Stability enhancement by joint phase measurements in a single cold atomic fountain

We propose a method of joint interrogation in a single atom interferometer which overcomes the dead time between consecutive measurements in standard cold atomic fountains. The joint operation enables for a faster averaging of the Dick effect associated with the local oscillator noise in clocks and with vibration noise in cold atom inertial sensors. Such an operation allows one to achieve the lowest stability limit due to atom shot noise. We demonstrate a multiple joint operation in which up to five clouds of atoms are interrogated simultaneously in a single setup. The essential feature of multiple joint operation, demonstrated here for a microwave Ramsey interrogation, can be generalized to go beyond the current stability limit associated with dead times in present-day cold atom interferometer inertial sensors.

Figure 1

(a) Schematic of the instrument. (b) Principle of the joint mode operation: (i) Preparation of cloud $N$, (ii) Raman light pulse shared by clouds $N-1$ (falling) and $N$ (rising), and (iii) detection of cloud $N-1$.

Figure 2

Allan deviations (ADEV) of the fountain relative frequency stability in normal and joint modes, for an interrogation time $T=480\text{ms}$. Stability without adding noise for the normal (black circle) and joint (blue rhombus) operations. Allan deviation for the normal mode (red triangle) and the joint mode (green square) when adding white noise over a bandwidth of $400\text{Hz}$. The $1/\tau$ (dashed) and ${\tau }^{-1/2}$ (dotted) lines are guide to the eyes. We observe a 14-fold gain in frequency stability from the normal to joint mode at $60\text{s}$. Integrating to this frequency stability level in a normal operation would require $12000\text{s}$.

Figure 3

Comparison of the normal mode (red triangles) and joint mode (green squares) for several cutoff frequencies $f_{\text{cut}}$ of added white noise to the Raman laser phase-lock loop: (a) $400\text{Hz}$, (b) $3.85\text{kHz}$, and (c) $61\text{kHz}$. The Raman pulse Rabi frequency is $f_R=11.4\text{kHz}$. Dashed blue lines: Theoretical calculation based on Eq. (1) without a free parameter.

Figure 4

(a) Schematic of the double joint operation where $T/T_c=2$, where three atom clouds simultaneously interact with the Raman laser pulses. (b) Short-term sensitivity at 1 s for each of the operation modes and $T=801\text{ms}$, from the normal operation $\left(T_c=1.6\text{s}\right)$ to the quadrupole joint mode $\left(T/T_c=4\right)$. The dashed line is a guide to the eye showing the $1/\sqrt{f_c}$ scaling.

Figure 5

Interference fringes for two different Ramsey interrogation times: (a) $T=480\text{ms}$ for the normal (black dots) and joint (red triangles) modes; (b) $T=801\text{ms}$ for the normal (black dots), joint (red triangles), and multiple joint operations (double joint: blue triangles; triple joint: green squares; quadrupole joint: violet stars).

Figure 6

Power spectral density of the white added noise for the three different values of $f_{\text{cut}}$. Black (top) $f_{\text{cut}}=400$ Hz; red (middle) $f_{\text{cut}}=3.85$ kHz; blue (bottom) $f_{\text{cut}}=61$ kHz.