Phys. Rev. A 78, 032508 (2008); doi: 10.1103/PhysRevA.78.032508