Continuing our pursuit in understanding coupled systems, we developed a simple graphical loop theory in calculating transmission and reflection for a general coupled systems with multiple internal modes. This graphical method is so simple that no calculation is needed.
For its important role in the fundamental physics as well as its intriguing docking with the quantum information technology, understanding and manipulating the light-matter interaction ranging from macroscopic scale to nanoscale is a long-lasting topic in many disciplines of physics, including the condensed matter physics, atomic, molecular and optical physics. A common knob to explore the interaction of light and matter is to put the matter into a high-quality cavity and measure the transmission/reflection spectrum.
Building an input-output formalism is critical to interpret the underlying physics of such hybrid systems. The existing theory usually handles the cavity systems with only one internal mode. However, the recent rising physics in the cavity-matter system naturally involves the contribution of multi-modes from the cavity and matter (see figure on the right), and the present theory becomes unmanageably complex as the number of modes increases.
By mimicking the Feynman diagram approach and utilizing the basic concepts in Graph Theory, we propose a graphical loop theory to calculate and visualize the reflection and transmission spectra of such multi-mode cavities. This loop theory is so simple to apply to arbitrary complex problems without carrying out tedious calculations. This theory is widely applicable to all types of multi-mode cavity with both Hermitian and non-Hermitian interactions, such as the pure photonic systems, optomechanical systems, opto-magnetic systems, and even the classical coupled-oscillators.
This paper is carried out with a collaboration with Dr. Huaiyang Yuan from SUSTECH (now moved to Utrecht Univ. in the Netherlands) and Dr. Weichao Yu from Tohoku University. This work is published on Physical Review A [1].
[1]. Yuan, H. Y., Yu, W. & Xiao, J. Loop theory for input-output problems in cavities. Phys. Rev. A 101, 043824 (2020).