We study phonon emission in a GaAs/AlGaAs double quantum dot by monitoring the tunneling of a single electron between the two dots. We prepare the system such that a known amount of energy is emitted in the transition process. The energy is converted into lattice vibrations, and the resulting tunneling rate depends strongly on the phonon scattering and its effective phonon spectral density. We are able to fit the measured transition rates and see imprints of interference of phonons with themselves causing oscillations in the transition rates.

Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of the stability of rare-earth magnetic atoms exposed to crystal or ligand fields of various symmetry and to exchange scattering with an electron bath. By analyzing the properties of the atomic wave function, we show that certain combinations of symmetry and total angular momentum are inherently stable against first or even higher-order interactions with electrons. Further, we investigate the effect of an external magnetic field on the magnetic stability.

We study a system of two quantum dots, each with several discrete levels, which are coherently coupled to a microwave oscillator. They are attached to electronic leads and coupled to a phonon bath, both leading to inelastic processes. For a simpler system with a single level in each dot it has been shown that a population inversion can be created by electron tunneling, which in a resonance situation leads to lasing-type properties of the oscillator. In the multilevel system several resonance situations may arise, some of them relying on a sequence of tunneling processes which also involve nonresonant, inelastic transitions. The resulting photon number in the oscillator and the current-voltage characteristic are highly sensitive to these properties and accordingly can serve as a probe for microscopic details.

Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the conventional time-non-local master equation into dispersed time-local equations-of-motion. The validity of our approximations is discussed and we find that the non-Markovian terms have to be included for short times. While calculations of the density matrix at short times suffer from the initial value problem, a correlation function has a well defined initial state. The resulting formula for the non-Markovian correlation function has a simple structure and is as convenient in its application as the conventional quantum regression theorem for the Markovian case. For illustrations, we apply our method to investigate the spectrum of the current fluctuations of interacting quantum dots contacted with two electrodes. The corresponding non-Markovian characteristics are demonstrated.

Due to underlying symmetries, the ground states of magnetic adatoms may be highly stable, which opens perspectives for application as single-atom memory. A specific example is a single holmium atom (with J = 8) on a platinum (111) surface for which exceptionally long lifetimes were observed in recent scanning tunneling microscopy studies. For control and read-out, the atom must be coupled to electronic contacts. Hence the spin dynamics of the system is governed by a quantum master equation. Our analysis shows that, in general, it cannot be reduced to a classical master equation in the basis of the unperturbed crystal-field Hamiltonian. Rather, depending on parameters and control fields, "environment-induced superselection" principles choose the appropriate set of basis states, which in turn determines the specific relaxation channels and lifetimes. Our simulations suggest that in ideal situations the lifetimes should be even longer than observed in the experiment. We, therefore, investigate the influence of various perturbations. We also study the initialization process of the state of the Ho atom by applied voltage pulses and conclude that fast, high fidelity preparation, on a 100-ns time scale, should be possible.

Due to underlying symmetries the two degenerate angular-momentum ground states of a single holmium atom (with $J=8$) on a Pt(111) surface have exceptionally long lifetimes, as observed in recent scanning tunneling microscopy studies. This opens perspectives for the application as a single-atom memory bit. For control and read-out the atom is coupled to electronic contacts. Hence the spin dynamics of the system is governed by a quantum master equation. In general it cannot be reduced to a classical master equation in the basis of the unperturbed crystal-field Hamiltonian. Rather, depending on parameters and control fields, "environment induced superselection" principles choose the appropriate set of basis states, which in turn determines the specific relaxation channels and lifetimes. Our results suggest that in ideal situations the lifetimes should be even longer than observed in the experiment. We, therefore, investigate the influence of various perturbations. We also study the initialization process of the state of the Ho atom by applied voltage pulses and conclude that fast, high fidelity writing into the memory, on a 100ns timescale, should be possible.

We present an exact expansion of the master equation for an open quantum system. The resulting equation is time local and enables us to calculate clearly defined higher-order corrections to the Born-Markov approximation. In particular, we show that non-Markovian terms are of the same order of magnitude as higher-order terms in the system-bath coupling. As a result, we emphasize that analyzing non-Markovian behavior of a system implies going beyond the Born approximation. Additionally, we address with this approach the initial-state problem occurring in non-Markovian master equations.

Single magnetic atoms on non-magnetic surfaces have magnetic moments that are usually destabilized within a microsecond, too speedily to be useful, but here the magnetic moments of single holmium atoms on a highly conductive metallic substrate can reach lifetimes of the order of minutes.