Atomic sensing is, at large, based on measuring energy differences. Specifically, magnetometry is typically performed by using a superposition of two quantum states, the energy difference of which depends linearly on the magnetic field due to the Zeeman effect. The magnetic field is then evaluated from repeated measurements of the accumulated dynamic phase between the two Zeeman states. Here we show that atomic clock states, with an energy separation that is independent of the magnetic field, can nevertheless acquire a phase that is magnetic field dependent. We experimentally demonstrate this on an ensemble of optically trapped ^{87}Rb atoms. Finally, we use this effect to propose a magnetic field sensing method for static and time-dependent magnetic fields and analyze its sensitivity, showing it essentially allows for high-sensitivity magnetometery.
According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian
He which depends on the polarization and spectral profile of the incident light. In order to check the structure of
He, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to
He. We have been able to obtain experimentally in the ground state of
199Hg,
201Hg, and
87Rb, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of
He can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.
A theory of the optical Zeeman effect is developed in terms of the angular polarisability, **i, a fundamental property of both atoms and molecules. It is shown that **i is negative to motion reversal T and parity inversion P, and forms an interaction hamiltonian with the T negative, P positive conjugate product pi(i) of a circularly polarised pump laser. This activates the T negative **i, which is the axial vector equivalent of the imaginary part of the atomic or molecular electronic polarisability, an antisymmetric polar tensor. The quantity pi(i) is proportional to the square of the electric field strength of the laser, and disappears if the latter is not circularly polarised. This distinguishes the optical Zeeman effect from the experimentally measured optical Autler Townes effect, which is mediated by the symmetric, T positive, real part of the dynamic electronic polarisability. The optical Zeeman effect is accompanied by circular birefringence and the bulk magnetisation of the inverse Faraday effect.