Abstract
Recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. We discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid state systems. We consider a system of impurity atoms localized by a strong optical lattice potential and immersed in a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity atoms probe OC in the time domain, while radio-frequency (RF) spectroscopy probes OC in the frequency domain. The OC in such systems is universal for all times and is determined by the impurity scattering length and Fermi wave vector of itinerant fermions. We calculate the universal Ramsey response and RF absorption spectra. In addition to the standard power-law contribution, which corresponds to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel contribution to OC that comes from exciting one extra particle from the bottom of the itinerant band. This gives rise to a non-analytic feature in the RF absorption spectra, which evolves into a true power-law singularity with universal exponent 1/4 at the unitarity. Furthermore, we discuss the manifestations of OC in spin-echo experiments, as well as in the energy counting statistic of the Fermi gas following a sudden quench of the impurity state. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying non-equilibrium impurity physics, allowing one to explore non-equilibrium OC and to simulate quantum transport through nano-structures. This provides a useful connection between cold atomic systems and mesoscopic quantum transport.
Highlights
Interest in nonequilibrium quantum dynamics has increased dramatically in the last few years following the experimental realizations of synthetic many-body systems with ensembles of ultracold atoms [1,2]
With ultracold atoms it is possible to prepare microscopic systems with desired many-body Hamiltonians but, crucially for studying dynamics, parameters of such Hamiltonians can be changed on time scales that are much faster than intrinsic microscopic time scales
A rich toolbox of atomic physics makes it possible to provide a detailed characterization of many-body systems, which is crucial for describing complicated transient states resulting from nonequilibrium dynamics
Summary
Interest in nonequilibrium quantum dynamics has increased dramatically in the last few years following the experimental realizations of synthetic many-body systems with ensembles of ultracold atoms [1,2]. The origin of this novel feature is the following: After the impurity is introduced, there is a class of processes in which, in addition to a large number of lowenergy particle-hole pairs, an extra hole with energy of approximately EF is excited near the bottom of the band. A generalization of the setup shown in Fig. 1 to the case of a multicomponent Fermi gas (with multiple internal states) allows one to realize a wide range of dynamical impurity phenomena in nonequilibrium Fermi gases This is an even richer class of problems that arises in mesoscopics [28]; in particular, problems of this kind describe the quantum transport through any mesoscopic structure (e.g., a point contact), where the Fermi seas in two or more leads are kept at different chemical potentials.
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