Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

In this thesis I present experiments investigating controlled coupling between mechanical oscillators and ultracold atoms. I report on three different coupling mechanisms.

In a first experiment, the surface potential experienced by atoms close to the mechanical oscillator is employed to couple the oscillator motion to the center of mass (COM) motion of a trapped Bose-Einstein condensate (BEC).

The magnetic trapping potential is modified by the surface potential arising from the oscillator surface which results in a reduced trap depth. Vibration of the oscillator leads to a modulation of the trap frequency and the minimum of the trapping potential. Observing the loss of atoms from the BEC allows us to read out the amplitude of the mechanical oscillator with the atoms.

In a second experiment, we study the coupling of a mechanical membrane oscillator and thermal atoms trapped in a 1D optical lattice. The membrane is the end mirror of the lattice, and oscillation of the membrane couples to the COM mode of the atomic ensemble. Conversely, the center of mass motion of the atomic ensemble redistributes photons between the two running waves forming the 1D optical lattice, effectively modulating their power, and hence the radiation pressure acting onto the membrane.

We observe the action of the oscillating membrane onto the atoms by detecting the resulting temperature increase of the atomic ensemble in absorption imaging.

To observe the backaction of the atoms onto the mechanical oscillator, the mechanical damping is measured in experiments with and without atoms in the lattice, and we measure higher damping in the presence of atoms in agreement with the theoretical predictions. These experiments are the first demonstration of backaction of an atomic system onto a mechanical oscillator.

We investigate a third coupling mechanism, where the motion of a mechanical oscillator is coupled to the collective spin of a BEC.

The tip of a mechanical oscillator is functionalized with a magnet, which transduces the oscillators' motion into oscillations of the magnetic field. This drives spin-flip transitions of trapped atoms to untrapped motional states. The coupling strength is not limited by the square root of the mass ratio of atoms and oscillator as in the other coupling schemes discussed in this thesis.

We investigate this coupling scheme theoretically, and discuss the realization of a nanometer-sized mechanical oscillator with a magnetic island. I report on the status of the fabrication, and propose a simplified fabrication method.

This thesis presents an entirely novel approach for frequency comb generation based on nonlinear frequency conversion in micrometer sized optical resonators. Here, the comb generation process can be directly described in frequency domain as energy conserving interactions between four photons (four-photon mixing). This process is a result of extremely high light intensities that build up in microresonators with long photon storage times. The thesis is composed of four main parts that answer fundamental questions in the context of microresonator-based frequency comb generation as well as providing insights in the control and possible applications of this type of comb generators.

The first topic of this thesis is the study of many-body effects in an one-dimensional strongly correlated electronic system - the Kondo lattice model. This system is tackled numerically by means of the density matrix renormalization group, since analytic method, i.e., perturbation the- ory fail due to competing coupling constants. The Kondo lattice model consists of a conduction band of electrons which couple via a spin exchange coupling to a localized spin lattice.

We study the spectral properties of the one-dimensional Kondo lattice model as a function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phases. We compute the dispersion relation of the quasiparticles, their lifetimes, and the Z factor. The exact ground state and the quasiparticle-dispersion relation of the Kondo lattice model with one conduction electron are well known. The quasiparticle could be identified as the spin polaron. Our calculations of the dispersion relation for partial band fillings give a result similar to the one-electron case, which suggests that the quasiparticle in both cases is the spin polaron. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phases and depends strongly on the quasimomentum. Further- more, we study the effects of the Coulomb interaction on the phase diagram, the static magnetic susceptibility and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest neighbor Coulomb interaction drives, depending on the elec- tron filling, either a paramagnetic or ferromagnetic order. Furthermore, we calculate electron quasiparticle life times, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate.

In the second topic of this thesis, we numerically calculate the electron transport through carbon nanotube based quantum dot devices. We use a master equation’s approach in first order of the tunneling rate to the leads and an extended constant interaction model to model the carbon nanotube system. This work has been done in collaboration with two experimental groups and we compare their respective experimentally obtained data to our numerical calculations. In both collaborations striking similarity between the numerical data and the experimental data is found.

In the first collaboration transport through a carbon nanotube peapod, i.e, a carbon nanotube filled with fullerenes, has been measured. We identify a small hybridization between a fullerene molecule and the surrounding carbon nanotube to be of crucial importance for the understanding of the transport data. In the second collaboration, electron transport through a carbon nanotube rope, i.e., a bundle of carbon nanotubes has been measured. Also here, hybridization between the different nanotubes plays a crucial role. Furthermore, an external magnetic field is applied, which enables the identification of specific spin states of the compound quantum dot system. This might be important for future applications of such devices in spin-dependent electronics.