Variational quantum trajectory description of driven-dissipative systems.

Variational principles are fundamental in our theoretical understanding of closed quantum systems at thermal equilibrium. For open, driven-dissipative systems, variational techniques are much less established. Classical examples of driven dissipative systems range from convection cells in hydrodynamics to electrical patterns in the heart. In recent years, progress in fabrication of electromagnetic resonators coupled to matter degrees of freedom, has spurred the theoretical interest in driven-dissipative quantum systems. An important motivation for this research is the possibility of realizing correlated quantum states with potential applications in quantum computing and quantum simulation.For the theoretical simulation of driven-dissipative quantum systems, two equivalent approaches exist: a master equation for the density matrix and a quantum trajectory equation for wave functions. These two techniques relate to each other as the diffusion equation to the Langevin equation in the theory of Brownian motion. A practical advantage of the quantum trajectory method for numerical purposes is that it works on the Hilbert space of wave functions instead of the quadratically larger Hilbert space of density matrices. A conceptual bonus is that it 'unravels' distinct macroscopic superpositions of the Schrödinger cat type and gives insight in the emergence of a classical configurations out of an entangled quantum state. In the present project, we will investigate variational approximations to the quantum trajectory dynamics. The advantage of applying the variational principle to the trajectory dynamics instead of the density matrix itself is that the unraveled states are expected to be more amenable to such a description. This expectation is borne out by a preliminary study with the Gutzwiller approximation to a photonic dimer. Encouraged by this success, we will set out to investigate various variational approximations to the quantum trajectory description of driven-dissipative quantum systems. One of the advantages of such a description is that it can be carried out even for large systems and in more than one dimension, where other numerical techniques become impractical. Access to large systems is in particular important for the descriptions of phase transitions, that only become sharp in the thermodynamic limit.The most important goal of this research project is to provide a new theoretical tool for the simulation of driven-dissipative quantum systems. We envisage to apply this technique to further our understanding of phase transitions, which can lead to new fundamental insights regarding the differences and similarities of driven-dissipative systems with respect to closed systems in thermal equilibrium.

Keywords:MONTE CARLO SIMULATIONS, THEORETICAL STUDY

Disciplines:Applied mathematics in specific fields, Astronomy and space sciences, Classical physics, Materials physics, Mathematical physics, Quantum physics