33 research outputs found
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 (,
: dot-reservoir coupling constant), or by the resonant tunneling of
single electrons at high temperature ().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 () sample is sandwiched between two leads each of
which can be either a ferromagnet () or a superconductor () 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