Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Abstract

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mi mathvariant="script">N</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> ) and the Gaussian interferometric power ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">G</mml:mi> <mml:mi>m</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="script">P</mml:mi> <mml:mi mathvariant="script">G</mml:mi> <mml:mi>m</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.