Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Thermal excitations of optical nanofibers measured with a fiber-integrated Fabry-Pérot cavity

Efficient coupling of light to quantum emitters, such as atoms, molecules or quantum dots, is one of the great challenges in current research. The interaction can be strongly enhanced by coupling the emitter to the eva-nescent field of subwavelength dielectric waveguides that offer strong lateral confinement of the guided light. In this context subwavelength diameter optical nanofibers as part of a tapered optical fiber (TOF) have proven to be powerful tool which also provide an efficient transfer of the light from the interaction region to an optical bus, that is to say, from the nanofiber to an optical fiber. rnAnother approach towards enhancing light–matter interaction is to employ an optical resonator in which the light is circulating and thus passes the emitters many times. Here, both approaches are combined by experi-mentally realizing a microresonator with an integrated nanofiber waist. This is achieved by building a fiber-integrated Fabry-Pérot type resonator from two fiber Bragg grating mirrors with a stop-band near the cesium D2-line wavelength. The characteristics of this resonator fulfill the requirements of nonlinear optics, optical sensing, and cavity quantum electrodynamics in the strong-coupling regime. Together with its advantageous features, such as a constant high coupling strength over a large volume, tunability, high transmission outside the mirror stop band, and a monolithic design, this resonator is a promising tool for experiments with nanofiber-coupled atomic ensembles in the strong-coupling regime. rnThe resonator's high sensitivity to the optical properties of the nanofiber provides a probe for changes of phys-ical parameters that affect the guided optical mode, e.g., the temperature via the thermo-optic effect of silica. Utilizing this detection scheme, the thermalization dynamics due to far-field heat radiation of a nanofiber is studied over a large temperature range. This investigation provides, for the first time, a measurement of the total radiated power of an object with a diameter smaller than all absorption lengths in the thermal spectrum at the level of a single object of deterministic shape and material. The results show excellent agreement with an ab initio thermodynamic model that considers heat radiation as a volumetric effect and that takes the emitter shape and size relative to the emission wavelength into account. Modeling and investigating the thermalization of microscopic objects with arbitrary shape from first principles is of fundamental interest and has important applications, such as heat management in nano-devices or radiative forcing of aerosols in Earth's climate system. rnUsing a similar method, the effect of the TOF's mechanical modes on the polarization and phase of the fiber-guided light is studied. The measurement results show that in typical TOFs these quantities exhibit high-frequency thermal fluctuations. They originate from high-Q torsional oscillations that couple to the nanofiber-guided light via the strain-optic effect. An ab-initio opto-mechanical model of the TOF is developed that provides an accurate quantitative prediction for the mode spectrum and the mechanically induced polarization and phase fluctuations. These high-frequency fluctuations may limit the ultimate ideality of fiber-coupling into photonic structures. Furthermore, first estimations show that they may currently limit the storage time of nanofiber-based atom traps. The model, on the other hand, provides a method to design TOFs with tailored mechanical properties in order to meet experimental requirements. rn