Central spin decoherence is useful for detecting many-body physics inenvironments and moreover, the spin echo control can remove the effects ofstatic thermal fluctuations so that the quantum fluctuations are revealed. Thecentral spin decoherence approach, however, is feasible only in some specialconfigurations and often requires uniform coupling between the central spin andindividual spins in the baths, which are very challenging in experiments. Here,by making analogue between central spin decoherence and depolarization ofphotons, we propose a scheme of Faraday rotation echo spectroscopy (FRES) forstudying quantum fluctuations in interacting spin systems. The echo control ofthe photon polarization is realized by flipping the polarization with abirefringence crystal. The FRES, similar to spin echo in magnetic resonancespectroscopy, can suppress the effects of the static magnetic fluctuations andtherefore reveal dynamical magnetic fluctuations. We apply the scheme to arare-earth compound LiHoF4 and calculate the echo signal, which is related tothe quantum fluctuations of the system. We observe enhanced signals at thephase boundary. The FRES should be useful for studying quantum fluctuations ina broad range of spin systems, including cold atoms, quantum dots, solid-stateimpurities, and transparent magnetic materials.
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