Fr\"ohlich Polarons from 0D to 3D: Concepts and Recent Developments

I analyse our present understanding of the Froehlich polaron with emphasis on the response properties, in particular optical absorption.Comment: 28 pages, 17 figures, invited lecture at the ESF Exploratory Workshop EW05-105 "Mott's Physics in Nanowires and Quantum Dots", University of Cambridge, United Kingdom, 31 July - 2 August 200

Note on the Path-Integral Variational Approach in the Many-Body Theory

I discuss how a variatonal approach can be extended to systems of identical particles (in particular fermions) within the path-integral treatment. The applicability of the many-body variational principle for path integrals is illustrated for different model systems, and is shown to crucially depend on whether or not a model system possesses the proper symmetry with respect to permutations of identical particles.Comment: 15 pages, 1 figure, E-mail address: [email protected]

Sum Rule for the Optical Absorption of an Interacting Many-Polaron Gas

A sum rule for the first frequency moment of the optical absorption of a many-polaron system is derived, taking into account many-body effects in the system of constituent charge carriers of the many-polaron system. In our expression for the sum rule, the electron-phonon coupling and the many-body effects in the electron (or hole) system formally decouple, so that the many-body effects can be treated to the desired level of approximation by the choice of the dynamical structure factor of the electron (hole) gas. We calculate correction factors to take into account both low and high experimental cutoff frequencies.Comment: 16 pages, 3 figures, revised version; new results adde

Ground state and optical conductivity of interacting polarons in a quantum dot

The ground-state energy, the addition energies and the optical absorption spectra are derived for interacting polarons in parabolic quantum dots in three and two dimensions. A path integral formalism for identical particles is used in order to take into account the fermion statistics. The approach is applied to both closed-shell and open-shell systems of interacting polarons. Using a generalization of the Jensen-Feynman variational principle, the ground-state energy of a confined N-polaron system is analyzed as a function of N and of the electron-phonon coupling constant. As distinct from the few-electron systems without the electron-phonon interaction, three types of spin polarization are possible for the ground state of the few-polaron systems: (i) a spin-polarized state, (ii) a state where the spin is determined by Hund's rule, (iii) a state with the minimal possible spin. A transition from a state fulfilling Hund's rule, to a spin-polarized state occurs when decreasing the electron density. In the strong-coupling limit, the system of interacting polarons turns into a state with the minimal possible spin. These transitions should be experimentally observable in the optical absorption spectra of quantum dots.Comment: 33 pages, 9 figures, E-mail addresses: [email protected], [email protected], [email protected], [email protected], accepted for Phys. Rev.

Path integral formulation of the tunneling dynamics of a superfluid Fermi gas in an optical potential

To describe the tunneling dynamics of a stack of two-dimensional fermionic superfluids in an optical potential, we derive an effective action functional from a path integral treatment. This effective action leads, in the saddle point approximation, to equations of motion for the density and the phase of the superfluid Fermi gas in each layer. In the strong coupling limit (where bosonic molecules are formed) these equations reduce to a discrete nonlinear Schrodinger equation, where the molecular tunneling amplitude is reduced for large binding energies. In the weak coupling (BCS) regime, we study the evolution of the stacked superfluids and derive an approximate analytical expression for the Josephson oscillation frequency in an external harmonic potential. Both in the weak and intermediate coupling regimes the detection of the Josephson oscillations described by our path integral treatment constitutes experimental evidence for the fermionic superfluid regime.Comment: 13 pages + 2 figure