Project A2: Linking electron and photon statistics in dissipative mesoscopic structures.

The goal of this project is to develop a theory for FCS and its coupling to light
emission within the equation-of-motion method (EoM) of the density matrix
formalism for current driven quantum dots. By doing so, we expect to be able
to calculate quantum light statistics and FCS within a formalism that is
complementary to  usual approaches,  i.e.  Born-Markov Master equations (ME)
or non-equilibrium Green functions.
In practice, the EoM hierarchy is terminated by using a factorisation (decoupling)
procedure, leading to a closed set of  non-linear equations, such as  the equation
for the average photon density, or higher order photon correlations. Here, the
nonlinearity results from Pauli-blocking, Coulomb-blockade, multiple electron-phonon
scattering and further many-particle interactions. This will be extended by either
time-dependent boundary conditions such as fluctuating couplings to electronic
reservoirs, or by introducing time-dependent counting fields  that describe single
charge/photon events right at the level of the microscopic equations and that lead to
(cumulant) generating functions for the photon distribution. For the stationary case
(e.g., in biased quantum dots), this has to coincide with the corresponding ME result
in lowest order dot-lead coupling. The general case requires higher order numerical
derivatives with respect to the counting fields, which can turn out to be a delicate task,
as the EoM method usually amounts to solving huge sets of coupled differential equations.
The reward will be a systematic theory  of the combined electron-hole-photon statistics
within a non-perturbative approach that allows one to describe non-Markovian effects in
phonon-induced dissipation (in principle up to very high orders) which is important in order
to realistically describe non-equilibrium heating effects in the environment and dephasing
of the electronic coherence.

Project leaders: Prof.Dr.  T. Brandes [1],   Prof.Dr.  A. Knorr [2]