In situ magnetic-field stabilization for quantum-gas experiments

Abstract

We demonstrate a minimally-destructive in situ technique for measuring and stabilizing slowly-drifting magnetic fields in ultracold-atom experiments. While conventional magnetic-field sensors such as Hall, giant magnetoresistive, or fluxgate-based devices are broadly used, their accuracy, precision and dynamic range can be limited. In addition, these sensors are typically positioned at least several centimeters away from the in-vacuum atomic system, as their operation creates perturbing magnetic fields, and their placement is limited by geometric constraints imposed by the vacuum system. We overcome these issues by using the atomic system itself as a built-in magnetometer. To that end, we employ a pair of weak measurements to determine the Zeeman splitting -- and thereby the magnetic field -- of a magnetically sensitive atomic transition. We provide closed-form expressions quantifying the trade-offs between measurement noise, dynamic range, and atom loss. This procedure is demonstrated with ultracold Rb-87, weakly measured using partial-transfer absorption imaging. We then incorporate a Kalman filter to stabilize the magnetic field; this eliminated long-term drift in the ambient field (as high as ~70 nT/hr) in exchange for a modest increase in shot-to-shot variability from 1.8(2) nT to 2.0(2) nT.

Figures (6)

• Figure 1: (a) Two pulse scheme for the measurement of detuning from resonance $\Delta$. Two fixed oscillators $\omega_1$ and $\omega_2$ centered around $\omega_0$ promote atoms from $\ket{g}$ to $\ket{e}$. (b) Typical differential in situ partial transfer absorption images from which the feedback signal is obtained at positive, zero, and negative $\Delta$. (c) Experimental magnetic field drift $\delta B$ with (gray) and without (brown) the feedback-locking scheme enabled for $B_0 = 80µT$.
• Figure 2: Two-pulse PTAI-magnetometry. (a) Atom number $N_{1,2}$ transferred by each pulse (red, blue) and their sum $N_T$ (black), (b) the error signal $\epsilon$ vs detuning $\Delta$. Here $\delta\omega=\Delta_d$ (dashed lines) and $f_{\rm max} \approx 0.02$. Each data point was averaged from 3 experimental measurements with $t=90µs$. The slope (black dashed line) is the dimensionless responsivity $R/t$. Solid lines are obtained from the two level model including finite $f_{\rm max}$. The shaded area indicates the uncertainty $\delta\epsilon$ given by Eq. \ref{['eq:sigma_epsilon']} for $\delta N/N_0 \approx 0.01$.
• Figure 3: Responsivity $R$ as a function of pulse duration $t$ with experimental data (markers) plotted along with our model prediction (curve) for $f_{\rm max} \to 0$. These data were taken with $\delta\omega = \Delta_d$, i.e., $t \delta\omega \approx 2.61$. Inset: $R$ is the linear component (dashed line) of a fifth order polynomial fit (solid curve visible under the data points) to measurements of $\epsilon$ taken as a function of $\Delta$. The reported uncertainties from the fit are used to generate the error bars in the main panel.
• Figure 4: Impact of pulse spacing $t \delta \omega$ in the small transfer limit for various $t \delta \omega$. (a) Total number transferred $N_T$ as a fraction of the zero detuning transfer $N_0$. (b) Error signal $\epsilon$. (c) The inverse of the error signal's uncertainty $\delta\epsilon$ as a fraction of its zero-detuning value $\delta\epsilon(0)$. The vertical dashed lines indicate the pulse frequency spacing $\pm \delta\omega/(2\pi)$.
• Figure 5: Lock performance. (a) Detuning $\Delta$ measured with the lock active. Top: $\Delta_L$ from PTAI magnetometry [also shown in Fig. \ref{['fig:intro']}(c)]; bottom: $\Delta_R$ from TOF Ramsey interferometry. Markers are experimental data and the solid curve is low-pass filtered. (b) Auto-correlation and cross-correlation functions of the data presented in (a).