A super-radiant interferometer of spin-1 atoms with Heisenberg scaling in sensitivity

Precision measurement in metrology has gained enormous attention in the last decade, both in optomechanics and atomic systems, where improvement in measurement sensitivity has acquired a pivotal role in research. Here we report that by storing an optical field in a laser-cooled  ⁸⁷Rb atomic cloud prepared in a spin-1 manifold, one can achieve a massive gain in retrieve signal by increasing coupling field strength due to collective spin excitation. This observation leads to a novel super-radiant interferometer where optical field first store in an atomic medium as dark state polaritons, evolve for a finite storage time, acquire an atomic phase difference, and finally interfere and convert back into optical signal. As a result, both the atomic and optical phases can be measured with high precision. The collective enhancement of sensitivity increases nonlinearly with number of atoms beyond the standard quantum limit. Moreover, one can further increase sensitivity by increasing the storage time, and the simplicity of the experimental setup can lead to a compact device that can be used as high precision magnetic field sensors with non-classical scaling in sensitivity.