Humboldt-Forschungsstipendiums für Postdocs an Herrn Dr. Johannes Petrus du Buisson

01.07.2025 bis 30.06.2027

Quantum systems which are in contact with an environment are known as open quantum
systems. Given that all practical quantum systems are open, it is a subject of great interest to
develop methods with which to study or control the behavior of such systems. This interest is
motivated by the desire to create useful quantum devices such as quantum computers and is
grounded in our growing ability to experimentally realize quantum many-body dynamics using,
for instance, ensembles of cold atoms or trapped ions which are coupled to an environment in
a controlled fashion.
In contrast to closed quantum systems, where the system’s state evolves deterministically
in time, the evolution of an open quantum system is a stochastic process, owing to the random
exchange of quanta, such as photons, between the system and its environment. By detecting
these exchange events via observation of the environment, we can resolve the system’s evolution
as a quantum trajectory. A problem of particular interest in the study of open systems is
understanding, on the level of individual quantum trajectories, the way in which they undergo
transitions from a given initial state to a specific final state. Especially important is the case
when the initial and final states are metastable states - long-lived states often corresponding
to different non-equilibrium phases. In this case, transitions between these states, which occur
on timescales much shorter than the characteristic life-times of the metastable states, constitute
rare events. By definition, rare events are difficult to observe experimentally or simulate
numerically, so that techniques which modify a system to manifest such rare quantum trajectories
are highly desirable. We therefore seek to develop tools to engineer an open quantum
system which produces exactly those rare trajectories of the original system corresponding to
transitions between two fixed states.
For classical stochastic processes, the framework of large deviation theory and related mathematical
tools, in particular a class of results known as Doob transforms, provide a systematic
manner in which to construct an effective stochastic process which has the rare behavior of the
original system as its typical behavior. The research group of Lesanovsky has done pioneering
work in formulating an analog of the Doob transform in the context of Markovian open quantum
systems for particular classes of rare events. However, the classical Doob transform which
constructs an effective process manifesting transitions between two fixed states - producing
as a matter of course only those trajectories lying in the so-called transition path ensemble -
has yet to be extended to Markovian open quantum systems. We aim to solve this problem
by combining my expertise of classical stochastic processes and the mathematical framework
of large deviation theory, developed over the course of my MSc and PhD degrees, with the
quantum-mechanical expertise of Lesanovsky’s group.
The value of this work is twofold. Firstly, we will attain greater control over the transient
dynamics of open quantum systems. In particular, we will understand how to modify the
Hamiltonian of a system and how to tune the coupling of the system to its environment in
order that the system, prepared in some initial state, ends up in a particular state at a specified
time. This will provide exciting opportunities for collaboration with experimentalists interested
in the fine-tuned control of open quantum systems.
Secondly, this work will provide us with a way to study and characterize the rare dynamics
governing the transitions between metastable states for open quantum systems. This will enable
us to identify the most likely pathways by which a reaction occurs, in addition to particularly
important intermediate states involved in the reaction. Furthermore, we will be able to study
those mechanisms involved in these reactions which are uniquely quantum mechanical in nature.