Postgraduate @ University of Rochester 

Wednesday June 29 – 9.45 BST

Stochastic path-integral analysis of the continuously monitored quantum harmonic oscillator

We look at the evolution of a quantum harmonic oscillator in general Gaussian states undergoing simultaneous weak continuous position and momentum measurements. The conditional state dynamics can be described in terms of stochastic diffusive evolution of the position and momentum expectation values. We extend the Chantasri-Dressel-Jordan stochastic path integral formalism (Chantasri et al., 2013, 2015) to this continuous variable system and construct a stochastic action and Hamiltonian, thereby characterizing the statistics of the measurement process. This stochastic path integral formalism helps us find the most-likely state dynamics and the final state probability densities of the system undergoing measurements. Numerical simulations confirm our analytical results. Our findings provide insights into the energetics of the measurement process, motivating their importance for quantum measurement engines/refrigerators construction. 

[1] T. Karmakar, P. Lewalle, and A. N. Jordan, PRX Quantum, 3, 010327 (2022). 
[2] A. Chantasri, J. Dressel, and A. N. Jordan, Phys. Rev. A 88, 042110 (2013). 
[3] A. Chantasri and A. N. Jordan, Phys. Rev. A 92, 032125 (2015).