Cold-Atom Buoy: A Differential Magnetic Sensing Technique in Cold Quadrupole Traps

Abstract

We present a technique for vectorial magnetic sensing using a cold-atom cloud trapped in a magnetic quadrupole. The center of the trapped cloud is determined by absorption imaging and compared for opposite polarities of the quadrupole. In the presence of an external magnetic field, the displacement of the cloud depends on both the field's direction and magnitude. By analyzing this shift under polarity reversal, we infer the two transverse components of a homogeneous external magnetic field relative to the imaging axis, without requiring spectroscopic interrogation. Assuming micron-scale position sensitivity and typical magnetic field gradients, the method enables resolution at the milli-Gauss level. It is compatible with standard cold-atom setups and offers a practical tool for field compensation in magnetically sensitive experimental stages. As such, it establishes a bridge between traditional macroscopic magnetic field probes and atomic-physics-based precision sensors.

Figures (9)

• Figure 1: Schematic of the cold-atom buoy concept. In the quadrupole configuration, the magnetic field grows linearly in the three Cartesian directions with the distance from the center (with opposite sign and doubled gradient in the vertical direction). This makes that an external homogeneous field shifts the center of the quadrupole (the $\vb B=0$ point – denoted with orange) with the same distance, but opposite directions from the true geometrical center (denoted with red) under a switch of quadrupole polarity. For the definition of $Q$, cf. \ref{['eq:Qpole']}. The buoy analogy is based on the identification of the shifting cold-atom cloud with the buoy floating on the surface of the water (the plane transverse to the imaging axis), and the true (zero-external-field) magnetic center with the anchor point of the buoy. The external field is the current that displaces the buoy.
• Figure 2: Demonstration of the buoy effect. Positions of the magnetically trapped cloud for various settings of the applied bias currents $(I_y, I_z)$, displayed in color code on the $(y, z)$ image plane in the field of view of absorption imaging, measured in CCD pixels. For each $(I_y, I_z)$ pair and each quadrupole polarity, 50 absorption images were recorded. Small triangular markers indicate the center-of-mass position of the cloud extracted from a two-dimensional Gaussian fit of each individual absorption image. Upward- and downward-pointing triangles denote shots with opposite quadrupole polarities. The identically colored label $(I_y, I_z)$ at each cloud cluster indicates the applied current pair in ampere for that dataset. For each $(I_y, I_z)$ pair, the cluster centers corresponding to the two quadrupole polarities – denoted by identical, but larger triangles – are connected by a dashed line segment. The midpoint of this segment (shown as a large rhombus of the same color) is the inferred field-compensated magnetic trap center. The difference between the scale of the currents $I_y$ vs. $I_z$ stems from the different geometry of the corresponding coil pairs, cf. \ref{['sec:system']}.
• Figure 3: Zoomed-in displacement data around the compensation point. Same measurement as in \ref{['fig:results1']}, but recorded over a finer grid of $I_y$ and $I_z$ values centered around the compensation currents inferred from that figure. Here, 100 shots were taken for each current pair and quadrupole polarity. This finer sampling allows for a more precise localization of the true magnetic center corresponding to $\vb{B}_\text{ext} = 0$, and provides further validation of the buoy effect at higher resolution.
• Figure 4: Finding the correct compensation Displacement of the cluster centers under polarity reversal as a function of the applied currents $I_y$ and $I_z$, extracted from the large triangle positions in \ref{['fig:results1', 'fig:results2']}. The correct compensation current $I_y$ ($I_z$) is the zero-crossing – the $\Delta y=0$ ($\Delta z=0$) point – of the fitted linear function plotted as an orange line in each panel.
• Figure 5: The stopping of the buoy at the compensation currents determined in \ref{['fig:aggregate']}, $I_y^@=-0.27A$ and $I_z^@=0.035A$. The figure shows the absorption imaging field of view with cloud centers stemming from individual experimental shots with alternating quadrupole polarities indicated with small triangles of opposite orientation as in \ref{['fig:results1', 'fig:results2']}, with the large triangles and the rhombus having the same meaning as in those figures as well. Here, for the sake of visualizing the two largely overlapping ensembles, we used red and blue colors for plotting the opposite polarities.