Coupling Modifies the Quantum Fluctuations of Entangled Oscillators

Roberto Baginski B Santos,Vinicius S F Lisboa

doi:10.1007/s13538-021-00878-8

Abstract

Coupled oscillators are among the simplest composite quantum systems in which the interplay of entanglement and interaction may be explored. We examine the effects of coupling on the quantum fluctuations of the coordinates and momenta of the oscillators in a single-excitation entangled Bell-like state. We discover that coupling acts as a mechanism for noise transfer between one pair of coordinate and momentum and another. Through this noise transfer mechanism, the uncertainty product is lowered, on average, relatively to its non-coupled level for one pair of coordinate and momentum and it is enhanced for the other pair. This novel mechanism for noise transfer may be explored in precision measurements in entanglement-assisted sensing and metrology.

Highlights

Entanglement and interaction are defining features of composite quantum systems
Coupled oscillators are among the simplest composite quantum systems in which the interplay of entanglement and interaction may be explored
This novel mechanism for noise transfer may be explored in precision measurements in entanglement-assisted sensing and metrology

Summary

Introduction

Entanglement and interaction are defining features of composite quantum systems. A strong coupling between the parts of a system is desired in order to enable the observation of certain phenomena, especially those involving just a few excitations in cavity QED [32–37] or in other systems [38–48] that are being explored more recently such as circuit QED, quantum dots, optomechanical resonators and semiconductor microcavities, for instance. We investigate the effect of coupling on coordinate and momentum fluctuations of two entangled coupled oscillators. We present closed form expressions for the time evolution of the fluctuations, discuss the strong and the very strong coupling regimes and show that coupling leads to a transfer of noise among one pair of coordinate and momentum and another. Understanding how coupling affects the fluctuations of entangled oscillators may be useful in areas such as quantum sensing and metrology

The model

Introduction of the ladder operators

Results

Conclusion