Multidimensional Spectroscopy of Time-Dependent Impurities in Ultracold Fermions

We investigate the system of a heavy impurity immersed in a degenerated Fermi gas, where the impurity's internal degree of freedom (pseudospin) is manipulated by a series of radiofrequency (RF) pulses at several different times. Applying the functional determinant approach, we carry out an essentially exact calculation of the Ramsey-interference-type responses to the RF pulses. These responses are universal functions of the multiple time intervals between the pulses for all time and can be regarded as multidimensional (MD) spectroscopy of the system in the time domain. A Fourier transformation of the time intervals gives the MD spectroscopy in the frequency domain, providing insightful information on the many-body correlation and relaxation via the cross-peaks, e.g., the off-diagonal peaks in a two-dimensional spectrum. These features are inaccessible for the conventional, one-dimensional absorption spectrum. Our scheme provides a new method to investigate many-body nonequilibrium physics beyond the linear response regime with the accessible tools in cold atoms.