In-Situ Differential-Light-Shift Cancellation for Trapped-Atom Clocks

Abstract

Differential light shifts (DLS) induced by optical trapping fields fundamentally limit the stability and accuracy of trapped-atom microwave clocks. We demonstrate an in-situ method to cancel DLS by simultaneously interrogating multiple spatially separated atomic ensembles at different trap intensities generated from a common light source. By operating the ensembles at set intensity ratios and performing Ramsey spectroscopy, the intensity-dependent frequency shifts are measured within each experimental cycle and extrapolated to the zero-intensity limit. This approach effectively enables shot-to-shot determination of a DLS-free frequency without requiring magic wavelengths or species-specific cancellation schemes. We validate the method for Rb atoms trapped in time-averaged potentials by introducing controlled variations of the total trap power and show that the extrapolated frequency remains insensitive to these fluctuations. The technique is general and can be extended to other systematic shifts, providing a scalable route toward improved stability and accuracy in compact trapped-atom clocks and related quantum sensors relying on optical dipole traps

Figures (4)

• Figure 1: (a) Sketch of the key elements of the necessary setup. Two laser beams are each modulated by a two-dimensional acoustic optical deflector (AOD) driven by a software-defined radio (SDR) and focused on cold $^{87}$Rb atoms forming a crossed optical dipole trap (cODT). A microwave antenna provides a source to interrogate the atoms. (b) Fluorescence imaging of the resulting vertically separated traps after a ballistic expansion of 0.1 ms. (c) Experimental sequence with typical time scales used to obtain multiple cold atomic ensembles and perform clock-like measurements.
• Figure 2: (b) Measurement of the detuning of trap-2 as a function of the detuning of trap-1. The green (red) ellipse indicates the $1(2)\,\sigma$ contour of a double Gaussian with a correlation angle. (a) + (d) Projection on the respective trap axis showing measurements per detuning as a histogram. (c) Fluctuations of the difference between the two detunings. (e)-(h) Total sequence of preparation and detection.
• Figure 3: (a) The fraction of atoms in the excited state as a function of frequency detuning. The red marked region depicts the zeroth fringe and the orange dashed line shows where the microwave frequency is set to for simultaneous measurements of all three traps. The overall intensity used here is 65 kW/cm$^2$ (b) Frequency detunings vs intensity ratio for three different set total intensities (59, 65 and 71 kW/cm$^2$).
• Figure 4: (a) Multiple individual runs with three traps at fixed intensity ratios (dashed black line) but varied overall intensity (colors). (b) Histogram for the extrapolated values at $f(I=0)$ for all three overall intensities. (c-e) Histogram for the measured detunings at the respective intensity for a given ratio of the overall intensity I$_\text{tot}$