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While two levels systems (TLSs) are ubiqitous in solid state systems,microscopic understanding of their nature remains an outstanding problem.Conflicting phenomenological models are used to describe TLSs in seeminglysimilar materials when probed with different experimental techniques.Specifically, bulk measurements in amorphous solids have been interpreted usingthe model of a tunneling atom or group of atoms, whereas TLSs observed in theinsulating barriers of Josephson junction qubits have been understood in termsof tunneling of individual electrons. Motivated by recent experiments studyingTLSs in Josephson junctions, especially the effects of elastic strain on TLSproperties, we analyze interaction of the electronic TLS with phonons. Wedemonstrate that strong polaronic effects lead to dramatic changes in TLSproperties. Our model gives a quantitative understanding of the TLS relaxationand dephasing as probed in Josephson junction qubits, while providing analternative interpretation of bulk experiments. We demonstrate that a model ofpolaron dressed electronic TLS leads to estimates for the density anddistribution of parameters of TLSs consistent with bulk experiments inamorphous solids. This model explains such surprising observations of recentexperiments as the existence of minima in the energy of some TLSs as a functionof strain and makes concrete predictions for the character of TLS dephasingnear such minima. We argue that better understanding of the microscopic natureof TLSs can be used to improve properties of quantum devices, from anenhancement of relaxation time of TLSs, to creating new types of stronglyinteracting optomechanical systems.

Polaronic model of Two Level Systems in amorphous solids