Anderson localization of a Rydberg electron

Highly excited Rydberg atoms inherit their level structure, symmetries, and scaling behavior from the hydrogen atom. We will demonstrate that these fundamental properties enable a thermodynamic limit of a single Rydberg atom subjected to interactions with nearby ground state atoms. The limit is reached by simultaneously increasing the number of ground state atoms and the level of excitation of the Rydberg atom, for which the Coulomb potential supplies infinitely many and highly degenerate excited states. Our study reveals a surprising connection to an archetypal concept of condensed matter physics, Anderson localization, facilitated by a direct mapping between the Rydberg atom's electronic spectrum and the spectrum of a tight-binding Hamiltonian. The hopping amplitudes of this tight-binding system are determined by the arrangement of ground state atoms and can range from nearest-neighbor to power-law-tailed to effectively infinite-range, giving rise to different localization scenarios. For arrangements yielding nearest-neighbor hopping amplitudes we identify clear signatures of the Anderson localization of the Rydberg electron.Comment: 6 pages, 4 figures, supplementary informatio

Topological edge states in a Rydberg composite

We examine topological phases and symmetry-protected electronic edge states in the context of a Rydberg composite: a Rydberg atom interfaced with a structured arrangement of ground-state atoms. The electronic Hamiltonian of such a composite possesses a direct mapping to a tight-binding Hamiltonian, which enables the realization and study of a variety of systems with non-trivial topology by tuning the arrangement of ground-state atoms and the excitation of the Rydberg atom. The Rydberg electron moves in a combined potential including the long-ranged Coulomb interaction with the Rydberg core and short-ranged interactions with each neutral atom; the effective interactions between sites are determined by this combination. We first confirm the existence of topologically-protected edge states in a Rydberg composite by mapping it to the paradigmatic Su-Schrieffer-Heeger dimer model. Following that, we study more complicated systems with trimer unit cells which can be easily simulated with a Rydberg composite.Comment: 5 pages, 4 figure

Interference of two electrons entering a superconductor

The subgap conductivity of a normal-superconductor (NS) tunnel junction is thought to be due to tunneling of two electrons. There is a strong interference between these two electrons, originating from the spatial phase coherence in the normal metal at a mesoscopic length scale and the intrinsic coherence of the superconductor. We evaluated the interference effect on the transport through an NS junction. We propose the layouts to observe drastic Aharonov-Bohm and Josephson effects.Comment: 8 pages REVTex, [PostScript] figures upon reques

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

Effect of Quantum Confinement on Electron Tunneling through a Quantum Dot

Employing the Anderson impurity model, we study tunneling properties through an ideal quantum dot near the conductance minima. Considering the Coulomb blockade and the quantum confinement on an equal footing, we have obtained current contributions from various types of tunneling processes; inelastic cotunneling, elastic cotunneling, and resonant tunneling of thermally activated electrons. We have found that the inelastic cotunneling is suppressed in the quantum confinement limit, and thus the conductance near its minima is determined by the elastic cotunneling at low temperature ($k_BT \ll \Gamma$, $\Gamma$: dot-reservoir coupling constant), or by the resonant tunneling of single electrons at high temperature ($k_BT \gg \Gamma$).Comment: 11 pages Revtex, 2 Postscript figures, To appear in Phys.Rev.

Electron Cotunneling in a Semiconductor Quantum Dot

We report transport measurements on a semiconductor quantum dot with a small number of confined electrons. In the Coulomb blockade regime, conduction is dominated by cotunneling processes. These can be either elastic or inelastic, depending on whether they leave the dot in its ground state or drive it into an excited state, respectively. We are able to discriminate between these two contributions and show that inelastic events can occur only if the applied bias exceeds the lowest excitation energy. Implications to energy-level spectroscopy are discussed.Comment: To be published in Phys. Rev. Let

Coherent photon assisted cotunneling in a Coulomb blockade device

We study cotunneling in a double junction Coulomb blockade device under the influence of time dependent potentials. It is shown that the ac-bias leads to photon assisted cotunneling which in some cases may dominate the transport. We derive a general non-perturbative expression for the tunneling current in the presence of oscillating potentials and give a perturbative expression for the photon assisted cotunneling current.Comment: Replaced with a longer paper which includes a non-perturbative calculation. 13 pages with 1 figure. To be published in Physical Review

Electronic Transport in Hybrid Mesoscopic Structures: A Nonequilibrium Green Function Approach

We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantities, such as the difference between chemical potentials, superconductor order parameter phases and ferromagnetic magnetization orientations, that only their relative value appears explicitly in the current expression. When applied to specific structures, the formula becomes of the Meir-Wingreen-type favoring strong correlation effects, and reduces to the Landauer-B\"uttiker-type in noninteracting systems such as the double-barrier resonant structures, which we study in detail beyond the wide-band approximation.Comment: 24 pages, 12 eps figures, Revtex