Continuous cloud position spectroscopy using a magneto-optical trap

Abstract

We demonstrate a continuous spectroscopy technique with frequency sensitivity well below the natural transition linewidth, while maintaining a locking range hundreds of times larger. The method exploits the position dependence of a continuous, broadband magneto-optical trap operating on the 7.5 kHz-wide intercombination line of strontium. We show that the frequency sensitivity is fundamentally insensitive to the effective MOT laser linewidth. By applying active feedback on the MOT position to a dispersion-optimized frequency comb, which serves as the reference for stabilizing the MOT laser [1], we achieve a frequency instability below $4.4\times10^{-13}$ after 400 s of averaging in both the optical and radio-frequency domains, surpassing the performance of conventional hot-vapor modulation transfer spectroscopy. Our method is a broadly applicable alternative route to frequency references in the high $10^{-14}$ range around 100 s.

Figures (8)

• Figure 1: Experimental schematic: (a) Atoms (green disks) are continuously loaded from an upper 2D blue MOT ((b), operating on the $\rm ^1S_0 \rightarrow ^1P_1$ transition at 461 nm) into a five-beam broadband $\mathrm{^{88}Sr}$ red MOT ((b), operating on the narrow $\rm ^1S_0 \rightarrow ^3P_1$ transition at 689 nm). The red MOT is monitored non-destructively via fluorescence imaging, and the center position along the vertical (gravity) axis is extracted every 50 ms. The red MOT laser is locked to an optical frequency comb, which provides short-term frequency stability, while long-term stability is achieved via the MOT position where the vertical displacement $\delta z$ serves as an error signal. Feedback is applied through a tunable RF oscillator used to synchronize the comb, which in turn transfers its stability to both the RF and optical domains.
• Figure 2: Frequency sensitivity of the broadband (BB) and single-frequency (SF) MOTs, demonstrating MOT laser linewidth independence. Despite differing forces, both MOTs exhibit similar sensitivities within error bars. Triangles: vertical magnetic field gradient $0.47\,\mathrm{G/cm}$, sensitivities $98.19(30)\,\mathrm{Hz/\mu m}$ (BB, blue) and $98.76(50)\,\mathrm{Hz/\mu m}$ (SF, red). Crosses: $0.37\,\mathrm{G/cm}$, with $77.91(30)\,\mathrm{Hz/\mu m}$ (light blue, BB) and $77.21(40)\,\mathrm{Hz/\mu m}$ (light red, SF). Stars: $0.27\,\mathrm{G/cm}$, with $57.37(24)\,\mathrm{Hz/\mu m}$ (light orange, BB) and $57.25(40)\,\mathrm{Hz/\mu m}$ (turquoise, SF). An offset magnetic field shifts the intersection point of the six curves to $\delta_{\text{start}}=1.05\,\mathrm{kHz}$. Bottom inset: MOT AOM RF spectra showing BB modulation (blue) and SF (red) tone.
• Figure 3: Measurement of the MOT response time following a step change in the red MOT laser frequency. The MOT position relaxes to a new equilibrium according to an overdamped harmonic oscillator model. (Red disks): $10~\text{kHz}$ jump; (light red triangles): $50~\text{kHz}$; (orange crosses): $150~\text{kHz}$; (light orange stars): $300~\text{kHz}$. Inset: Extracted response time $\tau$ as a function of frequency jump, fit with a square-root dependence resulting in an amplitude $A = 0.529(40)~\text{s/kHz}^{1/2}$ and a offset $\tau_{\text{offset}} = 18.49(57)~\text{ms}$. This relationship sets an upper bound on the MOT response time for a given frequency change.
• Figure 4: Overlapping ADEV of the free-running tunable RF oscillator (orange diamonds) and the same oscillator stabilized to the MOT position (red stars). Beat signal between the MOT-referenced and hot-vapor-locked lasers (red crosses). Between $100$–$1000~\text{s}$, the MOT position locked RF oscillator can outperform the optical reference based on the hot vapor modulation transfer spectroscopy, reaching a minimum instability of $4.4 \times 10^{-13}$ at $\sim400~\text{s}$, limited mainly by magnetic field fluctuations. All RF signals are compared to a stable 10 MHz RF reference from the Dutch Metrology Institute (VSL). The in-loop error signal (blue points) is fit by $\sigma(\tau) = (6.71 \pm 0.48) \times 10^{-12} / \tau^{0.84 \pm 0.03}$ (blue dashed line). Error bars indicate $1\sigma$ confidence intervals using a chi-squared distribution.
• Figure 5: (a) Schematic of the tuneable $800~\mathrm{MHz}$ source. Two quartz-oscillators ($780~\mathrm{MHz}$, digitally tuneable $20~\mathrm{MHz}$) are mixed and bandpassed to generate the $800~\mathrm{MHz}$ output. The optional $10~\mathrm{MHz}$ reference was not connected for both oscillators. (b) Frequency shift steps at $800~\mathrm{MHz}$ recorded with a counter while tuning the RF-source manually.