J an 2 00 6 Spin noise spectroscopy to probe quantum states ofultracold ferm ionic atom ic gases

Ultracold alkaliatom s [1,2,3,4]provide experim entally accessible m odelsystem s for probing quantum states that m anifest them selves at the m acroscopic scale. Recent experim entalrealizations ofsuper uidity in dilute gases ofultracold ferm ionic (half-integer spin) atom s [5,6,7]o er exciting opportunities to directly test theoretical m odels of related m any-body ferm ion system s thatare inaccessible to experim entalm anipulation,such asneutron stars[8]and quark-gluon plasm as[9].However,them icroscopic interactionsbetween ferm ionsarepotentially quitecom plex,and experim entsin ultracold gasesto datecannotclearly distinguish between thequalitatively di erent m icroscopic m odels that have been proposed [10,11,12,13]. Here,we theoretically dem onstrate thatopticalm easurem entsofelectron spin noise[14,15]{ theintrinsic,random uctuationsofspin { can probe the entangled quantum statesofultracold ferm ionic atom ic gases and unam biguously revealthe detailed nature ofthe interatom ic interactions. W e show that di erent m odels predict di erentsetsofresonancesin the noise spectrum ,and once the correct e ective interatom ic interaction m odelis identi ed,the line-shapes ofthe spin noise can be used to constrain this m odel. Further,experim entalm easurem ents ofspin noise in classical(Boltzm ann) alkalivapors are used to estim ate the expected signalm agnitudesforspin noise m easurem entsin ultracold atom system s and to show thatthese m easurem entsare feasible.