Stochastic action principle for Gaussian states of a simple harmonic oscillator

Subjecting an oscillator to continuous weak measurements is an integral part of quantum control and feedback. In my presentation, I will describe the application of Chantasri-Dressel-Jordan formulation (CDJ) of stochastic action principle for a quantum simple harmonic oscillator under weak position and momentum measurements. The selection of such a system paves the way to extend the CDJ formalism to infinite-dimensional systems. Using the preservation of Gaussianity of a state under Gaussian weak measurement, it is possible to find the stochastic Hamiltonian, stochastic trajectories, and the equations for optimal paths of the system. I will also describe the analytical solutions and behavior of the optimal paths under reasonable approximations. Finally, my presentation will delve into the energetics of the measurement process using the optimal path description.