Collisional Losses, Decoherence, and Frequency Shifts in Optical Lattice Clocks with Bosons

We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock on the highly forbidden transition ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ at 698 nm with bosonic ${}^{88}\mathrm{Sr}$. We were able to distinguish two loss channels: inelastic collisions between atoms in the upper and lower clock state and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with ${}^{88}\mathrm{Sr}$ shows no degradation due to collisions on the fractional uncertainty level of ${10}^{-16}$.

Figure 1

Inelastic losses by collisions between ${}^{3}P_0$ atoms (open circles), a mixture of ${}^{3}P_0$ and ${}^{1}S_0$ atoms (full symbols), and the results of fits (lines). The inset shows schematically the involved atomic levels. The initial number of ground state atoms is about $1.2\times {10}^6$.

Figure 2

Rabi oscillations (top row) and spectra of the clock transition (two lower rows) for different atom numbers $N$. Lines: Density matrix with dephasing constant ${\gamma }_{\mathrm{dep}}$ (red full lines) and with ${\gamma }_{\mathrm{dep}}\equiv 0$ (blue dashed lines). The frequency axes have arbitrary offsets.

Figure 3

Observed density dependent shift of the ${}^{88}\mathrm{Sr}$ clock transition. We assume linear scaling of density with atom number. The open symbols were excluded from the linear fit (full line, see text). The inset shows the dependence of the shift on the excitation probability with a linear fit. The triangle in the main graph represents the data in the inset. The shift was rescaled according to the trap parameters and atom temperature.