Synthesis of Linear Quantum Systems to Generate a Steady Thermal State

The purpose of this article is to synthesize a linear quantum system, which is strictly stable and has a steady thermal state. Specifically, we give a parameterization of a class of sta- ble linear quantum systems that have V = tau I/2, tau > 1, as their steady covariance matrsices. This is physically important since the covariance matrix tau I/2, tau > 1, corresponds to a quantum thermal state. Hence, we can say that these systems will asymptotically evolve into a quantum thermal state. An extension to the case where V = S diag (Lambda, Lambda)S-T/2 with Lambda > I being a diagonal matrix and S being a symplectic matrix will also be considered. Physically, a covariance matrix of the form V = S diag (Lambda, Lambda)S-T/2, Lambda > I, corresponds to a mixed Gaussian quantum state. So, we can alternatively say that the corresponding linear quantum systems will asymptotically evolve into a mixed Gaussian quantum state.

Automated summary

The purpose of this article is to synthesize a linear quantum system that is strictly stable and has a steady thermal state. The article presents a parameterization of a class of stable linear quantum systems and discusses the asymptotic evolution of the systems in two scenarios.