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We explain how gapped quantum spin liquids, both conventional and'fractonic', may be unambiguously diagnosed experimentally using the techniqueof multidimensional coherent spectroscopy. 'Conventional' gapped quantum spinliquids (e.g. $Z_2$ spin liquid) do not have clear signatures in linearresponse, but do have clear fingerprints in non-linear response, accessiblethrough the already existing experimental technique of two dimensional coherentspectroscopy. Type I fracton phases (e.g. X-cube) are (surprisingly) eveneasier to distinguish, with strongly suggestive features even in linearresponse, and unambiguous signatures in non-linear response. Type II fractonsystems, like Haah's code, are most subtle, and may require consideration ofhigh order non-linear response for unambiguous diagnosis.

Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic