Recently, new experimental techniques in ultracold atoms made it possible to study the real-time response of Fermi systems on, compared to the Fermi time, ultrafast time scales , which are hard to access in other condensed matter systems. Combined with spectroscopic NMR methods this allows to probe in detail the quantum dynamics of the system. Specifically we study the time- and frequency resolved response of a Fermi gas at arbitrary temperature which interacts with an impurity supporting a non-trivial molecular state. As such the system allows to study the extend of universality in the orthogonality catastrophe on all time scales [2,3].
We calculate the dephasing dynamics of the system and find excellent agreement with experimental measurements. We also predict the interaction and temperature dependence of the decoherence rate of the Ramsey response for which we find exact semi-analytical expressions from a first principle calculation. Our functional determinant approach, which is borrowed from mesoscopic physics , allows to implement in detail complicated sequences of spin rotations and interaction quenches which allows to model accurately experimental protocols. Having this in mind, we finally comment on future directions such as how the techniques can be used to exert real-time control of the Fermi system similar to recent proposals in mesoscopic physics .
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