Efficient Atomic Clocks Operated with Several Atomic Ensembles

Atomic clocks are typically operated by locking a local oscillator (LO) to a single atomic ensemble. In this Letter, we propose a scheme where the LO is locked to several atomic ensembles instead of one. This results in an exponential improvement compared to the conventional method and provides a stability of the clock scaling as $(\alpha N{)}^{-m/2}$ with $N$ being the number of atoms in each of the $m$ ensembles and $\alpha$ a constant depending on the protocol being used to lock the LO.

Figure 1

(a) Illustration of locking the LO using several ensembles. The feedback of the first ensemble stabilizes the LO such that the second ensemble can be operated with a longer Ramsey time. The feedback from the second ensemble then further stabilizes the LO. (b) Numerical simulation of the noise spectrum $S(f)$ of the LO when locked to between 1 and 3 ensembles. The data were simulated as described in the text for $N=20$ and $T_1=0.1/\gamma$ for the conventional Ramsey scheme. The first feedback lowers the noise of the LO and whitens the spectrum, even though the unlocked LO was assumed to be subject to $1/f$ noise. The second and third feedbacks further lower the noise of LO by a constant factor.

Figure 2

The stability of atomic clocks for a LO subject to (a) white noise and (b) $1/f$ noise. Circle, square, upward triangle, and downward triangle are the stability of a clock with the LO locked to 1, 2, 3, and 4 ensembles containing $N$ atoms each. The clocks were simulated with ${\beta }_1=0.1$ and $T_j=n{T}_{j-1}$. Counting from the left (low $N$), the points are for integers $n$ from 2 to 10. The dashed lines are the analytical calculations.

Figure 3

The stability of atomic clocks with adaptive measurements for a LO subject to (a) white noise and (b) $1/f$ noise. Circle, square, upward triangle, and downward triangle are the stability of a clock with the LO locked to 1, 2, 3, and 4 ensembles of $N$ atoms each. The adaptive protocol allows for (a) ${\beta }_1=0.3$ and (b) ${\beta }_1=0.2$. The clocks were simulated with $T_j=n{T}_{j-1}$, and counting from the left (low $N$), the points are for integers $n$ from 2 to 10. The dashed lines are fits of the simulated data.