Atom Interferometry with the Sr Optical Clock Transition

We report on the realization of a matter-wave interferometer based on single-photon interaction on the ultranarrow optical clock transition of strontium atoms. We experimentally demonstrate its operation as a gravimeter and as a gravity gradiometer. No reduction of interferometric contrast was observed for a total interferometer time up to $\sim 10\mathrm{ms}$, limited by geometric constraints of the apparatus. Single-photon interferometers represent a new class of high-precision sensors that could be used for the detection of gravitational waves in so far unexplored frequency ranges and to enlighten the boundary between quantum mechanics and general relativity.

Figure 1

(a) Simplified scheme of the apparatus in the double-cloud gradiometer configuration. Two cold ${}^{88}\mathrm{Sr}$ clouds are launched vertically upwards using an accelerated optical lattice at 532 nm (green arrows). The velocity selection and the $\pi /2\text{−}\pi \text{−}\pi /2$ interferometric sequence are realized using laser pulses resonant with the clock transition (vertical red arrows). Two laser fields with frequencies ${\omega }_1$ and ${\omega }_2$ and linear parallel polarizations are used to simultaneously interrogate the two clouds. The clock transition is induced by a static magnetic field $\mathbf{B}$ parallel to the polarization of the laser fields. At the end of the interferometer sequence, a vertical push beam at 689 nm from the bottom side (not shown) is used to decelerate atoms in the ground state for spatially separating them from atoms in the excited state. After repumping the excited atoms back into the ground state, the relative population in the two output ports of each AI is detected by collecting onto a photomultiplier tube the fluorescence light produced by a resonant sheet of blue light at 461 nm. (b) Space-time trajectories of the atoms in the single-photon gradiometer. $L$, launch; VS, velocity selection. (c) Typical fluorescence signals at the output of the two AIs.

Figure 2

(a) Clock spectroscopy signal on the free-falling, momentum selected cloud. The signal linewidth, by eliminating the effect of the finite spectroscopy pulse length (1.2 ms) and estimated from a Gaussian fit of the profile, indicates an atomic momentum spread of $0.04\hslash {\omega }_a/c$. (b) Rabi oscillations of the atomic excitation fraction as a function of the clock pulse length. The oscillation is recorded with typical values of the static magnetic field ($\mathit{B}=330\mathrm{G}$) and clock light peak intensity ($20\mathrm{W}/{\mathrm{cm}}^2$). The experimental result fits well with a damped sinusoid with a corresponding Rabi frequency of $\mathrm{\Omega }=2\pi \times 753(30)\mathrm{Hz}$ and a damping time of 1.18(0.15) ms.

Figure 3

Results for the single AI (gravimeter). AI fringes in (a) and (b) were observed for $2T=2\mathrm{ms}$, with and without the active fiber noise cancellation (FNC) system, respectively; AI fringes in (c) and (d) correspond to $2T=10\mathrm{ms}$, with and without FNC, respectively. (e) Measured contrast and fringe visibility as a function of $2T$. Fringe visibility (red open squares and circles) is given by the amplitude of the fitted sinusoidal function on each data set. Contrast (solid squares and circles) is estimated by data dispersion from the 2nd to the 98th percentile. Both contrast and visibility are measured with (squares) and without (circles) FNC. The inset shows the in-loop phase noise power spectral density of the 10 m–long optical fiber connecting the clock laser source to the AI, with (lower red curve) and without (upper black curve) FNC, respectively.

Figure 4

Allan deviation of the relative phase shift for the gradiometer for two different AI durations. The gradiometer configuration rejects the common-mode phase noise with an Allan deviation scaling down as the square root of the averaging time, as shown by the fit to the data (dashed lines). The inset shows the output signal of the upper AI versus the signal of the lower AI for $2T=10\mathrm{ms}$. The ellipse fitting (red dashed line) gives a relative phase $\mathrm{\Delta }\varphi =2.31(0.06)\mathrm{rad}$ that is consistent with the value of the applied synthetic phase $\delta \varphi =3\pi /4\mathrm{rad}$.