Quantum noise in atomic magnetometers

Introduction An atomic magnetometer, as any quantum device, has an intrinsic limit on its sensitivity that is imposed by the Heisenberg uncertainty principle. In this chapter we will discuss such fundamental limits as well as the practical means of approaching and in some cases even overcoming these limits by means of quantum measurements. As a model system we consider an ensemble of N_a atoms each with spin F and ignore for the moment hyperfine interactions present in alkalimetal atoms. Most atomic magnetometers operate using spin orientation of the atomic ensemble, so we will consider atoms that are initially optically pumped into a fully spin-polarized state, say along the ◯ direction, 〈F_x〉 = F. In a vector spin-exchange-relaxation-free (SERF) magnetometer (Chapter 5) or a radiofrequency magnetometer (Chapter 4) one measures a small transverse component of the spin, 〈F_z〉, that develops due to the interaction with a weak magnetic field B_y. In a scalar atomic magnetometer the observable is the frequency of spin precession about a large B_y field. This frequency is best measured by finding the time between two zero crossings of an oscillating 〈F_z〉 component while the spin polarization points in the ◯ direction. Thus, in all cases one measures the component of the spin perpendicular to the direction of the large spin polarization, and the quantum sensitivity limits are nearly the same for vector, RF, and scalar atomic magnetometers.