Combining Chemical Physics with Quantum Optics for Solving the Open Quantum System Dynamics of Strongly Interacting Oscillators*

Modeling the non-equilibrium dissipative dynamics of strongly interacting quantized degrees of freedom is a fundamental problem in several branches of physics and chemistry. We combine the Monte Carlo wavefunction method for Markovian open quantum systems from quantum optics [1] with the multi-configuration time-dependent Hartree method (MCTDH) from chemical physics [2], to efficiently model coherent and dissipative processes of strongly interacting quantum oscillators, for applications in cavity QED with molecules [3]. The open system evolution proceeds through a sequence of deterministic state propagation steps interrupted by stochastic quantum jumps with transition probabilities that depend on the instantaneous wavefunction and the details of the system-reservoir interactions. We benchmark the proposed hybrid propagation method against exact density matrix solutions for physical systems of interest in cavity QED, demonstrating accurate results for experimentally relevant observables using a tractable number of quantum trajectories [4]. We show the potential for solving the dissipative dynamics of finite size arrays of strongly interacting quantized oscillators with high excitation densities, which is challenging for conventional density matrix propagators, and discuss applications of the method in other areas of quantum science. 

[1] Klaus Mølmer, Yvan Castin, and Jean Dalibard, Monte Carlo wave-function method in quantum optics, J. Opt. Soc. Am. B 10, 524-538, 1993.

[2] H.-D. Meyer, U. Manthe, L.S. Cederbaum, The multi-configurational time-dependent Hartree approach, Chem. Phys. Lett. 165, 73-78, 1990.

[3] F. Herrera and J. Owrutsky, Molecular polaritons for controlling chemistry with quantum optics, J.Chem. Phys. 152, 100902, 2020.

[4] J. F. Triana and F. Herrera, Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps, J. Chem. Phys. 157, 194104, 2022.