Ultracold alkali atoms provide experimentally accessible model systems for
probing quantum states that manifest themselves at the macroscopic scale.
Recent experimental realizations of superfluidity in dilute gases of ultracold
fermionic (half-integer spin) atoms offer exciting opportunities to directly
test theoretical models of related many-body fermion systems that are
inaccessible to experimental manipulation, such as neutron stars and
quark-gluon plasmas. However, the microscopic interactions between fermions are
potentially quite complex, and experiments in ultracold gases to date cannot
clearly distinguish between the qualitatively different microscopic models that
have been proposed. Here, we theoretically demonstrate that optical
measurements of electron spin noise -- the intrinsic, random fluctuations of
spin -- can probe the entangled quantum states of ultracold fermionic atomic
gases and unambiguously reveal the detailed nature of the interatomic
interactions. We show that different models predict different sets of
resonances in the noise spectrum, and once the correct effective interatomic
interaction model is identified, the line-shapes of the spin noise can be used
to constrain this model. Further, experimental measurements of spin noise in
classical (Boltzmann) alkali vapors are used to estimate the expected signal
magnitudes for spin noise measurements in ultracold atom systems and to show
that these measurements are feasible
