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

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.

Intra- and interband excitations induced residue decay of the Bose polaron in a one-dimensional double-well

“…Here, the polaronic behavior should strongly depend on the involved interactions and an intriguing prospect would be to engineer specific entangled polaron states in certain interaction regimes with an additional knob provided by the interspecies mass-imbalance. Moreover, we should also emphasize that these hybridized systems are of further interest due to the fact that one subsystem (impurity) lies in the deep quantum regime while the other one (medium) can be potentially described semi-classically [72][73][74][75][76][77]. For instance, it has been demonstrated that following an impurity-bath interaction quench leads to chaotic signatures in the dynamics of the bath accompanied by significant coherence losses [77].…”

Out-of-Time-Order correlators in driven conformal field theories

“…The Out-of-Time-Order correlators (OTOC) are known to provide a diagnostic for scrambling which precedes thermalization in a typical non-integrable quantum many-body system [51][52][53][54][55][56]. Examples of such systems include large N spin and bosonic models [57][58][59]. For such models, which have well-understood semi-classical limits, the early time behavior of the OTOC constitutes an exponential growth and can be written as…”

Impurity induced quantum chaos for an ultracold bosonic ensemble in a double-well

“…In the present paper, we investigate a binary ultracold atomic mixture made of a single impurity and a noninteracting many-body bosonic ensemble that are confined within a 1D DW potential. Unlike most of the previous studies where the focuses are put on the weak-interacting regime, rendering the impurity being restricted into the lowest two modes of the DW potential [51][52][53][54][55][56], our discussions are not restricted to such a scenario. Specifically, we study the onset of the chaos for the majority bosonic species due to the presence of the impurity and put particular emphasis on the its dynamical response upon a sudden quench of the impurity-Bose interaction strength.…”