We present a detailed analysis of the usefulness of ultracold atomic collisions for sensing the strength of an external magnetic field as well as its spatial gradient. The core idea of the sensor, which we recently proposed in Jachymski et al. [Phys. Rev. Lett. 120, 013401 (2018)], is to probe the transmission of the atoms through a set of quasi-one-dimensional waveguides that contain an impurity. Magnetic-field-dependent interactions between the incoming atoms and the impurity naturally lead to narrow resonances that can act as sensitive field probes since they strongly affect the transmission. We illustrate our findings with concrete examples of experimental relevance, demonstrating that for large atom fluences N a sensitivity of the order of 1 nT/N for the field strength and 100 nT/(mm N) for the gradient can be reached with our scheme.
We present a detailed analysis of the usefulness of ultracold atomic collisions for sensing the strength of an external magnetic field as well as its spatial gradient. The core idea of the sensor, which we recently proposed in K. Jachymski \emph{et al.}, Phys. Rev. Lett. {\bf 120}, 013401 (2018), is to probe the transmission of the atoms through a set of quasi-one-dimensional waveguides that contain an impurity. Magnetic field-dependent interactions between the incoming atoms and the impurity naturally lead to narrow resonances that can act as sensitive field probes since they strongly affect the transmission. We illustrate our findings with concrete examples of experimental relevance, demonstrating that a sensitivity of the order of 1 nT for the field strength and 100nT/mm for the gradient can be reached using our scheme.