Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction

TL;DR

This paper demonstrates that the out-of-time-ordered correlation function (OTOC) of a single impurity qubit can effectively detect quantum phase transitions in fully connected many-particle systems like bosonic Josephson junctions, providing a sensitive and minimally invasive diagnostic tool.

Contribution

It introduces a method to measure the OTOC of a single impurity qubit in bosonic systems, showing its effectiveness in identifying quantum phase transitions and extracting finite size scaling exponents.

Findings

OTOC detects ground and excited state QPTs more sensitively than standard correlations.

Small probes can diagnose QPTs in fully connected models.

OTOC measurement induces weak chaos and information scrambling.

Abstract

We calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to fully a connected many-particle system such as a bosonic Josephson junction or spins with long-range interactions. In these systems the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an $N$ body system can also be accurately extracted from the long-time OTOC dynamics, however, for short times there is a discrepancy due to the fact that the qubit has not had enough time to couple to the larger system. Our results show that the OTOC of even the smallest probe is enough to diagnose a QPT in fully connected models but, like a continuous measurement, can still cause a backaction effect which leads to weakly chaotic dynamics and gradual information scrambling.