Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas

TL;DR

This paper explores how a qubit embedded in an ultra-cold Fermi gas experiences decoherence due to the orthogonality catastrophe, linking many-body physics phenomena with quantum information dynamics.

Contribution

It demonstrates the influence of the orthogonality catastrophe on qubit coherence and proposes methods to observe this effect via Ramsey interferometry.

Findings

Decoherence of the qubit is driven by the orthogonality catastrophe.

The Loschmidt echo relates to the retarded Green's function in this context.

Spectral broadening can be detected through Ramsey interferometry.

Abstract

We investigate the behaviour of a single qubit coupled to a low-dimensional, ultra-cold Fermi gas. The scattering between the system and the fermions leads to the loss of any coherence in the initial state of the qubit and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green's function - typically used to formulate the dynamical theory of the catastrophe - and demonstrate that the effect can be triggered and characterized via local operations on the qubit. We demonstrate how the expected broadening of the spectral function can be observed using Ramsey interferometry on the qubit.