One-dimensional coherent-state representation on a circle in phase space

Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation

We theoretically investigate transitions in a two-level system, which are induced by a sweep through an avoided crossing in the presence of coupling to a single, excited bosonic mode. This allows us to propose an initial number-state bosonic excitation as a new possible control parameter for the survival probability at long times. The expansion of number states in terms of coherent states centered around points on a circle in phase space makes a multi-Davydov-Ansatz the method of choice to perform the required numerical calculations. It is revealed that the starting time of the transition greatly affects the final transition probabilities. In addition, we found that the mixing angle, which is tuning between the diagonal and off-diagonal coupling, is decisive for the ability to control the transition via number state excitation. For a mixing angle of π/4, we found the maximal effect of number state excitation on the transition probability.

Operational representation of quantum states based on interference

We describe a real-valued and periodic representation of quantum states. This representation can be defined operationally using generalized position and momentum measurements on coupled systems. It turns out that the emerging quantum interference terms encode the complete state information and also allow us to formulate quantum dynamics. We discuss the close connection to the theory of analytic functions.