https://doi.org/10.1140/epjd/s10053-022-00352-3
Regular Article – Quantum Optics
Scrambling and quantum feedback in a nanomechanical system
1
Department of Physics, Indian Institute of Technology (Banaras Hindu University), 221005, Varanasi, India
2
Department of Physics and Medical Engineering, Rzeszow University of Technology, 35-959, Rzeszow, Poland
Received:
18
June
2021
Accepted:
20
January
2022
Published online:
3
February
2022
The question of how swiftly entanglement spreads over a system has attracted vital interest. In this regard, the out-of-time-ordered correlator (OTOC) is a quantitative measure of the entanglement spreading process. Particular interest concerns the propagation of quantum correlations in the lattice systems, e.g., spin chains. In a seminal paper of Roberts et al. (J. High Energy Phys. 03:051, 2015), the concept of the OTOC’s radius was introduced. The radius of the OTOC defines the front line reached by the spread of entanglement. Beyond this radius operators commute. In the present work, we propose a model of two nanomechanical systems coupled with two nitrogen-vacancy (NV) center spins. Oscillators are coupled to each other directly, while NV spins are not. Therefore, the correlation between the NV spins may arise only through the quantum feedback exerted from the first NV spin to the first oscillator and transferred from the first oscillator to the second oscillator via the direct coupling. Thus, nonzero OTOC between NV spins quantifies the strength of the quantum feedback. We show that NV spins cannot exert quantum feedback on classical nonlinear oscillators. We also discuss inherently quantum case with a linear quantum harmonic oscillator indirectly coupling the two spins and verify that in the classical limit of the oscillator, the OTOC vanishes.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
